The law of large numbers

On 11 November 2017 (11-11), I went to Groningen with my wife and son. While driving, I noticed the date and time on the clock in the car. The date was 11-11, and the time was 10:35. It made me think, ‘It would be nice to look at the clock at exactly 11:11 today because it is 11 November (11-11).’ Within a second, I noticed the distance recorder standing at 111.1. It had been 111.1 kilometres since I last filled up. Peculiar coincidences can occur by chance. With eight billion people on this planet and so many things transpiring, these things happen.

An example can illustrate this. Imagine you have five dice and make a throw. A remarkable incident is throwing five sixes. If you roll the five dice only once, it probably does not happen. On average, it only occurs once every 7,776 times. But if you throw the dice a million times, you should not be surprised to see it happen 120 to 140 times.

The chance of 111.1 kilometres appearing on the distance recorder is one in 5,000 if there is a reset every 500 kilometres. So once the thought about 11:11 had popped up, the probability of this happening thus was 0.02%. And the distance recorder was not far from the clock. The likelihood of the thought coming up on 11 November is hard to establish. In my case, it was not low.

The birthday problem demonstrates that strange coincidences happen more often than we think. If you share a birthday with another person in a small group, it might strike you as odd, but the chance of someone sharing a birthday with another person is already 50% in a group of 23. But two people sharing a birthday is not a mind-blowing coincidence. It is not as remarkable as the incident with the distance recorder.

And when you are a member of this group, the probability of you being one of the persons sharing a birthday is much smaller, namely 6%. And if you randomly pick two people, the odds of them having the same birthday is only 0.3%. Meaningful coincidences are likely to happen but less likely to you. And taking a small sample of events can seriously reduce the likelihood of meaningful coincidences. Furthermore, the more elaborate a scheme, the less likely it is to occur. The probability of three people sharing a birthday in a group of 23 is 1.3%, and for five, it is only 0.0002%.

Possible avenues to circumvent the law of large numbers

Perhaps there is a way to find out there is no such thing as coincidence. If some of the most significant historical events come with peculiar coincidences, that might be more telling for two reasons. First, there are only a few, so the law of large numbers does not apply. After all, it is a small sample. If no intelligence is coordinating events in this universe, it is not so likely that meaningful coincidences turn up in this sample, and elaborate schemes are unlikely to occur. Second, if the most significant historical events come with peculiar coincidences, it more likely suggests history is scripted than when it happens in someone’s personal life.

To make the argument, you need to answer questions like, what are the most important historical events, and what are peculiar coincidences? Events such as the sinking of the Titanic or the Kennedy assassination might not qualify, even though the coincidences surrounding them form a strange and elaborate scheme. The beginning and the end of World War I meet the requirements. D-Day, the fall of the Berlin Wall, and the terrorist attacks of 11 September 2001 are also historic events.

And what must I think of the number of meaningful coincidences in my life? It is not possible to establish the likelihood of that happening. You can make assumptions to get an idea. A highly unusual coincidence like the do-it-yourself store incident could be like throwing five sixes. Hence, the chance of such an event happening in any year in any life could be one in 7,776. If the same transpires again, it is like throwing five sixes twice in a row. The chance of that happening would be one in 60,000,000. On average, 100 people would experience something similar each year. But what if many more similar incidents occurred in one life? That boggles the mind unless you think there is a script.

Still, the number of possible unusual events is infinite, so the chance of something strange happening, such as the do-it-yourself store incident, could be higher than we intuitively think. It seems impossible to estimate the odds, but without intelligence coordinating events in this universe, we should at least expect these incidents to be distributed more or less evenly across all people and time frames.

Even then, significant deviations from the average are possible. Lightning strikes only a few people. It happens to some people twice, which might seem odd, but there is nothing suspicious about that. If lightning strikes one in 10,000 people once, then one in 100,000,000 get hit twice. But if one person runs into lightning ten times, and there is nothing unusual about this person and what he did. How would you explain that? Statistically, it can happen, but another cause is more likely, like living in a peculiar spot.

The limits of our minds

We are good at attributing causes but bad at guessing the likelihood of an event. The psychologist Daniel Kahneman came up with an example. It is a study of the incidence of kidney cancer in the counties of the United States. The research revealed a remarkable pattern. The incidence of kidney cancer was the lowest in rural, sparsely populated counties in traditionally Republican states in the Midwest, the South, and the West.¹ So what do you make of that?

You probably came up with reasons why kidney cancer is less likely to occur in these counties, such as a healthy rural lifestyle or low pollution levels. You probably did not think of randomness. Consider then the counties in which the incidence of kidney cancer is the highest. These counties were also rural, sparsely populated, and in traditionally Republican states in the Midwest, the South, and the West.¹

How can that be? Those counties all had small populations. And with smaller samples come more sizeable deviations from the average. Our intuition makes connections of causality, but our reason does not verify whether it could just be randomness. We like to think some cause makes unusual things happen, while they might be random accidents.

We might run into this if we consider the most significant historical events and use this small sample to establish that someone is ‘writing history’. On the other hand, a comparison with a sparsely populated rural county may not be apt. Perhaps it is better to compare this sample to a royal family, for it consists of the most significant events in history. If a high incidence of kidney cancer were to turn up in the royal family, an experienced physician would tell you that coincidence is an unlikely cause.

I am a single individual, the smallest possible sample. Some people ran into a lightning bolt twice. It could happen three or four times, but the chance of it happening ten times is so insignificant no one will ever have that. It suggests a cause rather than randomness. So, is it possible to establish that the number of meaningful coincidences in my life is so high that it is like being struck by lightning ten times? I wrote down what I still remember, and those incidents could fill a booklet like this one. Many people have experienced meaningful coincidences, but as far as I know, not close to the number and strangeness I have witnessed.

The things that could have happened but did not

In 1913, the ball fell on a black number twenty-six times in a row at the roulette wheel at the Casino de Monte-Carlo. Some people lost a fortune by betting the ball would fall on red the next time. They did not realise the chance of the ball choosing a red number never changed. The ball does not remember where it went the previous times. If we represent black with a B and red with an R and assume, for simplicity’s sake, there is no zero, we can write down falling twenty-six times on black like so:

B B B B B B B B B B B B B B B B B B B B B B B B B B

The probability of the ball falling on black twenty-six times in a row is one in 67,108,864. That is a long shot. What might surprise you is that the following combination of black and red numbers is precisely as likely to occur:

R B B R B R R B R B B R R B R R B R B B R R B B R B

You wouldn’t be thrilled if that happened unless you became a millionaire by betting on this particular series of twenty-six. And even then, you wouldn’t think of the 67,108,863 sequences that did not materialise. We tend to consider only the things that did happen, but we rarely think of all the things that could have transpired but didn’t. Events such as the ball falling on black twenty-six times in a row impress us. And I am even more impressed because twenty-six happens to be my lucky number.

This argument applies to meaningful coincidences but not to a prediction materialising as such a feat may imply that all the other things could not have happened. If I say with conviction that the coming sequence of black and red would be R B B R B R R B R B B R R B R R B R B B R R B B R B and it happens as I predicted, I might have the gift of prophecy. The chance of me being accidentally right was one in 67,108,864.

Imagine the probability of you sitting here reading this page on a tablet or a mobile phone but as a prediction from 3,600 years ago. Imagine Joseph telling the Pharaoh: ‘I see (your name comes here) reading a pile of papyrus pages, not real papyrus pages, but papyrus pages appearing on something that looks like a clay tablet. Do not be afraid, dear Pharaoh, for it will happen 3,600 years from now. But if we do not set up this grain storage, it will not happen, so we must do it. And by the way, Egypt will starve otherwise.’

The chance of this prediction to come true was not one in 67,108,864, and also not one in 1,000,000,000,000,000,000,000 either. It doesn’t help to add more zeroes to that number. The chance is far smaller. The probability is so close to zero that no one can tell. Nevertheless, you sit here reading this text, perhaps even on a tablet. So how could this happen? The answer to this mystery is that so many things could have occurred but did not, but something had to happen, and that is what transpired. In any case, Joseph could not have made such a prediction by accident.

The licence plate number

So what to make of the possible reference to the end date of World War I on the licence plate on Franz Ferdinand’s car? Few historical events are as important as the start and end of World War I. Hence, the law of large numbers does not apply. It is one of the most important historical events, so it is part of a sample comparable to a royal family. And so mere accident seems unlikely. The assassination could have gone wrong, or cooler heads could have prevailed, or the war could have proceeded differently to end on another date.

It might have been possible to guess the end date of World War I once it had started. If you presumed that the war would not take more than twenty years, a random guess of the end date could be correct one in every 7,305 times. But something does not add up here. Hardly anyone expected the war to last longer than a few months. And the licence plate originates from before the war. The assassination succeeded after a series of mishaps. If the licence plate number contained a prediction, it would include the assassination succeeding, Franz Ferdinand dying in this particular car, and this event being the trigger for the war.

That is hard to do unless you wrote the script. And so Mike Dash in the Smithsonian noted, ‘This coincidence is so incredible that I initially suspected that it might be a hoax.’² And because it is not a hoax, investigative minds could have probed other options, but they did not. Conspiracy theorists also ignored it, even though this incident perfectly agrees with their beliefs. After all, somebody might be pulling the strings.

There is a story about a Freemason named Alfred Pike, who allegedly disclosed a secretive plan of the Freemasons to bring about the New World Order. He supposedly predicted both world wars with uncanny precision in 1871. Nobody had ever heard of this plan before 1959. Contrary to the licence plate number, this is a hoax. In the Netherlands, they would call it a monkey sandwich story. The licence plate number could have added some credibility to it. But then again, most conspiracy theorists don’t care about the truth even when they are accidentally right.

Seeing meaning when there is none

Sceptics claim that AIII 118 is a random sequence of characters, but we see a reference to the end date of World War I. That is how our minds work. The argument is a bit odd. If you take it to the extreme, this text is also a random array of characters, as is any book or report. And still, you read words and sentences that have meaning to you. The critics would like you to believe you are delusional. Indeed, the licence plate number would have remained unnoticed if the war had not ended on 11 November 1918.

But the war ended on 11 November 1918 while AIII 118 is the car’s licence plate number that drove Franz Ferdinand to his appointment with his destiny. And destiny is the message the licence plate number radiates. And his destiny was the event that triggered World War I. That can make it meaningful and predictive. There are many times and locations where this sequence of characters could have turned up so that their appearance on this particular spot can have meaning. AIII 118 on a fish barrel in Vienna would not have attracted that attention. Ditto for the licence plate number AIII 117 on that particular car.

But sceptics are fanciful people indeed. Austrians speak German. Armistice in German is Waffenstillstand. So why does it not read WIII 118? Or even better, W1111 1918? If someone sends you a message, you do not quibble about details. If I said ‘hello’ to you, you don’t ask me why I didn’t use the word ‘hi’ instead. That is unless you are a philosopher with a lot of idle time and have a hobby of questioning everything. Arriving at conclusions is for peasants. They have stakes and must decide which crops to plant, so they place their bets. And so do I. Great Britain, the United States and France were all major participants in the war. These countries all use the word armistice.

Instead, it may be a good idea to ask yourself: which licence plate numbers were available in the Austrian-Hungarian Empire? Then, you could check which combinations fit the purpose. I do not know, but I suppose there are not many options. Perhaps, you end up with just one match: AIII 118. That makes it harder to believe that this sequence of characters is meaningless. This scheme became even more inconceivable because the war ended on 11 November (11-11). In other words, it seems impossible.

Only a few historical events are as important as the assassination of Archduke Franz Ferdinand and the Armistice of 11 November 1918, for instance, D-Day, the fall of the Berlin Wall, and 9/11. The scheme coincidences surrounding D-Day are even more puzzling. A historian correctly predicted the fall of the Berlin Wall in 1989, while the coincidences surrounding the terrorist attacks of 11 September 2001 are dumbfounding. They make a chapter on their own.

Other events of importance are the American, French, Chinese and Russian revolutions. A few peculiar coincidences relate to the American Revolution and the French Revolution. At best, they are circumstantial evidence for a script behind everything that happens. The Independence Day coincidence and the parallels between Napoleon and Hitler are not particularly elaborate.

The Chinese Revolution of 1911 started on 10 October 1911. It ended 2,000 years of imperial rule in China. The date being 10 October (10/10) is not as remarkable as 11 November (11/11), even more so because there are no related coincidences. The Russian Revolution started a communist empire that lasted for seven decades. A bad omen marked the coronation of the last Czar of Russia, Nicholas II. The communists later murdered him and his family. But nothing suggests a more elaborate scheme.

Hindsight bias

Then there is the benefit of hindsight. Countless strange coincidences could have happened but did not occur. We notice only things that did happen and do not think of those that did not. That is hindsight bias. The sample of the most significant historical events comes with hindsight. With hindsight, you may know things you cannot learn in advance. Hindsight knowledge is a favourite tool of critics when something goes wrong. But when you use hindsight, your critics argue you are biased. You can never beat your critics, so I will not try. They choose an angle that puts them in an advantageous position. They clip the wings of a bird and ask it to prove it can fly.

Using hindsight may be the only way of doing this investigation because we cannot predict the occurrence of meaningful coincidences. We may never establish that this universe is real, but perhaps we can discover that it is a simulation. So, if there is meaning, we must look for it to find it. But we should be careful as we are inclined to see intent when it could have happened accidentally. Nevertheless, it seems plausible that

• The meaningful coincidences related to the most important historical events are not mere accidents.
• There have been too many meaningful coincidences in my life for it to be just coincidence.

Latest revision: 20 January 2024

1. Thinking, Fast and Slow. Daniel Kahneman (2011). Penguin Books.
2. Curses! Archduke Franz Ferdinand and His Astounding Death Car. Mike Dash (2013). Smithsonian. [link]