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Statistical Laws Governing Fluctuations in Word Use from Word Birth to Word Death
Alexander M. Petersen, Joel Tenenbaum, Shlomo Havlin, H. Eugene Stanley
TL;DR
The paper examines aggregate word evolution, a dynamic aspect of language for which little is known. It analyzes word births, deaths, and growth over time, finding conflict-associated changes and a 30–50-year peak in new-word growth fluctuations.
Problem
Aggregate dynamics of word evolution in written history remain little known.
Source: Discussion · p. 7Method
The paper analyzes word birth and death rates and age-conditioned growth fluctuations in written language.
Source: Results · pp. 2, 5, Discussion · p. 7Results
Growth-rate variability rose during World War II in English, French, German, and Russian, while new-word fluctuations peak around 30–50 years of age.
Source: Discussion · p. 8Takeaways & Limitations
Nontrivial autocorrelations and leptokurtic growth distributions show that exogenous shocks can produce growth rates exceeding expectations from non-interacting proportional-growth models.
Source: Discussion · p. 8OCR errors may generate a significant fraction of misspelled and nonsensical forms, and computer-era digitization may bias recent comparisons.
Source: Results · p. 3
Abstract
from arXiv · showhide
We analyze the dynamic properties of 10^7 words recorded in English, Spanish and Hebrew over the period 1800--2008 in order to gain insight into the coevolution of language and culture. We report language independent patterns useful as benchmarks for theoretical models of language evolution. A significantly decreasing (increasing) trend in the birth (death) rate of words indicates a recent shift in the selection laws governing word use. For new words, we observe a peak in the growth-rate fluctuations around 40 years after introduction, consistent with the typical entry time into standard dictionaries and the human generational timescale. Pronounced changes in the dynamics of language during periods of war shows that word correlations, occurring across time and between words, are largely influenced by coevolutionary social, technological, and political factors. We quantify cultural memory by analyzing the long-term correlations in the use of individual words using detrended fluctuation analysis.
Results
Word-use dynamics show a 30–50-year growth-fluctuation peak for new words, shifts around historical events, and distinct patterns in word entry, growth, and persistence. These patterns connect word-use fluctuations with cultural memory and the changing competition among words.
Quantifying the birth rate and the death rate of words
- Since the 1950s, word death rates increased while birth rates decreased; new words tended to have higher median use, while dying words tended to have lower use.Hebrew word births increased fivefold around 1917 following the Balfour Declaration.Source: Results · p. 3, Figure 2 · p. 3, Figure 3 · p. 3
- OCR errors may account for a significant fraction of misspelled and nonsensical words in the birth-and-death calculations.The authors also note that computer-era digitization may introduce bias, although post-2000 statistical patterns were consistent with those extending back several hundred years.Source: Results · p. 3
The lifetime trajectory of words
- During World War II, growth-rate variability rose in participating languages, while Spanish showed no increase; conflict-era increases also appear in other historical periods.For relatively new words, the oldest cohort showed the strongest World War II increase, peaking around 1945.Source: Results · p. 3, Figure 4 · p. 4
- New-word growth fluctuations peak around 30–50 years of age, consistent with dictionary incorporation and the human generational timescale.The peak appears across the analyzed corpora and precedes saturation in a stable growth phase.Source: Results · p. 5, Figure 5 · p. 5
Empirical laws quantifying the growth rate distribution
- Normalized growth rates for new words are leptokurtic and Laplace-shaped rather than Gaussian, with a fivefold excess probability of events above 3σ; common words also follow a Laplace distribution.The reported probabilities beyond 3σ are approximately 0.014 for the Laplace distribution and 0.0027 for the Gaussian distribution.Source: Results · pp. 5–6, Figure 6 · p. 6
Scaling in the growth rate fluctuations of words
- For large cumulative word frequency S, growth-rate variability scales as σ(r|S) ∼ S^-β, with β between 0.10 and 0.21 across the reported corpora.Larger cumulative frequency is associated with smaller annual growth-rate fluctuations.Source: Figure 7 · p. 6, Results · p. 7
Quantifying the long-term cultural memory
- Detrended fluctuation analysis finds positive temporal correlations in common-word use, consistent with the predicted relation ⟨H⟩ = 1 − β.For the four illustrative words, H_i values were significantly greater than the uncorrelated-series benchmark H_r = 0.5.Source: Results · p. 7
Discussion
The discussion treats word use as competition shaped by historical events, social and technological change, and communication standards. It links these forces to distinct patterns across languages, word lifetimes, and language settings.
Discussion
- Digitized books offer editorial and market-based entry standards, unlike the difficult significance-filtering problem posed by voluminous internet feeds.The paper frames quantitative cultural trend analysis as a source of potential insight into human sociology.Source: Discussion · p. 7
- Words compete for writers’ and readers’ attention; frequent irregular verbs are less likely to be replaced, and irregular-verb death rates scale inversely with the square root of relative use.A study of word replacement across Indo-European languages found similar frequency dependence.Source: Discussion · p. 7
- X-ray-related words illustrate zero-sum competition, while spell-checkers boost recognized spellings at the expense of unstandardized counterparts.The authors connect word selection to diffusion and technological change.Source: Discussion · p. 7
- Word selection may vary across spoken, professionally published, and online settings, and depends on word correlations, polysemy, and writers’ demographic and social characteristics.The authors identify dictionaries and spell-checkers as standardization technologies that shape word evolution.Source: Discussion · p. 8
- Word growth-rate fluctuations peak at 30–50 years, a timescale the authors relate to dictionary acceptance and human generations.The authors also connect this interval to first-passage times to a frequency threshold and to the nativization of pidgin languages.Source: Discussion · p. 8
- Hebrew’s word birth rate rose fivefold around 1920 amid language revival, immigration, and political endorsement of a national homeland.Hebrew gained official status as a modern spoken language, while a centralized culture emerged.Source: Discussion · p. 8
- Historical episodes can perturb long-running languages, while nontrivial autocorrelations and leptokurtic growth distributions indicate effects of exogenous shocks.The authors report that shocks can produce growth rates exceeding those expected under non-interacting proportional growth models.Source: Discussion · p. 8
- During World War II, growth-rate distributions broadened in English, French, German, and Russian, but not Spanish.The authors associate the contrast with the relatively small roles Spain and Latin American countries played in the war.Source: Discussion · p. 8
Methods
The methods compare word-use trajectories across word ages and frequencies by normalizing use and growth rates. They also describe detrended fluctuation analysis as a way to quantify temporal autocorrelations in series with underlying trends.
Methods
- The trajectory analysis accounts for variation in word frequency and in the social and technological context of a word’s birth.These factors may affect word-growth dynamics.Source: Methods · p. 8
- Word age is measured from its first recorded appearance, and trajectories are normalized by each word’s average use over its lifetime.This normalization is intended to support comparisons across time and varying word frequency.Source: Methods · p. 8
- Relative growth-rate trajectories are normalized by their lifetime standard deviation to compare growth factors across word life stages.The method accounts for intrinsic maturity in growth-rate variation, rescaling standard deviations at each trajectory year to unity.Source: Methods · pp. 8–9
- Weighted trajectory averages and standard deviations use words with lifetimes at least Tc and first appearances from 1800 onward, weighting each word by its average use.The resulting statistics emphasize the lifetime trajectories of more common new words.Source: Methods · p. 9
- Detrended fluctuation analysis is used to quantify temporal autocorrelations in word-use series that may contain underlying trends.The method’s output is compared with expectations for a time series corresponding to a one-dimensional random walk.Source: Methods · p. 9
Statistical Laws Governing Fluctuations in Word Use
The reported analyses examine word-use memory, word-birth and death rates, and the life-course trajectories of new words. They find correlated memory in individual word series and pronounced growth-rate fluctuations at particular stages of word use.
Statistical Laws Governing Fluctuations in Word Use
- English birth-rate curves differ little at small relative-use thresholds, indicating births are largely comprised of words with relatively high median use; deaths are contributed mostly by low-use words.The figure compares rates for words above alternative thresholds on median lifetime relative use.Source: Figure S1 · p. 11
- DFA on individual word-use series illustrates bursts associated with jazz and rock and roll, wars, and technological advancement.Examples include “polyphony,” “Americanism,” “Repatriation,” and “Antibiotics”; the Repatriation series shows an approximate ten-year lag after WWII and the Vietnam War.Source: Figure S2 · p. 12
- English-fiction and Spanish word-use series have mean Hurst exponents of 0.77 ± 0.23 and 0.90 ± 0.29, respectively, indicating positive long-term correlations.Shuffled-series means are 0.55 ± 0.07 for English fiction and 0.55 ± 0.08 for Spanish, consistent with time series lacking temporal ordering.Source: Figure S3 · p. 13
- Growth-rate fluctuations exceed 1.25 standard deviations at ages 30–50 years and exceed 1.0 standard deviation from ages 10–80 years.The weighted average relative-use trajectory reaches a minimum and begins reversing around 40 years for words with long lifetimes.Source: from Word Birth to Word Death · p. 14