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 11-11.’ Then 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 seven billion people on this planet, and so many things going on, these things happen.
An example can illustrate this. Imagine you have five dice. A remarkable incident is like throwing five sixes. That seems very unlikely. If you throw the five dice only once, it probably does not happen. On average, it only happens 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 odds 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 was 0.02%. Considering the odds of it being 11 November, it is 0.00005%. And then I had to look at the distance recorder, but it is next to the clock, so the odds of that happening are pretty high. The likelihood of the thought coming up on 11 November is not so easy to establish, but it is not low in my case.
The birthday problem demonstrates that strange coincidences happen more often than we think. If you happen to 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.
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 sharing a 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 happening. Furthermore, the more elaborate a scheme, the less likely it occurs. 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
So if some of the most significant events in history come with peculiar coincidences, that might be more telling for two reasons. First, there are only a few of these events, so the law of large numbers does not apply. After all, this is a small sample. If no intelligence is coordinating events in this universe, it is not so likely that meaningful coincidences turned up in this sample, and elaborate schemes are unlikely to occur. Second, if the most significant historical events come with peculiar coincidences, it more plausibly suggests that history is a script than when they happen in someone’s personal life.
To make the argument, you need to answer questions like, what are the most important events, and what are peculiar coincidences? Events such as the sinking of the Titanic or the Kennedy assassination may not qualify, even though the coincidences surrounding them undoubtedly form a strange and elaborate scheme. The beginning and the end of World War I meet the requirements as they are top-tier historical events. The same may be true for D-Day, the fall of the Berlin Wall, and the terrorist attacks of 11 September 2001.
And what to think of the number of meaningful coincidences in my life? It is not possible to establish how likely it is to happen. But 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 odds of such an event happening in any year in any life could be one in 7,776. If the same happens again, it could be like throwing five sixes twice in a row. The odds of that happening would be one in 60,000,000. On average, 100 people might experience something similar each year. But what if many similar incidents have happened in my life? That makes coincidence less likely.
The number of possible unusual events is infinite, so the odds of something strange such as the do-it-yourself store incident occurring could be higher than we intuitively think. It seems impossible to estimate the odds, but without a script, we should expect these incidents to be distributed more or less evenly across all people and timeframes. So is it at all possible to establish that there is a script? A listing of all the strange coincidences in my life can fill a booklet like this one. Many people have experienced meaningful coincidences from time to time, but few have witnessed so many as I have.
Deviations in the human mind
Deviations from the average are likely to occur. And some might be large. We may think something causes a high or low number while it is just randomness. The psychologist Daniel Kahneman came up with an example. A study of the incidence of kidney cancer in the counties of the United States 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 think of that?
You probably came up with a few 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
The explanation is that those counties all had small populations. And with smaller samples, deviations from the average tend to be larger. Our intuition makes connections of causality, but our reason does not verify whether it could just be randomness. We like to think that some cause makes unusual things happen while they can be random events.
If we use a small sample of the most significant historical events to establish that someone is ‘writing history’, this issue may arise. On the other hand, a comparison with a sparsely populated rural county may not be apt. Perhaps it is better to compare this particular sample to the royal family, for it consists of the most significant historical events. If there is a high incidence of kidney cancer in the royal family, an experienced physician will tell you that randomness is an unlikely cause.
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 that the ball would fall on red the next time. They did not realise that the odds of the ball falling on 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 the sake of simplicity that there is no zero, we can represent falling twenty-six times on black like this:
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 would not be thrilled if that happened unless you became a millionaire by betting on this particular series of twenty-six. And even then, you did not 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 happened but did not. That could explain why 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. Just imagine the probability of you sitting here and now 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 a thing that looks like a clay tablet. Do not be afraid, dear Pharaoh, for it will happen over 3,600 years. 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 if you ignore my advice.’
The odds for this prediction to come true were not one in 67,108,864, and also not one in 1,000,000,000,000,000,000,000 either. Even if you add many more zeroes to that number, the odds remain much 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 happened but did not, but something had to happen, and that is what happened. In any case, Joseph could not have made such a prediction by accident.
Chaos theory does not allow us to make such exact predictions. Just imagine that another sperm fertilised the egg of Adolf Hitler’s mother. The world would have been a completely different place. And there were millions of sperms out there that day. A precise prediction coming true, if it is not accidentally accurate, might imply that nothing else could have happened other than what happened.
The licence plate number
So what to make of the 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. And it is one of the most important historical events, so it is part of a sample comparable to a royal family. And so accident seems unlikely. The assassination could have gone wrong, 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 longer than twenty years, a random guess of the end date would be correct once in every 7,305 times. But something does not add up here. First of all, no one 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. So if the licence plate number contained a prediction, it would include a prediction of the assassination succeeding, Franz Ferdinand dying in this particular car, and this event being the trigger for the war.
That is hard to do. 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.
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 and predicted both world wars with uncanny precision in 1871. Alas, nobody 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, the truth is overrated. Usually, conspiracy theorists do not allow facts to get in the way of their beliefs.
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 follow this reasoning to the extreme, this text is also a random array of characters. And still, you read words and sentences that have meaning to you. Indeed, the licence plate number would have remained unnoticed if the end date of the war had not been 11 November 1918. Only, the war did end on 11 November 1918. And it is the licence plate number of the car in which Franz Ferdinand drove to his appointment with destiny. And this event 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 could have meaning.
Austrians speak German. Armistice in German is Waffenstillstand. So why does it not read WIII 118, or even better, W1111 1918? But if someone sends you a message, you do not quibble about such details. If I said ‘hello’ to you, you are not going to discuss with me why I did not say ‘hi’ instead. Only a philosopher with a lot of time on his hands might do that. Great Britain, the United States and France were all major participants in the war. These countries all use the word armistice.
It may be better to ask yourself what series of licence plate numbers were available in the Austrian Hungarian Empire at the time? Then you could check which combinations fit the purpose. You may end up with just one match: AIII 118. That makes it harder to believe that this sequence of characters is meaningless. The war ending on 11 November (11-11) adds additional inconceivability to this scheme. 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 of coincidences surrounding D-Day is 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 intriguing.
Other events of great 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 there being 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 Nicholas II of Russia. The communists later murdered him and his family.
With the benefit of hindsight, we can see patterns and meaning, for example, the meaningful coincidences in the most significant historical events. It may be the only way of doing this kind of investigation as we cannot predict the occurrence of meaningful coincidences in advance. If psychic abilities do not exist while there is a script, then premonitions coming true are scripted events. Hence, premonitions may come true more often than mere chance suggests, but you cannot predict when they do.
If this universe is genuine, we probably will not be able to establish that, but perhaps we can discover that it is a simulation. So if there is meaning out there, we have to look for it to find it. A random sample may not produce meaning while it may be there. It is about finding the most plausible explanation. We need to be careful as we are inclined to see meaning in events that could have happened by accident. It is not possible to make exact statements concerning probability, but it is plausible that:
- The meaningful coincidences surrounding the most important historical events are not mere accidents.
- The number of meaningful coincidences in my life deviates too far from the average to be the result of chance.
Latest revision: 14 May 2022
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]