An Interactive Simulation to Support Understanding of Sustainability

Now let's add a little more realism into the model. Say I don't immediately respond to my needs for rest and push myself a little in order to do more work. It means I'm overshooting my capacity in the short term and using my reserves - I react to my need for regeneration with a delay, during which the tiredness accumulates. In the case of moderate overshoot, I will do more in the short term and then when tiredness catches up with me, I will maybe take a day off to rest. Such a dynamic will lead to damped oscillation around my level of capacity - I work more for some time and then take a little more time off later. Modelling such a scenario would look something like this:

Introduction to the key concepts

We'll introduce the concept of regenerative capacity and feedback through something familiar to everybody - rest and regeneration of our own body.

Say I enjoy the work I do and I'm achieving good results that motivate me to do more of it. This is a self-reinforcing loop leading to me working more and achieving more. Had this growth been unchecked, the amount of work I do would scale exponentially. It isn't unchecked though - I have only limited time and limited capacity for work before I need to sleep or rest or eat and exceeding that capacity is exhausting my reserves.

If I'm perfectly responsive to the signals my body is giving me (tune down work as soon as I feel I'm exhausting myself) and if I want to keep my work sustainable (meaning not over-exhaust myself), I will balance the amount of average work per day at some level where I can also properly regenerate. Say I start easy and then increase workload until I reach my balance. Over some days, the level of average work per day will rise and as I'm getting close to my capacity, it will slowly level off and settle there.

This, of course, is a highly idealized case where I'm all the time perfectly in tune with my body's needs and living a balanced life without any outside disturbances. In the simulation, we get this scenario in the case of feedback delay being 0, meaning we immediately follow our needs for regeneration and adjust the workload accordingly. The graph of work per day versus time would look something like this:

Image source: https://en.wikipedia.org/wiki/Collapse_of_the_Atlantic_northwest_cod_fishery

What if I increase the delay of my response even more, meaning that I keep disregarding the body's signals for rest? What if I keep overworking, cutting off my sleep and living on coffee? The overshoot in this case will be large - but so will the collapse. I work hard for some time, but then my body collapses and I can do very little work until I regenerate. The gentle oscillations of more work and more rest from the previous case now evolve into violent booms and busts, with periods of manic work punctuated by periods of exhaustion (hopefully in reality I learn something and don't mindlessly keep repeating the same pattern, like in this mathematical model):

The model in the simulation uses a logistic function, which is a basic mathematical function used for modeling constrained growth where an imperative for growth competes with some limiting factor that becomes stronger as the level approaches the capacity. It has been widely used to model cases such as population (population tends to grow exponentially, but is counteracted by limiting factors that become more influential as the population grows - such as resource availability or predators that are happy to see their food multiplying).

What does this have to do with sustainability?

The case presented above is a rich (and familiar) analogy to the way our societies function in relation to external limiting factors. We'll look at three different cases that follow the exact same dynamic: economic growth and resource depletion, stock markets, and population growth.

1. Economic growth and resource depletion

Substitute work per day in the model above for economic output and regenerative capacity of the body for regenerative capacity of the resources used to produce that output. A sustainable economy in a perfect and knowable world would settle its resource throughput approximately at the regenerative capacity of its environment, with some oscillations around that level. This would allow it to remain relatively stable through time and not exhaust its own resource base and the capacity of the environment to process its waste. As we have seen above, the condition for this to happen is a relatively timely feedback (short delays). In the case of the economy and its resource base, this refers to the time in which resource strain gets reflected in economic output. So how do these delays occur?

We can talk about delay in feedback as a consequence of natural systems and as a consequence of man-made systems, such as markets, technologies and institutions.

First, delays due to natural systems. Ecosystems and planetary systems are full of buffers and can absorb some stress. For example, it takes years of intensive agriculture to exhaust the soil to the point of infertility, and it took decades of greenhouse gas emissions to produce a noticeable rise in average temperatures. This means the consequences of overshooting hit with a delay (even though attentive observers such as earth scientists have been warning about it for a long time, the consequences weren't reflected in substantial economic damage or the damage could be offset by another economic activity or by substituting the resources, e.g. cultivating new land to replace the degraded one).

Second, delays due to man-made systems. The way economy balances out is with price signals. Naive economic theory would say that markets will balance out environmental strain, because the scarcer the resources become, the more expensive they will be. This is false. One way in which we delay this feedback is technology. Fishing is a good example. As we deplete more of the fish populations, we also keep developing technologies that are more effective in exploiting them - such as sonar and industrial trawlers. This means that even as fish populations drop, we get more and more effective at catching them and so the price can remain relatively low even while drastically overshooting the regeneration capacity. Effectively, this makes markets by themselves unable to respond to the physical capacity of the resource base - not because we don't have information, but because that information in and of itself does nothing to affect the economics of it. We exploit as if nothing is wrong until the fish population (and with it the economic output of fishing industry) collapses. By the time markets start feeling the feedback, the overshoot might already be so large that it's too late.

A textbook case of this is the collapse of the Atlantic northwest cod fishery in the 90s. Notice the typical shape of the curve, just as in the collapse scenario in the simulation - accelerating growth (overshoot), followed by a steep drop.

Finally, if we push the model to the extreme, the downward part of the curve becomes so large that I destroy my capacity to even regenerate - this is the case of an extreme burnout where I overexhaust myself to the point where my health completely gives way. In this case, I overshoot hard and then collapse completely and remain unable to do any significant work:

2. Stock markets

The speed at which a company can grow is also limited by various factors, such as the size of the market or how fast consumers can absorb new products. Firms are valued according to their potential for making profit. If the feedback between the actual capacity for making profit (i.e. a proven, solid business) and the stock market is relatively timely and reliable, the stock price will follow the real value of the company relatively smoothly. But this is not what happens with speculative stock markets. As is the case with AI right now, investors operate not with real feedback about the health of the business, but with belief of what will happen in the future. A firm can be making no profit at all, bleeding money, while its stock price rises into the sky. As we know from all the economic crises and bubbles so far, at some point a market correction is bound to occur. At this point, the real information about the actual potential of the business finally reaches the investors, the stock price drops and settles back around the realistic value. In the case of more extreme bubbles, the stock price can collapse to the point of bankrupting the company or shaking the entire economy - depending on how severe the overshoot was. This again produces similar dynamics as we have seen above, with the difference that the baseline (capacity of the business) is not constant, but typically growing and being influenced by many other market factors. Depending on delays in feedback (in this case linked to speculation), we can see anything from relatively moderate healthy growth to stock price exploding and then collapsing.

3. Population growth

If you insert a seed population into an environment where food is abundant and there are no other limiting factors, it will grow exponentially. In reality, the carrying capacity of the environment and relationships with the rest of the ecosystem limit the sustainable population levels - there is limited space, limited resources, predators and other limiting factors, such as higher probability of spreading diseases with higher population. When talking about feedback and its delays, we're talking about how fast population size feels and responds to these limiting factors.

There are natural delays present in this dynamic, such as maturing of the offspring (the decision to reproduce was made before the offspring started consuming the resources), natural buffers (the ability to consume beyond the regenerative capacity for some time) or other delays specific to the limiting factor (e.g. a disease takes time to spread and kill part of the population). In the case of human population, there are also the same factors contributing to delays as we mentioned in the case of economic growth - technology and productivity increases can overcome what would otherwise be limiting our consumption. This allows us to overshoot the carrying capacity for some time without enduring serious consequences. An important thing to note here is that not all productivity increase or technology means overshooting the regeneration capacity. All we can say for sure is that it CAN facilitate overshoot and in many cases it does.

Where exactly on the population curve we are at the moment is impossible to say - whether it will be a smooth stabilization or a drastic collapse to a lower level. What we do know for sure is that we're strongly overshooting in terms of resource consumption and pollution. This is not entirely linked to population size though, as consumption per capita is also growing. Earth Overshoot Days measure when in each year global consumption and pollution surpasses the estimated amount the Earth can regenerate in that year. In 2026, the Earth Overshoot Day was July 30, meaning we're overshooting the regeneration capacity by almost a factor 2.

Learning point: growth rate and feedback delay as critical leverage points

We see in the simplified model and in the examples that feedback delay makes a fundamental qualitative difference in how the system behaves. Timely feedback (relative to the growth rate) produces a smooth growth curve that levels off at appropriate levels, while delayed feedback produces oscillations and in the extreme case a large overshoot and sudden collapse.

The key question for designing sustainable and stable systems is then - how do we shorten feedback delays and make the consequences of economy's impact more immediate and direct? Often the focus is on information. We equate feedback with having data and knowledge and we think that having more and faster information will solve the issue. But that's not quite the feedback we're talking about here. Feedback in our context is not the information we (the people) have but the information the system (for example the economy) senses - the actual response of the system and the effect resource strain has on it. As we saw in the example, knowing that fish populations are dropping does not cause fish prices to rise or fishing industry to become less profitable (due to technology and productivity increase). Markets don't sense the state of the fishery, therefore there is no effective, timely feedback.

In the times when economic growth was constrained by its internal productivity (e.g. dependence on manual work), environmental constrains were not a key limiting factor. But with the productivity of today, heavily facilitated by technology, complex global organization and huge energy throughput, they are. If we want to avoid catastrophic overshoot and collapse, we need systems with proper feedback between the environment and the economy and/or a much slower growth rate. We will briefly point out three places to intervene: the imperative for economic growth, governance of technological progress and governance of markets.

1. The imperative for economic growth

Two parameters can fix an overshoot-collapse dynamic - lower growth rate or shorter delay. In the simulation, try selecting "Steady oscillation" or "Overshoot and collapse" scenarios and then gradually tune down any one of the two parameters. You will see the curve transition from boom and bust into ever more gentle stabilizing oscillation.

What growth rate corresponds to in the case of the economy is obvious - economic growth. Removing the imperative for economic growth would remove the force that is driving the overshoot. In practical terms, it would allow the economy to transition from constantly pushing through the regenerative capacity to stabilizing around it. At the moment, with the growth obligation present, this is impossible - however much "green" technology there is and however much more efficient we get, the growth imperative forbids stabilization in the overall regenerative sense.

How to move beyond economic growth imperative is a huge topic that the majority of decision makers and economists are working hard to avoid. There is a growing movement pushing for it though. Degrowth and Post-growth are the terms you should explore, with just a few of the recommended resources including Research & Degrowth, degrowth.info, Degrowth Journal, Post-Growth Institute and many others you can find with a web search.

At Bright3r, one of our research projects is aimed at conceptualizing new monetary systems that would remove the growth obligation that is currently enforced by the presence of debt and interest. Follow our posts to be up to dat with the project progress.

2. Governance of technological progress

As already mentioned, technology is one way in which we cause delayed feedback between the state of environmental stocks and the economy. What would otherwise be a prompt feedback that we're reaching the limits of regenerative capacity (say, a dried-out river that causes water shortages, directly impacting people and economic activity) can be circumvented by technological means (say, deep water wells and complex infrastructure).

The point we're making is not that this technological means of circumventing limits are necessarily bad. They also guard against environmental instability and have facilitated the development of stable civilizations. The point of utmost importance we are making is that such technological progress must go hand in hand with regulatory safeguards that re-establish the prompt feedback. The appropriate quote for this would be "with power comes responsibility". Of course we can build the water infrastructure to ensure stable water supply, but this also means we're pumping out Earth's natural buffers. If we let such perceived abundance lead to water consumption beyond acceptable regenerative capacity, this is a catastrophically foolish development.

Going deeper into the ways in which technological progress could be governed in order to re-establish the prompt feedback is beyond the scope of this post and it will be covered in a future one. For the purpose of this post, let's just reiterate the point that development of proper regulatory feedback loops in concert with technology is essential. Such regulatory loops must ensure that when we're in overshoot, the economy actually feels the consequences - either through enforcing direct consumption limits or through taxation or other kinds of social structures.

3. Governance and de-complexification of markets

Modern markets, especially financial ones, function as an abstraction. With complex global supply chains, we have no idea what is going on in places where the goods we consume are produced.

This complexity and abstraction introduces feedback delays that lead to detachment of markets from physical reality and, consequentially, overshoot. There is probably no better recent example that demonstrates this better than the last big financial crisis of 2008. Financial products that banks were selling to investors got so complex that nobody knew what was packed into them. Investors thought they were making lucrative investments while the reality was that those financial products were filled with subprime mortgages. Once reality caught up, those investments turned out to be worthless.

Such complexity thus introduces delayed feedback because the information about the true state of the resource base simply gets buried. Does that mean complexity should be avoided?

That depends. Joseph A. Tainter in his book The Collapse of Complex Societies presents a good case for describing the evolution of societies in terms of marginal return on complexity. At first, increasing complexity (in terms of technology, social organization etc...) is a good problem solving strategy - it allows societies to cope with stress, such as developing water infrastructure to cope with volatility of water supply. However, rising complexity is subject to diminishing returns. At some point, the cost of complexity surpasses its benefits and from then on, more complexity actually makes the society worse off.

This is coherent with the description the logistic model provides. When complexity is relatively low and limiting factors are predominantly linked to productivity of the economy, complexity can make the system more efficient. But eventually, complexity starts being a burden and makes feedback less efficient, not more. A drop in complexity is at that point favourable.

A note on the limitations of the model

The model presented here and used in the simulation is just that - a model. And a very simple one indeed. The purpose of the model is not to present an accurate description of any real system - the purpose is to demonstrate a key underlying dynamic that many real-world systems exhibit. As is common in science, we try to find the simplest possible model that produces the key features under consideration to a satisfactory degree of detail needed for the particular analysis. With that in mind, we need to point out the following key limitations of the model.

1. The model is one dimensional

In the model, all the environmental factors contributing to the regeneration capacity are collapsed to a single dimension and represented by an aggregate value for capacity. This, of course, is not the case in real life. For example, many resources are substitutable and systems are adaptable - exhausting one resource or process might not produce any collapse because it can be substituted for another. Still, as we see in many examples, the basic behaviour can be modeled in such an aggregated way because substitutability and adaptability are not infinite - there is an overall capacity limit somewhere, even though we don't know where and even though we can often overcome what were previously thought to be limits.

2. The model assumes constant capacity

In the simulation, capacity remains constant. This is very rarely the case in real systems. Systems adapt, grow, evolve in concert with their environment. Analysis taking this into account would make the model much more complex and for the purpose of this article isn't necessary because even if the capacity changes, it is still limited and we're interested in what happens when the system tries to grow relative to that limit.

3. Natural volatility and unpredictability

Systems behave in an inherently volatile and unpredictable way and our understanding of them is limited. Also, there are always distortions in feedback that can cause erratic behaviour. For this reason, achieving zero feedback delays is not only impossible, but also unwanted. If a system were to respond exactly to each erratic fluctuation, it would be unstable. That's why some feedback delay and damping are actually necessary to filter out fluctuations and stabilize the system.

4. Unknown factors

We were talking about lessons for designing sustainable systems. Internalizing feedback from environment into man-made systems would require knowledge about all the environmental processes, which is always partial. Thus, tolerance for unknowns needs to be designed into the systems as well. Not only optimizing with respect to what we know, but also leaving enough slack for what we don't know yet.