Irregular Verbs Regularize Inversely to the Square Root of Usage Frequency

A toddler proudly announces, "I runned all the way home," and a parent gently corrects them to "ran." This daily exchange in living rooms worldwide seems like a simple vocabulary lesson. In reality, it is the frontline of a linguistic evolutionary battle that has been raging for more than a millennium.

English is actively shedding its complex, ancient conjugations in favor of a single, ruthless rule: adding the dental suffix "-ed" to form the past tense. While everyday words like "go" and "see" resist this pressure, less common words do not. The exceptions are dying out, and they are doing so according to a strict mathematical law.

In 2007, a team of researchers led by Erez Lieberman and Martin A. Nowak at Harvard University published a landmark study in the journal Nature. They quantified exactly how fast English is smoothing out its quirks. The team discovered that the half-life of an irregular verb scales inversely to the square root of its usage frequency.[1]

"Before, language was considered too messy and difficult a system for mathematical study," Lieberman noted upon the study's publication. "But now we're able to successfully quantify an aspect of how language changes and develops." The formula means that a verb used 100 times less frequently will regularize 10 times as fast.

Tracking a millennium of decay

To prove this, the Harvard team tracked 177 irregular verbs from Old English, spoken 1,200 years ago, through Middle English to the present day. The attrition has been steady and measurable. Of those 177 original irregulars, 145 survived into Middle English, and only 98 remain irregular in Modern English.[1]

The transition from Old English to Middle English was accelerated by the Norman Conquest of 1066, which flooded the language with French vocabulary and disrupted formal English education. Yet, even through this massive cultural upheaval, the regularization of verbs followed the strict mathematical curve dictated by their usage frequency.[4]

The researchers utilized the CELEX lexical database, a massive corpus containing 17.9 million English words drawn from diverse textual sources. By dividing the verbs into six logarithmically spaced frequency bins, they mapped how often each word appeared in modern usage against its historical survival rate. The correlation was absolute.[1][4]

In the lowest frequency bin, which included words occurring less than once per million words, the regularization rate was devastating. Verbs that modern speakers conjugate with "-ed" without a second thought—such as "help," "laugh," "reach," "walk," and "work"—were all once irregular. They lost their unique past-tense forms because they were not spoken often enough.[1]

Although irregular verbs make up less than 3 percent of the modern English vocabulary, they account for the ten most frequently used verbs in the language. Words like "be," "have," "do," "go," and "say" are so deeply embedded in daily speech that their irregular forms are constantly reinforced.[1]

The mathematics of the square-root law grant these high-frequency verbs near-immortality. The Harvard researchers calculated that the verb "be" has a half-life of 38,800 years, while "think" boasts a half-life of 14,400 years. They will effectively never become regular, because no generation will ever forget how to conjugate them.[1]

The engine of overregularization

The mechanism driving this decay is not adult forgetfulness, but childhood learning. When children acquire language, they do not just memorize words; they extract productive grammatical rules. A child who says "goed" instead of "went" has successfully learned the "-ed" rule and is applying it logically to an exception.[2]

Linguists call this phenomenon overregularization. A 1992 study by developmental psychologist Gary Marcus analyzed 11,521 irregular past-tense utterances from 83 children. Marcus found that overregularization errors are actually quite rare, occurring in just 2.5 percent of irregular past-tense forms, but they affect almost every irregular verb a child attempts to use.[2]

"Children extend regular grammatical patterns to irregular words, resulting in overregularizations like comed, often after a period of correct performance," Marcus wrote. This creates a U-shaped learning curve. The child initially memorizes "went," later deduces the "-ed" rule to say "goed," and finally learns that "go" is an exception.[2]

This cognitive process sits at the center of a major debate in psychology between rule-based learning and connectionist models. Connectionists argue that the brain uses a single neural network to process all verbs based on statistical input. Rule-based theorists argue that the brain explicitly separates memorized exceptions from a universal affixation rule.[2][5]

Regardless of the underlying neural architecture, the correction process relies entirely on frequency. If a child says "holded," a parent hears the error and models the correct word, "held." Because "hold" is a common verb, the child receives enough corrective feedback to internalize the exception. The irregular form survives into the next generation.[2]

Words on the brink

But when a verb is rare, the correction mechanism breaks down. If a child applies the "-ed" rule to a low-frequency verb like "shrive" or "smite," they might never hear an adult use the correct irregular past tense. Without that constant reinforcement, the overregularized form takes root and eventually becomes the standard.[1][2]

The numbers bear this out perfectly. The Harvard study found that "shrive" and "smite" have half-lives of just 300 and 700 years, respectively. They are actively dying. Meanwhile, the verb "wed" is currently teetering on the brink of complete regularization, as "wedded" increasingly replaces "wed" in the past tense.[1]

"Now may be your last chance to be a 'newly wed'," the researchers quipped in their 2007 paper. "The married couples of the future can only hope for 'wedded' bliss." As new verbs enter the English language—like "google" or "tweet"—they are universally adopted as regular verbs, ensuring the irregular class will never grow.[1]

A universal law of language

This frequency-dependent survival is not unique to English verbs. In a parallel 2007 study, evolutionary biologist Mark Pagel demonstrated that the same mathematical principle governs lexical evolution across the entire Indo-European language family. Words used frequently evolve slowly, while rare words are rapidly replaced.[3]

Pagel tracked 200 basic meanings across 87 languages, finding that high-frequency concepts like "two" or "water" share closely related word forms across the globe. Conversely, low-frequency concepts like "tail" or "bird" evolve rapidly and are expressed by entirely unrelated words in different languages. Frequency acts as a universal anchor.[3]

The square-root law of language evolution demonstrates that human culture operates with the same mathematical precision as genetics. The "-ed" rule acts as a dominant linguistic trait, relentlessly overwriting exceptions. Only the daily, repetitive force of millions of conversations can protect the ancient quirks of English from being entirely smoothed away.[1][3]