09-28-2026, 09:24 PM
Summary
The article explains how randomness and probability can create events that appear to be miracles. For example, two friends may call each other at exactly the same moment, or someone may dream about a person’s death shortly before it happens. Although these events seem extraordinarily unlikely, they become increasingly probable when we consider the enormous number of opportunities for them to occur. Even if an event has a probability of one in a million, millions of opportunities can produce several seemingly miraculous coincidences over time.
The author illustrates this with a calculation based on human perception. Assuming we receive one bit of information per second while awake for 12 hours a day, we process approximately $43,200$ bits of information daily. Even if $99.999%$ of this information is meaningless, the remaining information could still produce approximately $1.3$ seemingly miraculous events per month, or about $15.5$ per year. Confirmation bias then explains why we remember extraordinary coincidences while forgetting the enormous number of ordinary events. We tend to notice evidence that confirms our beliefs and discount evidence that contradicts them.
The article also examines death premonition dreams using probability. An average person experiences approximately five dreams per night, or $1,825$ dreams per year. If only one tenth are remembered, this gives about $182.5$ remembered dreams per person annually. Across $300$ million Americans, this would produce approximately $54.7$ billion remembered dreams per year. Given millions of deaths and billions of social connections between people, it is statistically unsurprising that some dreams will coincidentally correspond to subsequent deaths. In fact, considering the enormous number of possible combinations, it would be surprising if no such coincidences occurred.
Finally, the author introduces the concept of folk numeracy — our natural tendency to misunderstand probability, randomness and statistical trends. Human perception evolved in what Richard Dawkins calls Middle World, the range of sizes, speeds and timescales that humans can directly experience. We easily perceive short-term changes but struggle with extremely large numbers, very slow processes and very long timescales. As a result, we often mistake random fluctuations for meaningful patterns and overlook broader statistical trends. Statistical thinking and probabilistic reasoning can therefore help us distinguish genuine patterns from coincidences.
KEY TAKEAWAYS
ARTICLE
The article explains how randomness and probability can create events that appear to be miracles. For example, two friends may call each other at exactly the same moment, or someone may dream about a person’s death shortly before it happens. Although these events seem extraordinarily unlikely, they become increasingly probable when we consider the enormous number of opportunities for them to occur. Even if an event has a probability of one in a million, millions of opportunities can produce several seemingly miraculous coincidences over time.
The author illustrates this with a calculation based on human perception. Assuming we receive one bit of information per second while awake for 12 hours a day, we process approximately $43,200$ bits of information daily. Even if $99.999%$ of this information is meaningless, the remaining information could still produce approximately $1.3$ seemingly miraculous events per month, or about $15.5$ per year. Confirmation bias then explains why we remember extraordinary coincidences while forgetting the enormous number of ordinary events. We tend to notice evidence that confirms our beliefs and discount evidence that contradicts them.
The article also examines death premonition dreams using probability. An average person experiences approximately five dreams per night, or $1,825$ dreams per year. If only one tenth are remembered, this gives about $182.5$ remembered dreams per person annually. Across $300$ million Americans, this would produce approximately $54.7$ billion remembered dreams per year. Given millions of deaths and billions of social connections between people, it is statistically unsurprising that some dreams will coincidentally correspond to subsequent deaths. In fact, considering the enormous number of possible combinations, it would be surprising if no such coincidences occurred.
Finally, the author introduces the concept of folk numeracy — our natural tendency to misunderstand probability, randomness and statistical trends. Human perception evolved in what Richard Dawkins calls Middle World, the range of sizes, speeds and timescales that humans can directly experience. We easily perceive short-term changes but struggle with extremely large numbers, very slow processes and very long timescales. As a result, we often mistake random fluctuations for meaningful patterns and overlook broader statistical trends. Statistical thinking and probabilistic reasoning can therefore help us distinguish genuine patterns from coincidences.
KEY TAKEAWAYS
- Randomness creates coincidences: Extremely unlikely events can occur when there are enough opportunities for them to happen.
- Confirmation bias distorts perception: We remember extraordinary coincidences while forgetting countless ordinary events.
- Large numbers matter: Billions of events and relationships make seemingly extraordinary coincidences statistically unsurprising.
- Anecdotes are not statistical evidence: A coincidence does not by itself establish a causal or supernatural explanation.
- Folk numeracy leads to errors: Humans naturally struggle to understand probability, randomness and very large datasets.
- Short-term fluctuations can be misleading: We often focus on temporary changes while ignoring long-term trends.
- Human perception has limitations: Our brains evolved for everyday scales rather than atomic, cosmic or geological timescales.
- Statistical thinking is essential: Probability helps us distinguish meaningful patterns from random events.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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