An exponential challenge

The greatest shortcoming of the human race is our inability to understand the exponential function.

Professor Al Bartlett

You have a beautiful pond in your back garden. On Monday you spot a lily pad in one corner.

By the end of Friday lily pads are starting to take over a noticeable area of the pond, if they cover too much your fish will suffocate. You have other plans for the weekend and it’s not yet urgent so you add it to the list of things to tackle next week.

But when you take a look again on Monday this is what you see.

Cognitive psychologists explain the difficulty of grasping exponential change as an ‘exponential growth bias’, where we treat exponential change as if it was linear. We have an intuitive preference to see growth as a steady increase. This means we experience exponential change as initially slow then suddenly as rapid, surprising, disruptive, uncontrollable, incomprehensible.

In linear arithmetic growth, quantities increase by a fixed amount over a given period of time.

In exponential growth the amount by which a quantity of something increases in a given time period is proportional to the quantity already there, this amount is therefore continuously getting larger from one time period to the next. The time required for a quantity growing exponentially to double is constant. Interventions or interactions with other systems may change the doubling time, but the if the pattern of growth remains exponential the rate of increase is itself increasing. A few doublings can lead quickly to enormous numbers.

The difficulty is that effective preparations and interventions need to be made at a point where the rate of growth is apparently very small. Scenario planning that engages properly with exponential growth is difficult. This is clearly demonstrated in the rapid escalation of the COVID19 pandemic in the UK. On 22nd January 2020 Public Health England moved the risk level from “very low” to “low”, there were no confirmed cases in the UK. Two cases were confirmed by 30th January. Confirmed cases exceeded 100 on 2nd March, and 1000 on 11th March. By the time lockdown restrictions were implemented by law on 26th March there had been 20,823 confirmed cases.[1]

Exponential growth can bring unexpected consequences because very large numbers are generated so quickly, which means fixed limits are reached far more suddenly than anticipated. The lily pads are growing at an exponential rate with a doubling time of one day. This means that when the lily pads cover half of the pond, there is just one day left to take action before the whole pond is overrun.

Life exists on Earth as part of a complex network of inter-related systems. Human populations consume a mix of renewable and non-renewable natural resources and emit waste and pollution. There are limits to the rate of extraction and emission that can be sustained globally without exceeding the finite productive or absorptive capacities of the world. Exponential patterns of consumption and emission mean that we are likely to reach and overshoot these capacity limits much faster than we expect. The discovery of additional resources or the use of technology to reduce the rate of emission do not fundamentally change this as long as resource consumption continues exponentially.[2]

Growth in global emissions of CO2 has been exponential since the Industrial Revolution, a consequence of an exponential growth in energy demand that primarily continues to be satisfied from the consumption of non-renewables.[3][4]

There is a strong correspondence between temperature and the concentration of carbon dioxide in the atmosphere observed during the glacial cycles of the past several hundred thousand years. This is because CO2 acts as a greenhouse gas. Solar energy absorbed at Earth’s surface is radiated back into the atmosphere as heat. As the heat makes its way through the atmosphere and back out to space, greenhouse gases absorb much of it, which results in a warming effect on the Earth. The greenhouse effect is what makes the Earth inhabitable by keeping the temperature above freezing. However the warming of the 20th century is, given the perspective of the previous millennium, unprecedented.

Neither solar nor volcanic activity can explain the dramatic warming of the 20th century, in fact both of these factors acting without any other influences would have resulted in a small amount of cooling since 1960. The models are only able to explain the unprecedented warming by the addition of the human-caused increase in greenhouse gas concentrations that started with the Industrial Revolution. The exponential increase in CO2 and other greenhouse gases is resulting in an exponential warming effect.[5]

Comparisons of simulated and reconstructed Northern Hemisphere temperature changes. Simulations are shown by colored lines, thick lines showing the mean of multiple model simulations (using, e.g., models such as ECHAM and CSIRO) and thin lines showing the 90% confidence range of this mean. Red lines show models forced by stronger solar variability and blue lines show models forced by weaker solar variability. Reconstructed temperatures are shown by grey shading. All data are expressed as anomalies from their 1500–1850 mean and smoothed with a 30-year filter. Graphic from the Intergovernmental Panel on Climate Change Fifth Assessment Report.

CO2 levels are currently just below 410ppm, at the current increasing rate of change they will reach 1000ppm by 2100. The last time the earth experienced 400ppm of CO2 was around 4 million years ago when the average temperature was 2-4oC warmer and the sea level 10-25m higher. The concentration of CO2 was last over 1000ppm around 50 million years ago when the average temperature was 13oC warmer and the sea level around 70m higher.[7]

The Earth’s resources are finite. Exponential patterns of consumption mean we will approach the limits to one or more resources or emissions far more rapidly than we expect. The limit we are currently facing is the maximum temperature rise beyond which the consequences on the network of inter-related biological, social and economic systems that support human life are deemed to be intolerable. The UNPCC has set this temperature limit at 1.5oC above pre-industrial levels, embodied in the Paris Agreement. Impacts on natural and human systems from the currently measured global warming of 1oC have already been observed, with deaths of 150,000 annually according to the WHO [6]. The consequences of further temperature rises are complex, uncertain, and likely to be non-linear with the possibility of positive feedback loops causing a cascade of uncontrollable impacts.

Our intuitive preference to view all change as linear means that making decarbonisation an immediate and urgent priority seems an overreaction. It isn’t. Decarbonisation is a global and national race against time.

The UK has set a world–leading net zero
target, the first major economy to do so,
but simply setting the target is not enough
– we need to achieve it. Failing to act will
result in natural catastrophes and changing
weather patterns, as well as significant
economic damage, supply chain disruption
and displacement of populations.

Alok Sharma, Energy White Paper Dec 2020

Transition to a net zero economy demands that we permanently transform how we do business. Successful business strategy will now need to address environmental, social and economic performance in an integrated way, not as optional add-ons.

Agilis supports organisations in Net Zero planning, climate risk management and disclosure, and sustainability and ESG reporting through the tailored deployment of our partner CGR’s established risk and compliance software platform.

  2. “Limits to Growth: The 30 Year Update” Donella Meadows, Jorgen Randers, Dennis Meadows. 2004.