The third time is the signal
Your deploy pipeline fails on a Friday afternoon. You fix it, move on. Two weeks later it fails again — same symptoms, same time window. You grumble about infrastructure, patch it, move on. Three weeks after that, same failure, same window. This time something shifts. You stop treating it as an incident and start treating it as a structure. You pull the logs, overlay the timelines, and discover that a scheduled batch job collides with deploy resource limits every time the monthly data refresh lands on a Friday.
One occurrence is an event. Two occurrences are a coincidence. Three occurrences are a pattern. This is not a folk rule. It reflects how human cognition, statistical inference, and engineered systems all converge on the same threshold: recurrence is the minimum viable evidence that a structure exists and will repeat.
L-0101 established that patterns exist at every scale. This lesson answers the operational question: how do you know when you're looking at one?
Your brain is a statistical learning engine
In 1996, Jenny Saffran, Richard Aslin, and Elissa Newport at the University of Rochester ran an experiment that reshaped our understanding of how humans detect regularities. They exposed 8-month-old infants to a continuous stream of nonsense syllables — no pauses, no emphasis, no cues. The only structure in the stream was statistical: certain syllable pairs co-occurred with high probability (forming "words"), while syllables spanning word boundaries co-occurred with low probability.
After just two minutes of passive exposure, the infants could distinguish the high-probability pairs from the low-probability ones. No instruction, no feedback, no conscious effort. Their brains extracted the recurring structure from raw repetition alone.
This is statistical learning — and it is not limited to language. Subsequent research extended Saffran's findings to visual sequences, musical patterns, and action sequences. The mechanism is domain-general: your brain tracks transitional probabilities across any repeated input. When the same structure recurs, the neural representation strengthens. When it doesn't recur, the representation decays.
The practical implication is profound. You do not need to consciously decide to look for patterns. Your perceptual system is already doing it. The question is whether you notice what your brain has already detected — and whether you record it before working memory flushes it.
Why three, not two
Two data points create a line. Three data points create evidence of a curve. This asymmetry is not arbitrary — it maps onto fundamental principles in both Bayesian inference and signal detection theory.
In Bayesian updating, each observation shifts your posterior probability that a pattern is real versus coincidental. Your prior after one occurrence is low — events happen once all the time. After the second occurrence, the posterior increases, but not by much. The base rate of coincidence is still high enough to explain two co-occurring events. After the third occurrence, the update is disproportionately large. The probability that three identical structures appeared by chance drops below the threshold where "coincidence" remains the simplest explanation.
Signal detection theory frames this differently but arrives at the same place. Every observation is a mixture of signal (real pattern) and noise (random variation). With one observation, the signal-to-noise ratio is undefined. With two, you have a tentative signal buried in noise. With three, you can begin to estimate the consistency of the signal — is the structure stable across occurrences, or does it shift?
Kahneman and Tversky's work on the representativeness heuristic (1972, 1974) explains why people often skip this discipline. Humans have a deep bias toward seeing patterns in small samples — what Tversky and Kahneman called "the law of small numbers." We intuitively treat a sample of two as representative of a population, when statistically it tells us almost nothing. A coin lands heads twice and we feel like it's a biased coin, even though two consecutive heads has a 25% probability with a fair coin.
The three-occurrence threshold is a cognitive corrective. It forces you to wait one beat longer than your intuition wants to, accumulating enough evidence that the pattern deserves cognitive resources.
The frequency illusion: when your attention masquerades as evidence
There is a trap waiting at the two-occurrence mark, and it has a name: the frequency illusion, also called the Baader-Meinhof phenomenon.
Stanford linguist Arnold Zwicky coined the term "frequency illusion" in 2005 to describe a specific cognitive sequence. First, you notice something for the first time — a word, a concept, a behavior. Your brain flags it as novel. Then you start encountering it everywhere. Not because its frequency increased, but because your selective attention is now primed for it.
The mechanism relies on two reinforcing biases. Selective attention makes you more likely to notice subsequent occurrences. Confirmation bias makes you more likely to interpret ambiguous instances as matches. Together, they create a subjective experience of escalating frequency that has no basis in objective reality.
This is why the discipline of recording occurrences matters. Your memory is not a reliable frequency counter. If you rely on the feeling that "this keeps happening," you will over-count pattern matches and under-count non-matches. A written log with dates forces you to confront the actual base rate. Sometimes the pattern is real and your log confirms it. Sometimes your log reveals that the "constant" occurrence happened twice in six months — hardly a pattern worth building infrastructure around.
The frequency illusion is not a failure of intelligence. It is your brain's statistical learning engine running at high sensitivity with low specificity. It would rather generate a false positive (seeing a pattern that isn't there) than a false negative (missing a pattern that is). Evolution optimized for this asymmetry — it is safer to flee from a rustling bush that contains no predator than to ignore a rustling bush that does. But in knowledge work, false pattern detection wastes the most valuable resource you have: focused attention.
Apophenia: what happens when pattern detection runs unchecked
Take the frequency illusion to its extreme and you get apophenia — the tendency to perceive meaningful connections between unrelated events. Psychiatrist Klaus Conrad coined the term in 1958 while studying the early stages of schizophrenia, defining it as "unmotivated seeing of connections accompanied by a specific feeling of abnormal meaningfulness."
Apophenia is not limited to clinical populations. Researchers have established that it sits on a spectrum. At the healthy end, it drives scientific hypothesis generation, creative association, and entrepreneurial pattern-matching. At the unhealthy end, it produces conspiracy thinking, superstitious behavior, and delusional frameworks where every event confirms a pre-existing narrative.
The mechanism is a miscalibrated signal detector. In signal detection terms, apophenia represents a liberal response criterion — the threshold for declaring "pattern detected" is set so low that noise regularly clears it. The result is an excess of Type I errors: false positives.
The three-occurrence threshold serves as a simple criterion adjustment. It does not eliminate false positives — three coincidences can still happen — but it dramatically reduces them compared to a threshold of one or two. More importantly, it creates a decision point: at three occurrences, you stop reacting and start investigating. You ask whether the three instances share a common structure, whether the structure is stable, and whether the pattern has predictive power. That investigation is what separates disciplined pattern recognition from apophenia.
Repetition in engineered systems
Software engineering formalized this principle decades ago, though it uses different language.
The Gang of Four — Erich Gamma, Richard Helm, Ralph Johnson, and John Vlissides — published Design Patterns in 1994 with an explicit methodology: a solution qualified as a "pattern" only if it appeared independently in at least three different systems. This "Rule of Three" was not arbitrary rigor. It was an empirical filter. A solution that works in one system might be an accident of context. A solution that works in two systems might reflect shared constraints. A solution that works in three unrelated systems probably captures a genuine structural regularity.
Martin Fowler and Kent Beck applied the same logic in reverse with code smells. A code smell is a recurring structural problem — duplicated logic, overly long methods, feature envy — that appears across codebases with enough regularity to warrant a named refactoring. The smell is the recurrence. The pattern is the structural problem that produces it. The refactoring is the intervention.
In production systems, the same principle governs incident response. A single outage is a postmortem. Two similar outages are a concerning coincidence. Three similar outages are a systemic pattern that demands architectural remediation, not just tactical fixes. Site reliability engineering explicitly tracks incident recurrence as a signal for systemic investment — you don't redesign a system because of one failure, but you absolutely redesign it after three failures with the same root cause.
Andrew Koenig, who introduced the term "anti-pattern" to software engineering, set an explicit bar: to distinguish an anti-pattern from a simple mistake, you must demonstrate a repeated pattern of action that produces bad consequences, plus a documented alternative. Repetition is what elevates an observation from anecdote to actionable knowledge.
How machines detect repetition
Machine learning systems operationalize the same principle at scale. A neural network trained on text, images, or log data learns by detecting statistical regularities across repeated examples — the same mechanism Saffran demonstrated in infants, implemented in silicon.
Log anomaly detection systems illustrate this cleanly. These systems ingest millions of log lines, build a model of "normal" patterns (recurring sequences, expected frequencies, typical timing), and then flag deviations from the model. The key insight: the system defines "normal" as "what repeats reliably." An error message that appears once is an event. An error message that appears at the same frequency every day is baseline. An error message that stops appearing — a break in the repetition — is the anomaly.
This inverts the naive assumption that repetition is boring and novelty is interesting. In complex systems, repetition is the signal. It is the evidence that a structure is stable enough to model, predict, and build upon. Novelty is noise until proven otherwise — and it proves otherwise by repeating.
Anomaly detection researchers have found a counterintuitive result: if the same critical error appears 500 times in a log, the system scores it as normal, because it clusters with its own history. The repetition itself is the pattern. The anomaly is what breaks the repetition. This maps directly to human pattern recognition: you notice the meeting that doesn't follow the usual format, the deploy that doesn't produce the usual metrics, the conversation that doesn't follow the usual script. You notice the break because you internalized the repetition.
Habit formation: repetition that rewires the brain
Philippa Lally and her team at University College London (2010) studied how repetition transforms conscious behavior into automatic habit. In a 12-week study, 96 participants chose a new behavior — eating, drinking, or exercise — and performed it daily in a consistent context. Lally measured automaticity (how little conscious effort the behavior required) using a self-report index.
The results mapped an asymptotic curve. Automaticity increased rapidly in the first weeks, then decelerated, reaching a plateau at a median of 66 days. But the range was enormous: 18 to 254 days depending on the person and the behavior's complexity. Simple actions (drinking a glass of water after breakfast) reached automaticity far faster than complex ones (doing 50 sit-ups before dinner).
The relevant insight for pattern recognition is not the 66-day headline. It is the shape of the curve. Each repetition contributes less marginal automaticity than the last, but the early repetitions contribute the most. The first three to five repetitions are where the brain shifts from "novel event" to "recognized structure." After that, the structure stabilizes and deepens, but the recognition is already in place.
This maps onto the three-occurrence threshold. By the third repetition, your brain has enough data to form a preliminary representation — a pattern candidate. It may not be automatic yet, but it is recognized. And recognized patterns can be named, which is exactly where the next lesson picks up.
The protocol: from raw recurrence to pattern candidate
Here is the operational sequence for converting repetition into actionable pattern recognition:
1. Maintain a recurrence log. This is a simple running list in whatever capture system you already use. When something feels familiar — a meeting dynamic, a deployment symptom, an emotional reaction, a decision bottleneck — add a one-line entry with the date. Do not analyze it. Just log it.
2. Count before you conclude. Resist the pull to declare a pattern at two occurrences. Your frequency illusion is strongest at exactly this moment. Instead, note the second occurrence, flag it mentally, and wait. If the structure is real, the third instance will arrive.
3. At three occurrences, investigate. Pull your log entries. Compare the three instances for structural similarity. Ask: Do they share a trigger? Do they produce the same outcome? Is the mechanism plausible? If yes, you have a pattern candidate.
4. Write the pattern as a conditional. Express it in the form "When [trigger/context], then [behavior/outcome]." This strips away narrative and isolates the mechanism. "When I take on a third concurrent project, my response time on all projects degrades within a week" is more useful than "I'm bad at multitasking."
5. Promote or discard. A pattern candidate that holds up across three occurrences and survives structural scrutiny gets promoted to a named pattern — the subject of L-0103. A candidate that dissolves under scrutiny gets discarded without guilt. The log did its job: it prevented premature commitment while preserving the evidence for evaluation.
Connecting forward
Detecting that something recurs is necessary but not sufficient. A pattern you can see but cannot name remains trapped in intuition — it influences your behavior without your conscious participation. L-0103 addresses the next operation: giving the pattern a name, which converts a felt regularity into a manipulable cognitive object.
The sequence is deliberate: see the recurrence (this lesson), name the structure (L-0103), then use it. Repetition is the raw signal. Naming is the act that makes it operational. But you cannot name what you have not yet learned to notice — and noticing begins with the discipline of counting to three.