A Surprising Mathematical Pattern Was Found Hiding in Earth’s History : ScienceAlert

According to a recent study, events geologists use to distinguish transitions between geological chapters in Earth’s story follow a hidden hierarchical pattern, one that could shed light on both past and future tumult.

“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.

Related: The Human Epoch Doesn’t Officially Exist. But We Know When It Began.

The history of our planet is full of upheavals, some dramatic enough to trigger whole new blocks of geological time. This includes changes between comparatively short divisions like ages and epochs, as well as much longer units of time like eras and eons.

The asteroid that decimated the dinosaurs 66 million years ago, for example, caused enough overall disruption to help conclude the Mesozoic Era and kick off the Cenozoic. The Cenozoic, which continues today, is further subdivided into three periods and at least seven epochs.

A cataclysmic impact 66 million years ago is used as a transition point between eras. (Science Photo Library/Canva)

The processes driving these transitions are complicated, yielding variable intervals of relative stability punctuated by apparently unpredictable calamities of different types and magnitudes.

Yet there are signs this may be less capricious than it seems.

The new study focuses on the current Phanerozoic Eon, which dates back around 540 million years and includes the Cenozoic, Mesozoic, and Paleozoic eras. It’s one of Earth’s four eons so far, preceded by the Proterozoic, Archean, and Hadean.

geologic time scale
Chapters in Earth’s geologic history. (TefiM/Getty Images)

Spiridonov and his colleagues used time divisions established by the International Commission on Stratigraphy, but also analyzed boundaries based on stratigraphic ranges of marine animals and on ancient taxa such as conodonts, ammonoids, graptolites, and calcareous nanoplankton.

The boundaries between time units consistently formed intriguing clusters, they found, separated by lengthy spans of relative calm.

This uneven distribution suggests a multifractal system, or one whose complex dynamics are dictated 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.”

The researchers sought to estimate Earth’s ‘outer time scale,’ or the amount of time needed to reveal the breadth of our planet’s natural variability.

Based on their findings, they conclude this span is at least 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.

Studying shorter time scales may fail to convey the extremes our planet is capable of producing, the researchers warn.

Since all of human history has occurred within just a recent sliver of tranquility, a more robust grasp of Earth’s large-scale patterns would likely be valuable.

To help characterize the distribution of these time units and their boundaries, the researchers developed a new model, which they describe as a “compound multifractal-Poisson process.”

Their analysis points to a structure of stage-defining events nested hierarchically, forming a cascade of clusters within clusters.

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

Beyond helping us understand what has already happened on Earth over the past 4.5 billion years or so, these findings – along with future research building upon them – could offer invaluable insight about what to expect in the future.

“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.

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