The mathematics of the Anthropocene

There is wide recognition that humanity’s impact on the globe – in driving species to extinction, altering the chemistry of the world’s waters and air and shifting its climate – is staggering. But just how big is that impact? How does it compare, for example, to the asteroid that crashed into the Earth 65 million years ago, causing one of the major extinction events in the planet’s history.

In a new paper, Owen Gaffney and Will Steffen propose a new way of understanding how humans influence the Earth – and how this impact ranks among the “great forces of nature” that have shaped the planet over time. They call it the Anthropocene equation. Gaffney is an analyst and communicator for Future Earth and Steffen is senior research fellow at Stockholm Resilience Centre and Fenner School of Environment and Society at the Australian National University.

The two experts discussed this new equation in a recent interview and what it might mean for how people view the world.

Daniel Strain: Why is it important to represent the Anthropocene, the new geological epoch named for the impacts of humans on the planet, mathematically?

Will Steffen: Crystallising this evidence in the form of a simple equation gives the current situation a clarity that the wealth of data often dilutes. It also places the contemporary human impact in the context of the “great forces of nature” that have driven Earth system dynamics over billions of years.

Owen Gaffney: We followed Albert Einstein’s maxim that everything should be made as simple as possible, but not simpler. We wanted to make a very simple, unambiguous, robust mathematical statement in the academic literature about the current state of the Earth system.

We state the rate of change of the Earth system is now a function of industrialised societies. The major drivers of Earth system change, which have dominated Earth’s biosphere for four billion years, now approach zero compared with humans. This is new. While humans have always transformed their environment, they have never overwhelmed these forces.

The idea came when we were communicating the Anthropocene and Great Acceleration. We often use phrases like “the impact of humans now rival the big natural forces” or “humanity is a prime driver of change." We wanted to see if this could be formalised somehow. In 1999, Hans Joachim Schellnhuber published a paper in Nature where he expressed the growing role of humans in the Earth system in a abstract mathematical equation. He argued that the role of humans in the Earth system was now so significant it should be included alongside geological and astronomical forces. But this paper was prior to the Anthropocene proposal, the Great Acceleration and our knowledge of planetary boundaries.

Daniel Strain: You often hear people try to compare humanity’s current impacts to other catastrophic events – for instance, that humanity may be driving as many species extinct as did the asteroid that killed the dinosaurs. But you argue that these comparisons only get at part of the picture. How so?

WS: Great extinction events like the demise of the dinosaurs, and changes in biodiversity more generally, are certainly an important feature of the Earth system. But this paper examines the Earth System as a whole – as a single complex system – and assesses the impact of human activities on the trajectory of the system. This includes not only the planet’s biology, but also the physical climate system and other geological dynamics, and the important processes that link them like biogeochemical cycles.

DS: Does that mean that astronomical or geological forces aren’t having an influence on the globe anymore?

OG: We are not saying the astronomical forces of our solar system or geological processes have disappeared, but in terms of their impact in such a short period of time, they are now negligible compared with our own influence. Volcanic eruptions can influence the rate of change – creating a short-lived cooling effect and, potentially, increasing carbon dioxide in the atmosphere over long timeframes. But emissions from recent eruptions have been absolutely dwarfed by our own emissions from fossil fuel combustion.

There is often confusion in media reports about climate change and the role of humans because it is difficult to distinguish between natural variation, such as the strong El Niño like in 2016, and human-caused change. This has led U.S. President Donald Trump to doubt the need for great concern, for example. He argues that there is “some connectivity” between humans and climate change, “but it depends on how much.” El Niño’s effect on the global climate is immense, but it is followed soon after by La Niña, which cools the planet, so the rate of change of the Earth system caused by these climatic shifts is net zero.

The future trajectory of Earth’s life support system is now in the hands of industrialised societies. This is not a rhetorical statement. This is the new reality.
But what we are saying is not particularly groundbreaking. In the last two decades, dozens of research papers have provided ample evidence to support our conclusion.

However, we can say Earth is now outside the Holocene envelope and even beyond the interglacial envelope.

DS: Can you give an example?

WS: A very good example is the rate of change in the climate using global mean surface temperature as an indicator. Over the past 7000 years, the primary forces driving change have been astronomical – changes in solar intensity and subtle changes in orbital parameters, along with a few volcanoes. They have driven a rate of change of 0.01 degrees Celsius per century. Human forcing via greenhouse gas emissions has, over the past 45 years, increased the rate to 1.7 degrees per century. So the rate of change in climate driven by industrialised societies is 170 times faster than the rate of change driven by natural forcings. And it is in the opposite direction.

DS: In your equation you refer to “H” to represent the influence of humans. But it’s also true that humanity’s influence isn’t uniform. How can your new framework account for that variability?

OG: A decade ago, much discourse on the Anthropocene described humans as a homogenous group. This is now disputed and for good reason. Clearly the one billion upper and middle class people living in industrialised societies have driven Earth into the Anthropocene, not the six billion living in poverty. This one billion are part of an economic system that drives exponential consumption and production that has led us to crash through planetary boundaries.

WS: In fact, we have proposed an equation that breaks out H as a function of population, consumption and the technosphere, which is all of the things that humans have built, from buildings to computers. We break out the latter as a function of the energy system, the political economy and knowledge.

DS: Can you solve the Anthropocene equation?

OG: No, not fully – human societies are too complex. But for a start, the rate of change of the Earth system must approximate to zero as soon as possible. There is no doubt that continued disruption will lead to dramatic consequences for the stability and resilience of the Earth System. It would be prudent to avoid this if we value the long-term viability of a global civilisation. And we can. There is ample evidence the world can decarbonise and the economy can function equally well with zero emissions. Research shows, for example, that we can feed 9 billion people – the projected population by 2050 – a healthy diet without further deforestation and at the same time reducing greenhouse gas emissions.

DS: What are the next steps for representing the Anthropocene mathematically? What will be needed to actually be able to compare humanity’s impacts on the Earth quantitatively to other abrupt changes in the past?

WS: If we want to compare the current rate of change of the Earth System to abrupt events in the past, we’ll need better estimates of the rates of change for these earlier events. We’re actually making some progress on one of them -- the Paleocene-Eocene Thermal Maximum, or PETM, a large, abrupt spike in temperature that occurred about 56 million years ago.  For example, there is now good evidence that humans are releasing 10 times more carbon into the atmosphere than the maximum seen during the PETM. That suggests that H is at least an order-of-magnitude larger than the natural forcings during one of the most abrupt events in Earth’s history.