As well as a Coach, I am an Engineer. I do maths.

I began to think about writing this piece under the title of ‘Deus ex Machina’ – under the mistaken translation of ‘God outside of the Machine’. It may perhaps still be an appropriate title as humanity seems to be clinging to some belief that everything will be okay as God/Technology/Economic miracle will be winched into the picture from the wings and save everything.

I do not harbour such illusions. I think it us up to us. I believe it is how we have constructed our civilization and the myths that sustain it that lie at the root of what ails us. So my intention is to look there. Covid-19 is just a symptom. A very informative one.

Before I go there – let’s talk briefly about the Malaise. Since 1970 we have lost 60% of our wild animal population. In the last 50 years more resources have been consumed than in the entirety of prior Human history. The oceans are acidifying. The incidence of heat-waves, drought, wildfires, category 5 hurricanes and cyclones has significantly increased. The Arctic is 3-5C warmer than it was a hundred years ago. Greenland is melting. So is the Antarctic. Ice-free polar summers are soon to be a reality. The list goes on.

In short – we are in very deep shit. All of these are symptomatic of a climate system that simply has too much energy and is trying to figure out what to do with it. And, being a chaotic system what it does with this is to find new patterns in which to express this higher energy state. And it does not give a shit about Hom. Sap. In fact, whether we make it as a species is only of interest to us. And for some strange reason we seem uniquely dis-interested at a scale that matters. What will it take to convert the dis-ease of so many with how things are into the movement for transformation that is required to give us a fighting chance?

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Exponential functions. We have all just had a crash-course in exponentials as Covid-19 has shown us what unchecked growth looks like on short timescales, and the draconian measures that have to be applied to ‘flatten the curve’ with disastrous impact for ‘normal’ life.

Humans are not good at understanding exponentials. Most of the experiences we have in nature are linear – small changes lead to small changes. What has defeated every civilization is a failure to appreciate exponential functions. 

As recently as 1600CE a civilization self-destructed on Easter Island. Polynesian settlers arrived on the island in about 400CE. They learned how to live on this 160 square kilometre remote volcanic island – evidence is that it was a heavily forested tropical haven. The Rapanui (the Polynesian name for the island – and its people) grew. They developed a society and surplus that allowed them to focus on more than mere survival. They developed culture. By 1150 it is estimated there were over 9,000 people living there. By 1600CE it was game over. The only thing that remains of that once thriving culture are the iconic Moai – gigantic volcanic rock statues. When western civilization encountered Rapanui in 1722, and named it Easter Island due to an accident of timing, it was a barren wasteland. The few remaining inhabitants were scratching a poor living from what was left after ecological armageddon.

So how did smart people – they were just like us, and we are smart (ish) – end up doing this to themselves? I imagine it went something like this. 

We clear land for farming and make a surplus. Life is good. We have more children and our kids are surviving longer. Our population grows. The Gods have been kind so we worship them and dedicate artworks to their glory and to invoke their protection of our place in the world (insert your deities of choice). And in the pursuit of this greater ‘culture’ we have an impact beyond our mere survival needs. We start taking resources. At first it is below the rate at which nature can keep up and replenish them. But at some point – un-noticed at first – the rate of extraction exceeds the rate of replenishment. At that point – if unnoticed, and we do not do anything about it, our fate is sealed.

Here is a simple model. We rely on some natural resource (forest, farmland, topsoil, clean air, clean water etc…). Nature is good at this and so each year if depleted it can renew a resource by some proportion – lets call it ‘r’ for ‘regeneration’, and the amount of the resource ‘A’ (for abundance). Each year we take an proportion of A for our own purposes – ‘u’ for ‘use’. So next year, the new A remaining is last years’ A less our use of A, which is A x u. Multiplied by the regenerative potential of nature r this gives next years’ value of A. So:

A_year2 = A_year1 x (1 – u) x (1 + r)

The model is a little incomplete as there will be an upper limit set by the space available, solar energy etc… which will limit r towards zero as A approaches the capacity of the system. However for this exercise I am focussing on the lower limit – the relationship between r and u. 

By a bit of algebra, this is stable – ie. A_year2 is the same as A_year1 and every year thereafter if:

u_sustain = r  / (1 + r)

Putting some numbers to this – if A regenerates at a (very generous) 10% per year (r = 0.1) then the sustainable usage rate is:

u_sustain = 0.1 / 1.1 = 0.0909 = 9.09%

If we use less than 9.09% per year, we are golden. We can sustain this indefinitely. If we exceed this level, depletion sets in. In this model our extraction year-on-year will compensate reducing, as it is calculated as a fraction of the remaining total. Whilst this reduction in A is calculated in, there is a comforting self-stabilization to the resulting curves of A remaining versus year for different usage-above-sustainable-rate scenarios.

The trouble is however, this model is not what we are collectively doing, and not what the ill-fated Rapanui population did. They continued to use the resource at the same rate, and perhaps a growing rate year on year based on the initial (and supposed inexhaustible) size of the original resource.

Model 2, the one that has us in serious trouble, is therefore:

A_yearN = ((1 + r) x A_year(N-1)) – (A_year1 x (1 – u))

If we exceed by just one percent and use 10% per year, then A is gone in 26 years. If we overshoot by just 0.1% then A is gone in 74 years. In fact, any value of u that exceeds 9.09% leads to the rapid demise of the resource. The outcome is exquisitely sensitive to u. For the 1% overshoot case, the depletion is an exponential that doubles every 7 years.

Now, if this result is not intuitive – there is a reason for that. We humans have grown up in a world where u was so mindbogglingly huge that if we locally exceeded the critical value of u, then when we realized our crops were not growing in the depleted soil, or we were running out of firewood we could move on, and take advantage of A elsewhere. Modern economic theory encodes this as the theory of substitution. It reasons that if some resource becomes scarce, then it becomes expensive which incentivizes the development of a new resource which can substitute for A. The theory is exactly the same as slash-and-burn agriculture. The trouble is it does not work in a closed system. If A is the system itself, you are in unbelievably serious trouble. I leave it as an exercise to the interested and constitutionally-robust reader to thoroughly terrify themselves with a 3% annual growth rate in the use of a resource above its sustainable usage rate. This growth rate sounds modest until you realize that 3% growth means the rate of consumption doubles in size every 20 years.

The Easter Islanders missed the signs. Their un-subsitutable A was the islands’ forest. I do not know what the doubling time of their resource losses looked like. Say it was 20 years. For a long time; beyond a human lifetime – it seemed like nothing was changing. Then with 20 years to go – half the trees were gone. Still – nothing to worry about, right? Except that last 20 years was hell. A battle to the death over the remaining resources to sustain a rapidly decaying population on devastated land. I cannot begin to imagine what that was like, except for remembering the images of the Ethiopian famine in 1986 that shaped my late teenage years. I have lived all of my life in a world of abundance. I have no personal reference on which to imagine a world of spiraling depletion.

Yet this is what we are collectively staring into.

We have lost 60% of the wild animals on this planet in the last 50 years and consumed more resources than in the previous entirety of human history.

Will we wake up in time?

Perhaps the alarm call may come with a deeper appreciation of exponentials. They are monstrous…