Knowledge theory

What is knowledge theory?

What is truth, and what is knowledge? Philosophers have been discussing these questions for thousands of years. Knowledge theory is also called epistemology. It is about the nature of knowledge. It deals with truth, belief, and the justification of beliefs. It aims to answer questions such as: What do we know? What does it mean that we know something? And what makes beliefs justified? We usually acquire knowledge in two ways:

  • by induction, which is using observations to formulate general rules or theories and
  • by deduction, which is applying these general rules and these theories to specific situations.

For instance, after carefully observing the available records of all the people that have lived and still live, you arrive with the help of induction at a general rule that people die before turning 120 years old. Then, using this rule and deduction, you infer that you will die before the age of 120. That seems straightforward, but there are lots of pitfalls. That is why philosophers are still discussing these issues.

There is a difference between rules and theories. A rule is that if A occurs, B happens. A theory is that A causes B. And if we cannot observe A, the theory assumes the existence of A. For instance, an explanation of electricity assumes the existence of electrons. We cannot see electrons, not even with a powerful microscope, so we presume that electricity proves their existence.

This treatise on knowledge theory is a historical account as new ideas usually build upon previous thoughts. It discusses Western philosophy as Western thinkers have been the most inquiring. As a result, the scientific revolution took place in the Western world. Science is the result of thinking but has also greatly influenced thinking. And so, this approach is the easiest way to tackle the most relevant topics.

Classical philosophy

The ancient Greek philosophers already speculated about the nature of reality. Some believed that everything consisted of four ingredients: fire, water, earth and air. Later on, a few philosophers argued that the building blocks of reality are small particles called atoms. These atoms differ in size and shape. The objects we see are groups of atoms stuck together. That was already close to the modern understanding of reality. This kind of speculation is called metaphysics. It is speculation because atoms are invisible, but by assuming that atoms exist and have different shapes and sizes, you can explain the presence of different types of substances.

There were other issues the ancient Greeks were pondering. Some figured that the earth is a sphere. They could infer it by looking at the sea. The sea horizon is slightly curved, while boats disappear in the distance before their sails do. A philosopher named Xenophanes doubted religion. He realised that people believed that the gods were like themselves. For instance, black people thought that the gods were black, while red-haired people believed the gods were red-haired. Xenophanes then claimed it was not possible to know the gods and how they looked. It was an early form of scepticism.

And why would you worship the Greek gods if the Persians and the Egyptians have other gods? If your place of birth determines what you believe, your beliefs probably are false. The sophists were an early group of philosophers who had come into contact with other cultures. They claimed that absolute knowledge is impossible. Everything is subjective, they argued. This view is called relativism. Socrates is known for his dialogues in which he debated with the sophists.

According to Socrates, there is absolute truth even though we do not know it. His pupil Plato later claimed that ideas are the basis of knowledge and that ideas, not objects, are the building blocks of reality. His view is called idealism. Plato’s pupil Aristotle asserted that knowledge comes from observations. His approach is called empiricism. Both methods come with problems. If you imagine a unicorn, you have the idea of a unicorn, and the idealist could claim that unicorns exist. On the other hand, if you see a unicorn after eating some mushrooms, the empiricist could reason that unicorns exist.

And so, knowledge can always be called into question. If no one has ever seen a unicorn, this still is not definite proof of their non-existence. These creatures could still be hiding deep down in the forests. And perhaps the consumption of mushrooms improves your perception. It is for that reason that scepticism emerged. In ancient times there were two groups of sceptics. The first claimed that nothing is certain. They aimed at refuting the claims of other philosophers. The second argued that it is better to postpone judgement until the matter is sufficiently clarified.

These ideas were revived in Europe in the late Middle Ages after the texts of the classical philosophers had turned up in Arab libraries. European philosophers like Thomas Aquinas and William of Ockham were also theologians. They believed that there is no difference between theology and science. Over time science and religion became separated. Science became based on observations and reason. Religion was a result of divine revelation.

William of Ockham is known for his simplicity principle named Ockam’s Razor. It states that if several hypotheses can explain a phenomenon equally, the one that comes with the fewest entities should be selected. Entities can be assumptions that need to be true. Ockam’s Razor is an argument for minimalism in reasoning or preferring obvious explanations if they suffice. So, if you intend to prove a point, you better use as few unproven assumptions as possible.

Modern philosophy

After 1500 AD, European thinkers realised that Christopher Columbus had discovered an entirely new continent. It became clear that traditional knowledge had failed dramatically. Nothing in the Bible or other ancient sources indicates that America exists. At the same time, Protestants began to challenge the authority of the Roman Catholic Church by making religion a personal matter. The ensuing religious wars ravaged Europe, and they ended without a clear winner. The question arose as to how to evaluate the claims of the different branches of Christianity. After all, they cannot all be true.

brain in a vat believing itself to be a person who is walking

These developments spurred a renewed scepticism and a new search for the foundations of knowledge. As our senses can be deceptive, only rational thinking can produce knowledge, philosophers like René Descartes, Gottfried Leibniz and Baruch Spinoza argued. This school is called rationalism, but it was a new branch of idealism. In a thought experiment similar to the brain-in-a-vat scenario Descartes questioned everything the senses register. Your brain could be inside a vat filled with a life-supporting liquid and connected to a computer that generates the impression that you are a person who is walking. What is beyond doubt, according to Descartes, is that you exist, even when you are just a brain-in-a-vat. And you can establish this fact by thinking. ‘I think therefore I exist,’ he concluded. Other philosophers like Francis Bacon, Thomas Hobbes, John Locke, and David Hume argued that knowledge comes from observations. It was a renewed empiricism.

It was an era marked by advances in the natural sciences. These advances were the result of thought, and they, in their turn, spurred further thinking. It was the combination of observation and thought that led to scientific progress. For example, you can investigate the influence of gravity on the motion of objects by dropping an iron ball from a tower. If you release the ball from different heights, you can measure how long it will take for the ball to hit the ground. The table below shows the possible results of these measurements.

Height (in metres)Time (in seconds)

It requires considerable thought to figure out the formula representing the relationship between height and fall time. This formula is: fall time = 9.81 * √ (2 * height). For instance, 3.19 = 9.81 * √ (2 * 50.0). If the tower is only 50 metres high, you cannot measure how long it will take for the ball to fall from 100 metres. With the help of the formula, you can calculate the fall time without the need for measuring it, so: 9.81 * √ (2 * 100) = 4.52 seconds. It is observation and thinking combined that made this possible.

Finding the mathematical formula that matches the data is like fitting the pieces of a jigsaw puzzle. This way of reasoning is called induction. It is about producing a general rule with the help of observations. You can never be sure that the outcome is correct. For instance, using your sightings and with the help of induction, you might conclude that all swans are white. And if you go to the Moon to drop an iron ball from a tower over there, you will discover that the relationship between height and fall time is different.

Another way of reasoning is deduction. It is working from assumptions to conclusions using logic. If the premises are all true and the rules of logic are correctly applied, then the inference must be correct. Deduction usually is about applying general rules to specific situations. For example, if all humans are mortal (first premise), and Socrates is a human (second premise), then Socrates is mortal (conclusion). Also, if the relationship between height and fall time is: fall time = 9.81 * √ (2 * height) (first premise), and the tower is 100 metres (second premise), then the fall time is 4.52 seconds (conclusion).

Immanuel Kant realised that knowledge arises from observation (empiricism), but it is impossible to know without thinking (idealism). We interpret observations. Our thinking imposes its structure upon these observations. Furthermore, we do not know what reality is (relativism). We do not perceive trees or gravity. These are categories of human thought we attach to the world. The things themselves remain unknown. Hence, metaphysical speculation about the nature of reality is pointless, for instance, asking yourself whether or not gravity or electrons exist. It was a synthesis of previous thoughts and a higher level of insight. Such major leaps in philosophy are rare.

Subsequent idealist philosophers argued that absolute knowledge is possible because the mind creates reality. Reality is subject to our intellect, and reason can uncover it. For instance, the fall of a ball is subject to mathematical laws invented by the human mind. Georg Wilhelm Friedrich Hegel saw Napoleon annihilating the old order and spreading enlightenment ideas all over Europe. Impressed by these events, he claimed that history is a dialectic struggle of ideas resulting in progress. More generally, a reasoned debate using argument and counterargument can lead to a higher insight called synthesis.

Contemporary philosophy

Kant more or less had ended the idea that metaphysics can be a source of knowledge. Philosophers became less ambitious from then on. One reaction was pragmatism. Evolution theory suggests that we hold beliefs to help us survive and reproduce. American thinkers such as Charles Sanders Peirce and William James viewed thinking as a means of solving problems. They were not interested in truth or the nature of reality. Another approach, hermeneutics, with thinkers such as Wilhelm Dilthey and Martin Heidegger, concerns interpreting human communication. Dilthey argued that natural sciences are about interpreting observations while humanities are about understanding meaning.

There was a renewed search for the foundations of knowledge. Analytical philosophers like Bertrand Russell and Ludwig Wittgenstein believed that the main tools of philosophers are language and logic. They aimed to develop a new method to gather knowledge. They assumed there is an outside world and claimed that language expresses facts that correspond to elements of reality. This view is called realism, which is related to empiricism. They claimed that there are justified true beliefs. For instance, Jane might think that something is true. If this is indeed the case, then her conviction is justified.

Karl Popper came up with the idea of falsification. You can never prove that a hypothesis is correct, but you can prove it is wrong when you find contradicting evidence. For instance, you might presume that all swans are white. As soon as you spot a black swan, your theory is proven wrong. Subsequently, you assume that most swans are white while some are black. It is the way knowledge progresses. The belief that most swans are white and some are black is closer to the truth than all swans are white. It may still be incorrect as there could still be a red swan somewhere out there no one has ever seen.

Scientific theories are falsifiable. They allow us to make predictions that we can check. For instance, you can go out and look for swans and check their colour. You can use the mathematical formula reflecting the relationship between height and fall time to calculate the fall time from 100 metres. And if you do an experiment and the outcome differs from the calculation with formula, the theory is proven wrong unless your measurement or computation is inaccurate.

Edmund Gettier criticised the notion of justified true beliefs. You can be correct for the wrong reasons. For instance, Jane looks at her watch that says the time is two o’clock. She believes it. She does not know that the timepiece stopped exactly twelve hours earlier. Her belief is therefore not justified. The watch accidentally gives the correct time, so her belief is true.

As our knowledge increases over time, our understanding of reality also changes. Scientific discoveries drive these changes. It also applies to science itself. Thomas Kuhn noted that there is a succession of paradigms in science. A paradigm is a theory or a system of ideas that dominate a field in science. Usually, it is not possible to explain everything. The theories that clarify the most phenomena, and leave the fewest unexplained, are the best and form the paradigm in the field. For instance, the presumption that swans are either black or white is better than the assertion that they are all white, even if red swans exist.

If you compare reality to a jigsaw puzzle, the paradigm is the solution that makes the most pieces fitting. Unexplained phenomena are pieces without a place in the solution, for instance, unexpected readings on instruments. These readings might indicate that the paradigm is incorrect. As long as no better explanation is at hand, most scientists probably attribute them to errors. At some point, the evidence piles up and cannot be ignored any longer. Then, a scientist might come up with a better hypothesis, and out of the confusion, a new paradigm could arise.

Paradigms in science affect the views ordinary people hold. Only 500 years ago, most people in Europe believed that the Earth is flat, a few thousand years old, and at the centre of the universe. The ancient Greek discovery that the Earth could be a sphere was only known to a few educated people. When Columbus set sail to the West, he expected to end up in Indonesia. Nowadays, most people believe the Earth is a sphere, billions of years old, and an insignificant dot in the universe.

The evidence contradicting existing religions and the failure of ideologies gave rise to post-modernist claims that great stories like religions and ideologies are dead and that absolute knowledge is impossible. Words such as reality and truth became seen as totalitarian concepts. In post-modernism, there is only room for small stories and fragments of realness, depending on perspective. A great source of inspiration was Friedrich Nietzsche. He proclaimed the death of God and heralded the end of the Christian story of God’s people on the road to Paradise giving meaning to our existence. Post-modernism is a renewed relativism. This view was, not surprisingly, criticised by philosophers who claimed that the truth is not subjective.

And so we are more or less back at the point where Socrates was refuting the sophists. With the simulation hypothesis, speculation about the nature of reality or metaphysics re-emerged. We could all be living inside a computer simulation run by an advanced post-human civilisation. And so, it appears that knowledge theory has gone nowhere. At least, it is clear that, while our knowledge increased dramatically during the last 2,500 years, knowledge theory did not progress accordingly.

Data, information, knowledge and wisdom

There is a difference between data, information, knowledge and wisdom. Data refers to signals or symbols like letters or numbers. Data does not need to have meaning. A noise you hear is data. The sequence Q&7nn?9Y is also data. Information refers to what data means. If you know that the noise you hear comes from a car engine, this is information. There is a car with a running engine nearby. Characters together can form words and sentences that can have meaning if you know the context. So, if you read sales are up 25% last month, this can be information, but only if you know the corporation it applies to and when it is written, so that you know the month.

To acquire knowledge, you need information, and it needs to be correct. You may read that the sales are up by 25%, but it does not have to be true. And the noise you hear might be a recording. Wisdom refers to understanding. Knowledge itself does not always lead to better insights and decisions. It can be hard to discern between the important and the insignificant. And so, you may become indecisive when information appears to conflict, or you might ignore information to be decisive.

The amount of data used and stored is growing fast. Most data is not information, but entertainment, for instance, cat videos on YouTube. A small portion may be information like sales data. Whether or not data is information depends on your objective. For any investigation, only a fragment of the available data is relevant. It requires wisdom to understand which data is helpful and what it means for the inquiry. The amount of data increases faster than the amount of information. The amount of information increases faster than knowledge. And wisdom cannot be measured.

Proof and evidence

Proof and evidence are not the same, even though we use these words interchangeably. The definition of proof is a final verdict that removes all doubt, whereas evidence only supports a particular explanation. Proving is usually done by deduction, while induction works with evidence. Proof requires the premises to be correct, which is problematic. The premises used in deductive reasoning, for instance, the relationship between height and fall time, are attained by induction. In mathematics, proving is possible. It is pure deductive reasoning without applying it to reality. For instance, 1 + 1 = 2 is always true. But if you think you see two trees, someone else may not agree. Perhaps, the other person sees three trees or only bushes.

Evidence is related to empiricism. Only, you may not have all the information. With a limited sample of swans and induction, you could conclude that all swans are white. We support claims about reality with evidence, for instance, experiments, but we cannot be sure that relationships like those between height and fall time are always the same.

Hence, there is no proof in reality, not even in science, but scientific evidence meets specified quality standards. The scientific method involves careful observation and rigorous scepticism. That is because observations involve our fallible senses. It further includes formulating hypotheses via induction based on the observances, followed by testing deductions made with the theses using experiments and measurements.

The words establish and conclude can bridge the gap between proof and evidence. They denote achieving the best explanation for the observations. The observations need to be reliable. Only, it may be impossible to use a theory like this universe being a simulation to make testable predictions. A hypothesis needs evidence, and must explain the observations better than the alternatives. By assuming that this universe is a simulation, we can explain phenomena that would otherwise remain unexplained.

Something similar happens in science. No one has ever seen electrons, but by postulating their existence and behaviour, we explain electricity. The simulation hypothesis can explain the paranormal in cases where claims of fraud and delusion fail to be convincing. The main difference is that assuming the existence of electrons allows us to make predictions that we can subsequently test in experiments. Paranormal phenomena tend to be unpredictable, so the simulation hypothesis is not scientific.


There are a few takeaways from what has been discussed so far:

  • We can always debate assertions because the foundations of knowledge themselves are questionable. Empiricism and induction but also idealism and deduction can lead to wrong conclusions.
  • The truth or falsity of a statement depends on whether or not it accurately describes (some part of) reality. With the help of empiricism and induction, you might arrive at better conclusions.
  • The truth or falsity of a system of statements depends on its logical consistency. Contradictions are evidence of errors. With the help of idealism and deduction, you might arrive at better conclusions.
  • An assertion is plausible if there is sufficient evidence supporting it and no evidence contradicting it. In science, it often means that experiments support the theory and no experiments contradict it.
  • Pragmatism implies that usefulness is more important than truth. For instance, religions make large-scale cooperation possible. Religions allowed tribes to grow larger and muster more men for war.
  • Minimalism argues for using as few assumptions as possible to establish a point. It prompts us not to engage in unnecessary speculation or to use irrelevant data.
  • There can be progress in thought. Contradicting arguments can be correct in their own right as there could be a higher level of truth or synthesis resolving the contradiction. For instance, the simulation hypothesis may resolve the contradiction between the religious idea of creation and the big bang and evolution theories.
  • Proof means the absence of doubt, which is not possible when we deal with reality. Evidence can support a particular explanation or theory. In the absence of proof, one can look for the best available explanation for the observations.

Latest revision: 10 May 2022

Featured image: Owl eyes. Brocken Inaglory (2006). Public domain.

Other images: Brain-in-a-vat. Alexander Wivel (2008). Public domain.

Declassified Pentagon UFO footage

The ufo mysteries

In April 2020, the Pentagon declassified three videos showing pilots running into unidentified flying objects (UFOs). These videos vindicated people who believe that extraterrestrials visit us. Former Senator Harry Reid tweeted that the videos only scratch the surface of research and materials available. Now think of crop circles. Not all of them may have been the work of pranksters trying to poke fun of the UFO crowd. Only, the Pentagon claims that it does not have evidence of UFOs being extraterrestrial.

A few months later, Netflix resuscitated the once-popular documentary series Unsolved Mysteries. Most of its episodes are not so mysterious, and many so-called mysteries cannot be dubbed unsolved. But one particular creepy story is keeping people awake at night. It is about the Berkshire UFO sightings that took place on 1 September 1969.

Four unrelated families are said to have been picked up by a UFO and moved by a ray of light on that fateful day. Apart from a few personal accounts, there hardly is any recorded evidence that this happened. Not even a local newspaper reported about it. The documentary compensates for the omission. Indeed, this is a mystery worthy of being labelled unsolved.

What might strike you about the stories of the people involved is that they appear credible. Thomas Reed, who was nine at the time, claimed that he and his family missed more than two hours of their lives while driving in their car. Reed said that his family saw an amber glow on both sides of the road. Then everything got calm. After that, they found themselves back inside the car, but his mother and grandmother had changed places.1

Reed also noted that he saw the then 14-year-old Melanie Kirchdorfer aboard the UFO. She confirms his story. Tommy Warner, who was a child back then, also claimed he was abducted that evening. His babysitter Debbie confirms his account, saying that she saw him vanish into a bright ray of light. The people involved were not eager to tell their stories as that could make a laughing stock out of them. This Unsolved Mysteries episode has left many viewers feeling anxious.2 There are other alien abduction accounts, but few are as convincing as this one.

There is no evidence that aliens are visiting us. Unidentified flying objects can be anything. They are part of an array of mysteries, including evidence suggestive of reincarnation, ghosts, meaningful coincidences, and premonitions. This universe could be a simulation created by an advanced civilisation. That makes more sense because that may allow us to explain the other mysteries too. And this civilisation most likely is post-human, not alien.

Featured image: Declassified Pentagon UFO footage

1. 1969 Berkshire UFO Event Gains Recognition. Jim Levulis (2015). WAMC. [link]
2. Berkshire UFO sightings: Unsolved Mysteries episode is spooking viewers – but what happened next? Jacob Stol (2020). The Guardian. [link]

What are the odds?

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:


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:


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.

Hindsight bias

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]

The curse of The Omen

Rumours go that some films have been cursed, for example, The Poltergeist, Superman and Rosemary’s Baby. Numerous accidents have happened, making some people think these films come with a jinx.1 Not all of them are equally convincing. Accidents happen all the time. They have no relation to a movie, even when several actors of the same cast had bad luck. Still, the curse of The Omen stands out.

Danny Harkins wrote on ‘No film in history has had worse luck than The Omen. Hell, nothing in history has had worse luck than The Omen.’2 The Omen came with billboards featuring a 666-logo inside the title and the uplifting slogan, ‘You have been warned. If something frightening happens to you today, think about it. It may be The Omen.’ And the cheery notice, ‘Good morning, you are one day closer to the end of the world,’ and a conclusion stating, ‘Remember, you have been warned.’

In The Omen, the wife of the American ambassador to Italy gave birth to a son. The child died almost immediately. A priest then convinced him to replace his son with an orphan without telling his wife. Mysterious events soon started to haunt them. The child turned out to be the Antichrist. The Omen was first released on 6 June 1976 (6/6). The date refers to the number 666 as the last digit of 1976 is also a 6. The length of the film is 111 minutes.

It made The Omen a good candidate for a hefty curse. Two months before the filming started, the son of lead actor Gregory Peck committed suicide. In the film, he is the father of the child that died. When Peck went to the film set of The Omen, lightning struck his plane. A few weeks later, lightning struck executive producer Mace Neufeld’s flight. A lightning bolt in Rome just missed producer Harvey Bernhard. Later, the IRA bombed the hotel in which Neufeld was staying.1

A plane hired by the studio to take aerial shots was switched at the last moment by the airline. The people who took the original aeroplane were all killed when it crashed on take-off. An animal handler who worked on the film set died two weeks after working on the film when he was eaten alive by a tiger.1

Stuntman Alf Joint was seriously injured and hospitalised when a stunt went wrong on the set on A Bridge Too Far in Arnhem in the Netherlands, less than a year after the production of The Omen. He jumped off a building and missed the inflatable safety bags meant to cushion his fall. It nearly killed him. Joint said that he felt a push even though nobody was near him at the time.1 Perhaps the combination of these accidents is not exceptional. It might be the result of chance.

But then events took a most peculiar turn. On Friday, 13 August 1976, special effects consultant John Richardson drove through the Netherlands with Liz Moore. Both were working on A Bridge Too Far. They became involved in a car accident that killed Moore. The scene is said to have been eerily similar to one of the most gruesome scenes Richardson had designed for The Omen. The story goes that the accident happened near a road sign stating a distance of 66.6 kilometres to the town of Ommen, a name very similar to omen. And it happened on Friday the thirteenth.1

That caught my attention. There are no road signs in the Netherlands giving distances in fractions of kilometres. Only kilometre markers come with these fractions. Near Raalte is a junction where route N348 to Ommen joins Route N35 to Nijverdal. This location corresponds with kilometre marker 66.6 on Route N348. Road signs stating the direction towards Ommen are close to this marker. I am familiar with the area because I lived nearby in Nijverdal as a child. It appeared to me that this junction was the crash location.

Route N348 from Arnhem to Ommen
Route N348 from Arnhem to Ommen

And so I came to investigate the curse. In 2015 I started an inquiry. A journalist from the local newspaper De Stentor helped me. He did some research and emailed me on 14 April. He had managed to find a former police officer from the area. According to the police officer, the accident indeed took place on Route N348 close to Raalte, but between Raalte and Deventer near Heeten, where Route N348 passes the Overmeenweg. This location corresponds with kilometre marker 60.0. The police officer told the journalist he still remembered the car crash very well.3

According to the police officer, the accident happened when he was on duty. A man and a woman had parked their car in a parking lot alongside Route N348. When they drove away in the direction of Deventer, they entered the wrong lane and collided head-on with an oncoming vehicle driven by a resident of Nijverdal. The view there was somewhat limited because of two gentle curves in the road. He noted that there was no road sign mentioning Ommen near the crash site.3

The woman died on the spot. The car was destroyed and disposed to a fire station. It turned out that the couple were foreigners involved in the production of A Bridge Too Far, the police officer told the journalist. He suspected that Richardson, accustomed to driving on the left side of the road, was not paying attention.3

In a British television programme, Richardson said the following, ‘It was certainly very odd because it happened on Friday the thirteenth.’ He then added, ‘Right opposite the point where the accident happened, was an old mile-post with nothing but sixes on it.’ And he also noted, ‘What spooked me even more, was when I discovered it was on a road to a place called Ommen.’ It appears that Richardson has misread kilometre marker 60.0 and has taken the zeroes for sixes. The numbers might have been worn out if it was an old post like Richardson said.

Kilometre marker 96.1 of route A28 in the Netherlands
Kilometre marker 96.1 of route A28 in the Netherlands

Based on the current location of the marker and the details given by the police officer, another possible scenario is that Richardson was brought to Raalte or a hospital in Zwolle and crossed the junction of Route N348 with Route N35. He may have noticed kilometre marker 66.6 there and a sign stating the direction towards Ommen close to it. That may have freaked him out so that it became part of the legend of the curse. Recollections of an event that happened decades ago are often not accurate, and this applies to the memories of the police officer as well as Richardson.

Alan Tyler, who made a documentary about the curse of The Omen, noticed odd things happening when he was working on it. The strangest thing was that he had two different camera crews filming in separate locations but all the footage showed the same fault. It is at least remarkable that kilometre marker 66.6 is near a road sign stating the direction to Ommen on the same road that was the scene of the car crash so that I came to investigate the curse, most notably because of what happened next.

When I was compiling my findings after receiving the email from the journalist, a few curious events transpired. After reading the email, I took a glance at my stock portfolio. Apart from a few mutual funds, I owned stocks of three corporations. One of them was Heymans, a constructor. It came with a quote of € 13.13. Another position was Macintosh, a retail company. I owned 500 of these, and the price was € 2.626. Hence, the total value was € 1,313. It was peculiar because the car crash happened on Friday the thirteenth. Meanwhile, Macintosh is bankrupt, while Heymans stock went down 60% after the company ran into trouble.

That seems a bit of a curse already, and it suggests poor stock-picking skills on my part. But there was more to come. That evening I had an appointment with a contractor who came to make a tender for renovating my bathroom. He came from Almelo while I lived in Sneek. He cancelled because his van had broken down earlier that day. He could take two routes: via Nijverdal crossing Route N348 near kilometre marker 66.6 or the alternative route via Ommen.

Another curious finding was that my search for ‘Ommen 666’ in Google produced a link to the website At first glance, it appeared to be a site for dog training in Sneek, but it was a bit fishy. Somehow ‘Ommen 666’ had been inserted into topic titles such as ‘Dog Training Terry Ommen 66.6km.’5 The texts on the website were incoherent, with a few references to Ommen 66.6 in it. It is noteworthy as I currently live in Sneek and previously lived in Nijverdal while my enquiry uncovered that Richardson crashed into the car of a resident of Nijverdal.

A final titbit is that my wife has a heart condition that made her visit the hospital in Sneek around the same time I began investigating the curse. The name of her doctor happens to be Oomen, a name pronounced exactly like omen. She had an operation in 2018 and is still visiting dr. Oomen a few times per year. There certainly is something odd about The Omen, or perhaps this universe, where strange incidents happen.

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History’s oddities

US Presidents Thomas Jefferson and John Adams were both involved in drafting the US Declaration of Independence that was signed on 4 July 1776. Both died on 4 July 1826, fifty years after the Declaration of Independence. There are more of such oddities in history.

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11 September coincidences

What may strike you about the coincidences surrounding 11 September 2001 is that many of them could have happened accidentally but that the combination of these incidents might be too improbable to be just coincidence.

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Featured image: Film poster for The Omen. © 2002 20th Century Fox. [copyright info]

Other image: Route N348 from Arnhem to Ommen. User Michiel1972 (2007). Wikimedia Commons.

1. Curse of The Omen and other Hollywood hexes. Barry Didcock (2012). Scotland Herald. [link]
2. The Insane True Stories Behind 6 Cursed Movies. Danny Harkins (2008). [link]
3. Email exchange with De Stentor. [link]
4. Curse or coincidence?… ‘Conspiro Media’ re-examines the grisly chain of events connected to those involved in the ’70s horror-flick, ‘The Omen’… Matt Sergiou (2014). [link]
5. Dog training Terry Ommen 66.6km. [link]

Getting used to strangeness

Eleven is the fool’s number in the Netherlands. On 11 November (11-11) the Councils of Eleven are elected. It marks the beginning of the carnival season that ends in the celebrations of carnival in February. In the formerly Roman Catholic areas of the Netherlands, which mostly are in the south, forty days of fasting ended with carnival, a feast of excessive eating and drinking in which people disguise themselves in all kinds of costumes. In any case, in the Netherlands eleven is associated with oddity.

Apart from being the fool’s number, eleven is the first double-digit number. Eleven is like a repeating of the same strange event. This is what a coincidences are often about. Something strange might happen that might make you wonder, but if something similar happens again shortly afterwards for unexplained reasons, that could be amazing.

There have been several incidents of this kind in my life. For instance, once I was making a bike trip. A car door suddenly opened in front of me. I could barely avoid a collision. Within ten minutes on the same trip it happened again with another car on another road. Coincidences of this kind can happen by chance, but if many of such coincidences happen in one life, that could make you wonder.

For instance, my son Rob had two biking accidents in which he was injured. The first one happened near our home in Sneek just before the home of a retired physician who could help him with his injuries. The second accident happened on our holidays in Ameland just before the home of a retired physician who could help him. That is odd, even more so because these were the two only biking accidents Rob ever had.

Just before the discovery of Natural Money a strange accident occurred just before our house in Sneek. A car had crashed on a lamppost. The lamppost broke off. Two men stepped out and hared away. A few years later I realised that the accident may have been a prelude to the strange events that came later on. That same day I biked towards IJlst, a village near home. There I found a broken off lamppost that had been removed. This was remarkable because it was on the same road as our house is on the road to IJlst.

Once I was visiting my father. That day I was driving on a narrow road in the vicinity of Nijverdal where my father lived. An oncoming car hit the rear-view-mirror and it broke off. A few weeks later my father had exactly the same type of accident in his car. As far as I know never before had anyone I knew an accident of this kind.

In August 2014 we were waiting for a traffic light near home in Sneek. In the back of the car before us sat a guy who looked like my cousin Rob. And so I told my wife Ingrid about that. My cousin and I had been best friends for over a decade. We made a funny newspaper together. Immediately after I finished speaking, four trucks from transport company Leemans came from the right. My cousin Rob had once decorated a truck of Leemans. When I was eighteen years old my cousin and I went on holidays together, hitchhiking in Scandinavia. A truck driver from Leemans brought us to Sweden.

I had never seen a Leemans truck in Sneek before. They were there because of railroad construction work. My cousin came from Haaksbergen, a village halfway between Eibergen where I was born and Enschede where A******* was born. In June 2015 we were leaving Nijverdal after visiting my father. Haaksbergen was in the news because of a shooting incident.1 Haaksbergen had been in the news a few times before because of electricity failures,2 3, skating,4 and a monster truck accident.5 And so I said to Ingrid that Haaksbergen is in the news quite often. Just after I had finished speaking, we passed a Leemans truck by the side of the road.

In 2014 a woman rang our doorbell. Her father was about to turn eighty. He had lived in our house during the 1950s. As a birthday present she wanted to give him a tour in his old home. She made an appointment to visit us the next Saturday. She showed up with her sister and father and I gave them a tour around the house. A few hours later the door bell rang again. Ingrid opened the door to an elderly woman with her daughter and son in law. They asked if they could see the house because she had lived there in the 1960s. Both groups came independently and they hadn’t spoken to each other.

In July 2014 we went on holidays to Sweden and Norway. My son Rob wanted to visit Hessdalen Valley where mysterious lights have been sighted. Those lights look like orbs and so they are known as the Hessdalen orbs. Some people have claimed they were UFOs. When we were in Hessdalen we went to a viewing point on the top of a hill. Some Norwegian guys were standing there for hours already, hoping to photograph a UFO. We didn’t see anything unusual. We took some pictures of the environment. Only, after we came back we noticed orbs on one of the photos we made. But orbs on photographs are a phenomenon unrelated to the Hessdalen orbs so this is remarkable.

Featured image: Orbs on photograph taken at Hessdalen, Norway (2014).

1. Schietpartij Haaksbergen, politie geeft beelden vrij en toont auto schutter. RTV Oost (7 May 2015) [link]
2. Leger helpt Haaksbergen bij stroomstoring. (26 November 2005). [link]
3. Stroomstoring treft Haaksbergen en omgeving. De Volkskrant (29 March 2007). [link]
4. Natuurijsbaan. Wikipedia. [link]
5. Derde dode door ongeluk monstertruck Haaksbergen [link]