That a particular specified event or coincidence will occur is very unlikely.
That some astonishing unspecified events will occur is certain.
That is why remarkable coincidences are noted in hindsight, not predicted with foresight.
—David G. Myers
Scenario 1: You are going out and meet someone new in a bar. Both of you hit it off right away. You tell him/her that your birthday is next Monday. And to both of your surprise, you find out that you and your new acquaintance have the same birthday.
What an unbelievable coincidence! You must be soulmates.
Scenario 2: You are traveling Cambodia and are in the midst of finding yourself of course. Completely immersed in the most remote place you have ever been, you suddenly hear your name. A familiar voice? Impossible! You are in the middle of nowhere. You turn around to see who it is. It is your next-door neighbor from back home. Unbelievable. You finally have a great story to tell for the next 5-6 years.
I know most of us have neither met someone new in the past year or traveled to a remote place in Cambodia – please just follow along. Many arguments and stories are built around pointing out the lack of probability of something happening.
Out of all the possibilities – they say – this one is the one that occurred. This cannot be happening just by chance – it is just too amazingly miraculous.
But improbability is a preconception completely fabricated in our minds. It is an illusion. Improbable things happen all the time.
The misconception has very little to do with statistical truth. Too often we cannot grasp the difference between saying:
a) “I will roll these two dice ten times and get double sixes every time” and
b) “Some improbable pattern of numbers will appear if I roll these two dice ten times every day for the next ten years”
Improbability ≠ Impossibility.
Let me give you some further examples:
The Birthday problem
Consider a Bar filled with thirty random people: what are the chances that two of them have the same birthday (ignoring leap years, and assuming the attendees' birthdays are entirely random)?
The chance of that happening is 1/12 or roughly 8%.
After all, it´s a 1/365 chance someone will share your birthday. You got thirty people in that bar, which increases your chance to 30/365. This makes sense. If only it was true. Because the chances are significantly better than that. Because 8% is the chance that someone has the same birthday as you. When we ask “what is the chance that any two people have the same birthday?” you get a shot in the 30/365 lottery another thirty times. Every possible pairing of two individuals in the group of thirty people has a shot to find someone with the same birthday. The probability of two people having the same birthday in my random-thirty-people-bar-party is 70%. Does that make you second guess your new soulmate? It should!
Meeting your neighbor in Cambodia
On average we live for 78.3 years. Most of us remember people we meet after age 5. Assume we interact with 3 new people daily in cities, 365 days in a year plus leap years is 365.24. In total it will be (78.3 – 5) x 3 x 365.24 = 80,000 people.
Of course, you cannot remember all those people. Researchers suggest that the average person knows around 600 people. The chance, that you meet one of those somewhere, sometime during your travels is quite likely. That’s why it happens all the time and all of us have a story like this. You must remember, that you stop considering all the moments you have not met someone somewhere sometime.
Actually, it is wildly improbable that you are even alive in the first place. To be alive and for instance, reading this article, is so improbable a priori, that Borel's Law rules out your existence. For countless generations, a particular sperm cell had to encounter a particular egg and produce every single descendant — just to make your existence possible. The probability of that happening is so staggeringly low — and yet, here you are. It is so improbable, yet it happened to all of us and everyone you have ever known or will know.
Remember this guy?
This is Paul the Octopus. He got famous when he correctly predicted the outcome of eight matches in the 2010 South Africa World Cup. Paul must be a psychic octopus. Which is supported by the fact that serious scientists suggest that octopus could be from outer space (no joke). But the real explanation is much simpler. The probability that Paul could predict the outcome of eight games is only 1 in 256. Paul just happened to be that one in 256 chance that was reported in the media.
What about Flopsy the Kangaroo from Australia, who unfortunately only predicted 1 game right and 1 game wrong? Not newsworthy enough?
Have you all forgotten the psychic Scottish goat known as Boots the Goat? She correctly predicted the Brexit referendum but subsequently failed to correctly predict the 2016 US Presidential election. 1 right – 1 wrong. Not so newsworthy indeed.
Large sporting events like the World Cup, the Brexit Referendum, or US Presidential Election generate masses of interest and undoubtedly many people (or animals) will try to predict the outcome — in fact, it would be unlikely that an event of the size of the World Cup, for example, would attract less than the 256 people (or animals) required to statistically guess the 8 matches correctly.
As we stated in the beginning: That something particular will happen sometimes is not improbable – it’s certain.
Until next week,