Skepticism
Skepticism
June, 2004
Some times it happens that the lives of two people are linked to each other by Fate. I want to relate to you a true story from my own life that illustrates this.
The story is about a lifelong friend of mine called Michael and myself. We both grew up in the same Danish town, and we were both assigned to the same group in the same kindergarten. As far as I remember there were 4 kindergartens in our town, and the one we went to had 3 groups. The odds of us being assigned to the same group in the same kindergarten were 1 to 4 times 3 – that is 1 to 12. After the kindergarten we went to primary school, and we were assigned to the same school, and the same class. I believe that there were six primary schools in our town, and there were two classes for our age group at the school we attended. The odds of us ending in the same kindergarten group and the same class in school are then 1 to 12 times 6 times 2 – that is 1 to 144. After the primary school most children in Denmark choose to attend what is called a "gymnasium" in Danish, and Michael and I also chose to do this. While there were really only one gymnasium to choose from, where we lived, there were 6 different classes, and it turned out that we were assigned to the same one.
This brings the odds of the link between our lives happening by coincidence up to 1 to 864 (6 times 144). As the next step in our educations we chose to attend the same university, where we all students of the natural sciences are required to spend the first year taking courses from a broad spectrum of the natural sciences. 8 classes were started the year that we enrolled, and we were assigned to the same one. The odds of us always being assigned to the same groups and classes through out our education had now reached 1 to 6,912, and we were beginning to wonder about the way we seemed to be bound to each other.
Neighbors
While studying at the university we needed somewhere to live, so we applied for rooms in the student hostels in the university town. I think that there were 10 or more of those, and of course we were assigned to the same one, but we were quite astonished when we discovered that Fate had made us neighbors at the student hostel, even though it had 480 rooms. Since most rooms had two neighboring rooms the odds of us becoming neighbors by chance is 1 to 240. This means that the series of events described so far had odds of 1 to 16,588,800.
Our story was now very remarkable, but it was about to get even more improbable. The university had around 1,000 lockers available for students to use (they were distributed among the interested students once a year). One year Michael and I wanted a locker each, and it turned out that we independent of each other had picked two neighboring lockers!
So the already long odds were now increased to 1 to 8,294,400,000. Such odds offer irrefutable evidence that some people are destined to have their lives intertwined.
Or does it?
While all the facts in the story I just told is correct to the best of my knowledge, the story might not be as remarkable as it might appear at first. Lets go through the story once more. I started out by assigning the odds 1 to 12 to the event of us ending up in the same group in kindergarten. While these odds are correct they are misleading, because if it hadn’t been Michael I had been grouped with there would probably have been someone else with whom I would have become good friends.
Even though there were several schools in our hometown, we were bound to go to the same one, since we lived in the same area of the town, and pupils were assigned to schools based on their place of residence. The same was true of kindergartens, thus our geographical closeness more or less forced us to attend the same kindergarten and school. Furthermore the classes in our school were also divided according to geography, so we were also legally bound to end up in the same class.
We see that so far nothing remarkable has happened, it has just been a boring tale of two kids growing up in the same neighborhood. I stated that there were 6 different classes at the gymnasium, and that we ended up in the same one, however I neglected to tell you that our parents and we specifically requested this, so there was no intervention from Fate in this case either. When the students starting the same year as we did at the university were distributed into the 8 classes, I don’t know according to which criteria this was done, however considering the number of things that Michael and I had in common, it seems plausible that whatever the criteria were, we were quite likely to be assigned to the same class.
The Plot Thickens
Going on to the student hostels, I must admit that I cheated a little because I "forgot" to mention that out of the 10 or more hostels we only applied for rooms at three of them. Two of these had few rooms, and students lived there for long periods, while the one we got rooms in had many rooms and students often moved on quite fast. This means that it was exceedingly likely that we would end up in that exact hostel.
The fact that we ended up being neighbors is a bit more remarkable, but one must consider that it would also have been seen as a remarkable coincidence if we had been assigned to the same kitchen at the hostel (which we weren’t), or if we had gotten rooms just above/below each other, or rooms in the same position in the two different blocks, or if our rooms had been just opposite each other across the hallway, or...
So we see that the odds I used of 1 to 240 for the assignment of rooms, is actually misleading to use because I selected what I calculated the odds of, after I knew what had happened. The correct thing to do would be to select which room assignments we would consider remarkable ahead of time, and then compute the odds for one of these assignments being selected.
The odds of us getting two neighboring lockers are also misleading for the same reasons, and it gets even more misleading when I tell you that the lockers were located at several different entrances, and since we nearly always used the same entrance, we would of course pick lockers at that entrance, which means that the lockers at the other entrances shouldn’t be included in the calculation of the odds.
I should furthermore mention that we had previously chosen lockers together, and the year that we chose lockers independently we chose lockers in the same area as the previous years, thus ensuring that we would get lockers close to each other.
Further Explanations
That the story of Michael and I seemed so remarkable at the beginning is caused by several factors: I left out large parts of the story, such as the fact that we requested that we were assigned to the same class in the gymnasium, and the fact the we were assigned to kindergarten, schools and classes based on geography.
I focused on the parts of our lives where something apparently remarkable happened, while leaving out the parts of our lives that didn’t point to there being any special bond between us. For instance it would have supported the special bond hypothesis if we had been neighbors in our hometown, but we weren’t. Or if we had become neighbors again later in our lives, but we didn’t. Or if both of us had been to the military together (we weren’t). Or...
It is actually relatively easy to construct a remarkable sounding story based on the lives of two people who have been friends for around 25 years, when you allow yourself to pick the events that make the story sound remarkable, while ignoring those that doesn’t.
I picked the odds after the outcome of the events were known, such as with the odds for us being neighbors. This would be similar to rolling 10 dice and then remarking how extraordinary the outcome was since the odds of that particular result was 1 to 60,466,176.
I assigned equal probabilities to events that weren’t equally likely. E.g. I considered it to be equally probable that we were assigned to each of the student hostels, but in reality one of them was much more likely than the others.
All things considered my story actually isn’t improbable, and even if it were, it wouldn’t be proof of any intertwining of lives by Fate. There are billions of people going about their business each day, experiencing billions of events, so if no series of seemingly remarkable stories ever surfaced, then that would be the greatest statistical miracle of all times.
The Art of Improbablification
So after going through my story, what have we learned? Well we have learned the timehonored art of improbablification – the art of constructing a seemingly improbable story from a series of mundane events. That is, we have learned how to make ordinary stories appear remarkable. The techniques for doing this are the following: