The Half-Life of History

Five Thousand Years of Data, at a Glance

I assembled five distinct measures to capture the breadth of historical knowledge. Academic works (via OpenAlex⁷) counts research papers tagged to each period. Named individuals tallies Wikipedia biographical articles for people born in each century. Source proxy estimates surviving primary sources: cuneiform tablets and inscriptions for antiquity, manuscript production for the medieval period (following Buringh & Van Zanden 2009⁴), and print title counts for the early modern and modern eras. Ngram discourse measures how frequently each century is mentioned in the Google Books English corpus⁶. And films, a supplementary cultural metric, counts movies set in each period.

The chart below plots all five metrics for every time period, on a logarithmic scale (use the buttons to switch to linear). Toggle individual metrics on or off by clicking the legend. The pattern is unmistakable: every single metric climbs steeply as you approach the present.

The 20th century dominates every measure: 1.37 million Wikipedia biographies, 156,000 academic works, and an estimated 85 million publications. The 3rd millennium BC, by contrast, has just 385 known individuals and 50,000 surviving inscriptions. Recent history doesn't just have more. It has orders of magnitude more.

Knowledge Decays Like a Radioactive Isotope

Samuel Arbesman, in The Half-Life of Facts⁵, proposed that knowledge has a measurable decay rate. I tested this directly. After combining four metrics into a single composite index (using z-scores to put them on a common scale), I tested four candidate models: exponential decay, power law, logarithmic, and linear. The exponential model won decisively.

Just as uranium-238 decays at a predictable rate, historical knowledge follows a smooth exponential curve. The best-fit model gives a half-life of about 84 years. That means for every 84 years further back you look, the composite knowledge index roughly halves. The shaded band below shows the uncertainty range: the true half-life likely falls between 23 and 101 years.

The residual plot underneath reveals which centuries defy the trend. Points far from the zero line are centuries with unusual stories to tell. The 1st century CE spikes upward (driven by its biblical and Roman cultural footprint), while the 19th century overshoots the model's prediction.

When I went looking for prior work, I found that someone had already measured a version of the same thing. Michel et al., in their 2011 Science paper that launched Google Ngrams as a research tool⁶, tracked the fame trajectories of individual people by measuring how quickly a person's name rises and falls in book mentions. For people born around 1865, the post-peak half-life of fame was roughly 73 years. I arrived at a nearby number (~84 years) using an entirely different method: a composite of four metrics, z-scored, spanning five millennia instead of two centuries, measuring eras instead of individuals. A skeptic would note that Google Ngrams appears in both studies, and that is fair. But in my composite, Ngrams is one of four equally weighted metrics. The other three (academic papers, Wikipedia biographies, and surviving sources) have nothing to do with book mentions. Two independent approaches, different data, different scales, and yet half-lives within 15% of each other. That convergence suggests the number reflects something real about how collective memory works.

There may be a reason the number is 84 and not 200 or 500. The Egyptologist Jan Assmann drew a distinction between what he called “communicative memory” (what gets transmitted orally across three or four generations, roughly 80 to 100 years) and “cultural memory,” the kind that survives only when institutions write it down and teach it⁸. The 84-year half-life sits right at that boundary. It is approximately the point where the last person who heard the story firsthand dies, and whatever was not committed to text, stone, or institutional habit begins to vanish.

Historians Amplify the Decay, Not Compensate for It

The obvious objection is that of course we know more about recent history. More sources survived. The more interesting question is whether historians compensate for lost sources by studying ancient periods more intensely, or whether they make the imbalance worse.

The chart below answers this by comparing two curves: the green line tracks source availability (surviving tablets, manuscripts, and books), while the blue line tracks academic attention (OpenAlex publication counts). Where academic attention exceeds source availability, the green shading marks an era as overstudied. Where attention falls below sources, the red shading marks it as understudied.

The pattern is stark. Before the 12th century, every era is understudied. Historians give these periods less attention than their surviving source base would predict. From the 13th century onward, academic attention not only catches up but accelerates far beyond what sources alone would warrant. The 19th century is the most overstudied era, with a bias residual of +3.1, likely reflecting Anglophone historiographic priorities. The 21st century swings the other direction (−3.5), but this is expected: the present has not yet become “history.”

One important caveat: the source proxy changes measurement method across eras (inscriptions in antiquity, manuscripts in the medieval period, print titles after Gutenberg). Cross-era comparisons are therefore approximate, not exact. But the overall direction of the bias is clear regardless.

What Drove the Acceleration

When all four metrics (plus the supplementary films count) are overlaid on a single timeline, the overall trajectory is a smooth upward climb, consistent with the exponential model from the previous chapter. But three historical transitions contributed disproportionately to that acceleration. Around the 1450s, the printing press began a slow transformation of source availability; the named-individuals and academic-works lines begin to steepen in the centuries after Gutenberg, though the effect takes generations to appear. Around 1800, mass literacy, state record-keeping, and industrialization pushed most metrics into steeper growth: the 19th century shows the largest single-century jumps across multiple measures. And the 20th century's digital infrastructure produced a final surge in some metrics, though not all: academic works barely grew from the 19th century, while named individuals and source volumes exploded.

Use the Log/Linear buttons below to switch between scales. On a linear scale, the 20th century towers so far above everything else that ancient history becomes a flat line at zero. The log scale reveals the continuous nature of the acceleration: there is no single moment where everything changes at once, but rather a compounding process that these three transitions each amplified.

A Bird's-Eye View Reveals Dark Zones and Bright Hotspots

The heatmap below offers a compact view of all five metrics across all 33 time periods, with warmer colors indicating higher relative knowledge density (ranked within each metric, so colors reflect relative standing rather than absolute values). The “dark” zones (the 10th–9th centuries BC, the early medieval period) are the deep troughs of human knowledge, eras where very few named individuals survive, minimal inscriptions exist, and academic attention is nearly absent.

In contrast, bright hotspots mark periods with disproportionate cultural footprints: Classical Greece (5th century BC), Imperial Rome (1st–2nd century CE), and of course the entire modern era. The rightmost columns glow with intensity.

One visible anomaly: the 1st century CE has an inflated ngram score. This is a data quality issue. The phrase “first century” appears frequently in non-historical contexts (“the first century of the Industrial Revolution,” “the first century of American democracy”), artificially boosting the signal. I'm flagging this rather than smoothing it away.

All Four Metrics Independently Agree

If academic papers, Wikipedia articles, surviving sources, and book mentions all point in the same direction, the overall pattern is robust. The scatter plots below show this directly. Each dot is one time period. When two metrics track each other, the dots line up along a diagonal. They do, consistently: Spearman rank correlations range from 0.78 to 0.93, all statistically significant after Benjamini-Hochberg correction.

This validates combining the metrics into a single composite index. They aren't telling four different stories. They are four witnesses to the same underlying phenomenon: the exponential erosion of historical knowledge over time.

Other researchers have approached the question with narrower scope. Candia et al. tracked how quickly specific cultural products (songs, movies, biographies) fade from online attention, finding a two-phase curve: a fast-decaying communicative component with a half-life of 20 to 30 years for biographies, and a slow-decaying cultural component that persists for centuries⁹. When Kestemont et al. applied mark-recapture methods from ecology to medieval manuscripts, they estimated that more than 90% of chivalric and heroic narratives from the period were lost entirely¹⁰. My composite index blends both layers of memory into a single curve. The 84-year half-life likely represents the handoff point between these two regimes of forgetting.

What This Analysis Cannot Tell Us

I cannot distinguish knowledge decay from evidence destruction. Fewer named individuals from the 7th century BC does not necessarily mean less was known or done in that era; it may mean fewer records survived, fewer were translated, or fewer were deemed notable by later generations. Survivorship bias runs through every metric here. The exponential curve may describe the decay of evidence as much as the decay of knowledge itself¹⁰.

The source proxy stitches together three different measurement regimes: inscription and tablet counts for antiquity, manuscript production estimates for the medieval period, and print title counts for the early modern and modern eras. Each transition (clay to parchment, parchment to print, print to digital) introduces a discontinuity. I have normalized within eras where possible, but cross-era comparisons remain approximate.

Of the six metrics originally collected, two turned out to be redundant or empty. The Wikipedia people count (wikipedia_people_count) was identical to named individuals for all 33 periods, both drawing from the same PetScan category query. Wikipedia event counts were null across the board (the expected category structure does not exist). After removing these, the analysis uses four distinct metrics, not five. This reduces the apparent independence of the composite index, though Cronbach's alpha (0.88) and the first principal component (explaining 75% of variance) suggest the remaining four metrics do measure a coherent underlying construct.

The confidence interval is wide: 23 to 101 years. The point estimate of ~84 years falls within the range reported by Michel et al. for cultural fame decay, and near the boundary of Assmann's communicative memory horizon. But with 32 data points and a composite built from heterogeneous sources, the precision of this estimate should not be overstated.

Finally, the exponential model is the best available parametric approximation among the four candidates tested, but the residuals show systematic structure. The Durbin-Watson statistic (0.17) indicates strong positive autocorrelation, and the Shapiro-Wilk test rejects normality. The model consistently overpredicts for ancient periods and underpredicts for the most recent centuries. This suggests the true relationship may involve regime shifts or a more complex functional form that a simple two-parameter model cannot capture.