Chance is everywhere—from a coin toss to a lightning strike, from finding a parking spot to meeting someone unexpectedly. It feels random, even playful. But underneath, it’s one of the most complex ideas we know—deeply mathematical and philosophically debated.
To understand coincidence, we first need to explore its closest relatives: chance, probability, and chaos.
The Difference Between Chance and Probability
We often use “chance” and “probability” interchangeably. But they are not quite the same.
Chance refers to the occurrence of events without an apparent cause or design. It’s the language of randomness and unpredictability—a coin flip, a dice roll, a job offer after a missed bus.
Probability, on the other hand, is our attempt to make sense of that chaos. It’s the mathematical system we use to assign numbers to the likelihood of different outcomes. In this way, probability is a tool; chance is the mystery it tries to measure.
In everyday life, we speak in mixed terms: “There’s a 40% chance of rain” is shorthand for saying the probability is 0.4. But philosophically, “chance” suggests a metaphysical uncertainty; “probability” suggests a mental model for coping with it.
It’s worth noting that the word “chance” has ancient roots—from the Latin cadentia, meaning “falling,” as in the fall of dice. The randomness of gravity was our earliest metaphor for fate.
A Brief History of Probability
The science of probability arose not in universities, but at gambling tables.
In the 17th century, French mathematicians Blaise Pascal and Pierre de Fermat exchanged letters about a problem gamblers faced: how to divide winnings if a game was interrupted. From this practical dilemma emerged a foundational theory: the Doctrine of Chances.
Soon came Huygens, Bernoulli, Laplace—names now etched into the theorems of statistics. They transformed chance into something countable. What began with dice soon governed insurance policies, astronomical predictions, and life expectancy tables. By the 20th century, Andrey Kolmogorov had formalised probability with rigorous axioms.
It was a turning point in human thought: a shift from seeing chance as divine whimsy to treating it as manageable, even predictable—at least in the aggregate.
The Paradox of Predictable Randomness
Here lies one of probability’s greatest gifts: the ability to find order in apparent disorder.
Take a single coin flip—it’s unpredictable. But flip that same coin a thousand times, and a strange certainty emerges: around 500 heads.
This is the Law of Large Numbers: as trials increase, random outcomes average out. Similarly, the Central Limit Theorem shows that, across many kinds of random variables, the result will tend toward a bell curve.
The deeper irony? The more random the individual events, the more stable the collective outcome.
It’s this paradox that lets actuaries predict life expectancy and meteorologists forecast storms—not with certainty, but with statistical confidence.
Enter Chaos: When Determinism Looks Like Chance
Chaos theory arrives to complicate things.
At first glance, chaos might seem like pure randomness. But it’s not. Chaotic systems are deterministic—they follow strict rules—but are so sensitive to initial conditions that their outcomes become unpredictable in practice.
A classic example: weather. We can describe atmospheric dynamics with equations, but tiny changes—a butterfly flapping its wings—can lead to dramatically different results. This is the essence of the butterfly effect.
From a chaos perspective, coincidences may not be magical alignments. They might be inevitable outcomes of complex systems playing out—beyond our foresight but within the rules.
Imagine missing a train by seconds, taking a different route, and meeting someone who changes your life. A small nudge, a new trajectory. No divine intervention required—just nonlinear dynamics at work.
Seeing Patterns in Chaos
Our brains, meanwhile, don’t like randomness.
They seek patterns, even in noise. This is a survival trait—spotting predators in the bushes, finding fruit in the forest. But it also means we over-detect patterns. We remember the one time we thought of someone and they called, but forget the hundred times they didn’t.
Psychologists call this apophenia—seeing connections where none exist. Or pareidolia—seeing faces in clouds.
We’re also prone to confirmation bias, availability heuristics, and the gambler’s fallacy. These quirks of perception make us poor statisticians. But they also make us human.
When coincidences occur, we don’t just observe them—we interpret them. We assign meaning. We construct stories. And sometimes, those stories stick.
Philosophy’s Turn: Is Chance Real?
Philosophers have long asked: is chance an illusion?
Laplace’s demon imagined a universe where, if you knew every particle’s position and speed, you could predict the future entirely. In this view, what looks like chance is just ignorance.
But modern physics tells a different story.
In quantum mechanics, even the most precise knowledge can’t predict when a radioactive atom will decay. There’s an inherent randomness. Einstein resisted this idea—“God does not play dice”—but experiments confirm it. At the tiniest scales, reality appears to roll the dice.
This introduces a form of ontological chance—not just uncertainty in our minds, but true unpredictability in the universe.
Other philosophical questions follow. Can free will exist in a deterministic universe? Or if life is random, does that make it meaningless—or beautifully open?
The Stoics, ever pragmatic, suggested we focus on what we can control and accept the rest. As Boethius wrote, Fortune’s wheel keeps turning, indifferent to our plans.
Cultural Encounters with Chance
Across time and geography, chance has worn many masks: luck, fate, karma, destiny.
Some cultures invoke divine plans—“there are no coincidences,” they say. Others embrace randomness: dice games in Mesopotamia, casting lots in the Bible, drawing names from hats.
We build rituals to sway luck—rabbits’ feet, pre-game socks, prayers. We use random draws to preserve fairness—jury selection, school lotteries. We buy lottery tickets, knowing the odds, but hoping for a miracle.
Even art flirts with randomness: Dada poetry drawn from a hat, or jazz improvisation riding the chaos of the moment.
Chance delights, frustrates, astonishes. But above all, it reminds us we are not fully in control.
A Surprising Birthday Party
Consider this: in a room of just 23 people, there’s about a 50% chance two share a birthday.
This birthday paradox feels wrong. Our intuition says birthdays are rare coincidences. But math disagrees. With 30 people, the odds rise to 70%; with 50, to 97%.
It’s a playful lesson in probability—a gentle nudge that the world is more interconnected, more mathematically entangled, than it appears.
Conclusion
From the microscopic particles to the macro patterns of weather, from evolutionary shifts to personal turning points, chance operates everywhere.
But thanks to probability and chaos theory, we are not wholly lost. These disciplines don’t banish mystery; they give us ways to live with it—rationally.
Coincidences may be surprising. But they are not beyond understanding.
They are, in part, how the world works.
Important Note:
Although chaos theory is primarily a mathematical framework, a philosophy professor I met at a social function in Sydney drew my attention to it. She mentioned that she teaches coincidences as part of her chaos theory lectures. Learning more about it fascinated me—it offers a compelling way to explain many of the coincidences I’ve experienced, at least in part.
That said, there are many other mathematical models that also engage with coincidence—such as complexity theory, network science, and systems theory. I plan to revisit this chapter soon to explore those perspectives further.
Footnotes
Cadentia, from Latin, means “falling,” the root of “chance.” Think of dice tumbling or leaves dropping—movement without design.
The “problem of points,” discussed by Pascal and Fermat in 1654, asked how to fairly divide stakes in an interrupted game of chance. It became a foundational question in probability theory.
The Law of Large Numbers was proven by Jacob Bernoulli around 1700, showing that as sample size increases, the sample mean tends to approach the expected value.
The Central Limit Theorem, developed through the 18th–19th centuries, explains why aggregate outcomes of random variables often follow a normal (bell-curve) distribution.
Kolmogorov’s axioms (1933) gave a formal mathematical foundation to probability, treating it as a branch of measure theory.
Chaos theory, popularised in the 1960s by meteorologist Edward Lorenz, showed how deterministic systems like weather could still be unpredictable due to sensitive dependence on initial conditions.
Apophenia is the tendency to perceive meaningful connections in unrelated things. Pareidolia is a specific type, like seeing animals in clouds or faces in objects.
The birthday paradox shows that in a group of 23 people, there’s a ~50.7% chance two will share a birthday—not a paradox mathematically, but counterintuitive to most.
Laplace’s demon was a thought experiment proposing that if a superintelligence knew all physical laws and positions of particles, it could predict the entire future—a vision challenged by quantum physics.
In quantum mechanics, the timing of radioactive decay is ontologically random—no deeper cause exists, only a probabilistic likelihood per unit time.
Bayesian probability sees probability as a subjective degree of belief, updated via Bayes' Theorem, while frequentist probability defines it as the long-run relative frequency of events.
The butterfly effect metaphor comes from Lorenz’s 1972 paper, “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”
Nassim Nicholas Taleb’s concept of black swan events refers to rare, impactful occurrences that are only explained in hindsight—challenging our ability to predict.
Boethius, in The Consolation of Philosophy (~523 CE), personified Fortune as a spinning wheel—sometimes raising, sometimes crushing—teaching the virtue of equanimity.
In modern psychology, heuristics and biases, such as the availability heuristic or gambler’s fallacy, show how human reasoning about chance often deviates from statistical logic.
Research credit: Developed with support from ChatGPT Deep Research by OpenAI.