A Surprising Mathematical Pattern Was Found Hiding in Earth's History

A recent study suggests that the events geologists rely on to mark the handovers between chapters of Earth’s geological history are arranged in a concealed hierarchy-an underlying order that may help explain both ancient and forthcoming upheaval.

"Geological time scales may look like tidy timelines in textbooks, but their boundaries tell a much more chaotic story," says study co-author Andrej Spiridonov, a geologist and paleontologist at Vilnius University in Lithuania.

"Our findings show that what seemed like uneven noise is actually a key to understanding how our planet changes, and how far that change can go," Spiridonov says.

Geological time scales and the shocks that redraw them

Earth’s past is packed with disruption, sometimes severe enough to bring about entirely new slices of geological time. Those shifts occur across shorter divisions such as ages and epochs, and also across far larger spans including eras and eons.

One example is the asteroid impact that wiped out the dinosaurs 66 million years ago, creating enough global disturbance to bring the Mesozoic Era to an end and usher in the Cenozoic. The Cenozoic-still ongoing-breaks down further into three periods and at least seven epochs.

The mechanisms behind these transitions are complex, producing uneven stretches of comparative steadiness interrupted by disasters that can look random in both type and scale. Even so, clues suggest the pattern may not be as arbitrary as it appears.

Phanerozoic Eon evidence for a multifractal hierarchy

The study concentrates on the present Phanerozoic Eon, which began roughly 540 million years ago and encompasses the Cenozoic, Mesozoic, and Paleozoic eras. It is the latest of Earth’s four eons to date, following the Proterozoic, Archean, and Hadean.

Spiridonov and colleagues drew on time divisions defined by the International Commission on Stratigraphy, while also examining boundaries inferred from the stratigraphic ranges of marine animals and from ancient taxa including conodonts, ammonoids, graptolites, and calcareous nanoplankton.

Across these different approaches, they found that boundaries between time units repeatedly gathered into notable clusters, separated by long intervals of relative quiet.

That lopsided spread points to a multifractal system-one in which intricate behaviour is governed by a continuous spectrum of exponents.

"The intervals between key events in Earth's history, from mass extinctions to evolutionary explosions, are not scattered completely evenly," Spiridonov says. "They follow a multifractal logic that reveals how variability cascades through time."

Estimating Earth’s ‘outer time scale’

The team also aimed to approximate Earth’s ‘outer time scale’: the duration of record required to expose the full extent of the planet’s natural variability.

From their results, they infer that this window is no less than 500 million years.

"If we want to understand the full range of Earth's behaviours, whether periods of calm or sudden global upheaval, we need geological records that cover at least half a billion years. And ideally, a billion," Spiridonov says.

The researchers caution that analyses spanning shorter time frames may not capture the most extreme outcomes Earth is capable of generating. Because the entirety of human history has unfolded during a comparatively recent sliver of calm, a clearer understanding of these long-range patterns could prove especially useful.

A “compound multifractal-Poisson process” model

To better describe how time units and their boundaries are distributed, the authors introduced a new model they refer to as a "compound multifractal-Poisson process."

Their results indicate that the events defining stages are nested in a hierarchy, producing a cascade in which clusters contain further clusters.

"We now have mathematical evidence that Earth system changes are not just irregular," Spiridonov says. "They are deeply structured and hierarchical."

In addition to sharpening our view of what has taken place on Earth across roughly the last 4.5 billion years, the study’s conclusions-together with future work that builds on them-could also provide valuable guidance on what might lie ahead.

"This has huge implications not only for understanding Earth's past," Spiridonov says, "but also for how we model future planetary change."

The study was published in Earth and Planetary Science Letters.