This photograph is of a car I hired in California parked next to one in a car park in Arizona with a registration number one digit higher.
Such coincidences are amazing and worth a pint in a pub for the telling. Most people have similar stories of amazing coincidences.
In Koestler’s book “The Case of the Midwife Toad” the experiences of a certain M Deschamps are related. As a child, his first taste of plum pudding was offered by a M de Fontgibu. Two decades later, Deschamps ordered plum pudding at a Paris restaurant —the first time since his childhood
experience that he had tried to sample it again. Alas, the last piece of pudding had just been eaten — by M de Fontgibu at a nearby table. Many more years later he was offered plum pudding at a party —only the third time in his life that he had the opportunity to taste it. As the pudding was served, M de Fontgibu stumbled into the room - he had been invited to a party but had come to the wrong house!

Arthur Koestler and others such as Paul Kammerer and Carl Jung believed that a mysterious physical process encouraged and organised such coincidences. They kept notebooks filled with examples and the “Law of Synchronicity” was invented and was much later immortalized in Sting’s album named "Synchronicity".
Here I consider only coincidental encounters with acquaintances and friends, of the type that give rise to the exclamation in the title, and not to other types of numerical or other coincidences. To determine the probability of an amazing encounter we need several pieces of numerical data.
The first is the size of my social network. This is the group of people who are mutually known. The definition of ‘known’ is important. Thus, I know Cliff Richard, but he does not know me - I assume! If I met him strolling past my house it certainly would be an amazing encounter, but I limit myself here to those people in my social network I would go up to and shake hands with - or kiss - and be recognized in return.
The first step in my analysis was to list all the people that I knew by sight and name and who knew me similarly. At the time of writing, there are 212 people in the world with whom I have this relationship. About fifteen years ago I did the same exercise and came up with a figure of 202. Thus, my growing forgetfulness and ability to outlive my friends and colleagues seems to be almost balancing my gains.
The next thing we need to establish is the number of people we see in a year. Seeing a local friend or work colleague is not of interest. I only consider here seeing anyone in the social network non-locally in the United Kingdom. Accordingly, I counted the number of people seen on journeys around the United Kingdom. For example, on a trip from Weymouth in Dorset to a London hotel thence on to Heathrow Airport and waiting there for two hours, brought me into visual contact with 460 people. This was a surprisingly low figure. I had expected a value measured in thousands.
The criterion was that a person would have been recognized and one does not normally go around looking at every person’s face. If one does look too closely at passing faces, one is likely to have one’s data gathering limited to the inside of a police station. As it was, I feared an unfavourable reaction to
me counting under my breath in an airport departure lounge!
The number of trips I make away from my home locality in the UK averages about thirty each year. I take the population of the United Kingdom — excluding children - as 50 million. From these figures it is easy to show that the meeting in an unexpected place in the United Kingdom of someone on my list will occur about once every 14 years on average.

This seems intuitively to be about the right order of magnitude.
Thus, we should not be surprised to experience such events several times in a lifetime - and who hasn’t?
This may all seem like a whimsical piece of research but it can have important applications. One is to determine the incidence of rape or sexual abuse in society. Many victims do not report the incident officially. This can be for a variety of reasons - fear of retribution, fear of revealing that the abuser was a
relative, etc. However, we can be sure that some victims that do not appear in official statistics will have told close friends or relatives of their experiences.
Thus, if a random sample of people are asked if they know of anyone who has been raped or sexually abused and the size of the informant’s social network is known then an improved estimate of the number of victims can be obtained. Similar methods can be applied to determining the number of workers moonlighting, thieving from the workplace or being sexually harassed.
So, if you unexpectedly meet Aunty Hilda whilst visiting some remote extremity of the United Kingdom, it’s all perfectly in accord with the laws of probability — unless of course she has been dead for years!

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Keywords: Arthur Koestler Paul Kammerer Carl Jung Sting Synchronicity Unexpected Encounters Geoff Kirby Deschamps Plum Pudding de Fontgibu