Entropy, Peak Oil, and Stoic Philosophy, Part 2

Editor's Note: This editorial is continued from Part 1, Entropy, Peak Oil and Stoic Philosophy

5. A simple model of the economic system

Here, we have a very simple model that has three stocks: resources, the economy, and waste.

Note the arrows that connect stocks to valves. These arrows indicate feedback. But note also that the system is driven by thermodynamic potentials. Essentially, the economy is an engine that transforms resources into waste. Its "fuel" is, mainly, the chemical potential of fossil fuels.

Now, the model is made using a software called “Vensim” which does not just draw arrows and boxes. It “solves” the model, that is it calculates the flows as a function of the initial amounts of stocks and of the parameters of the system (the “ks” here) – those that are basically describing the potentials. Again, let me state that these SD software packages are not thought in terms of thermodynamic potentials. One day, we may have packages specifically defined for that purpose. For the time being, let's jut keep in mind this point. Now, let's go on and see how the system works. With Vensim, you can change the parameters in real time and see how stocks and flows change. Here are some results:

The software allows you to solve the model iteratively; you see what happens as you change the values of the constants using sliders. And, here, you already start seeing “bell shaped” curves. We can plot the results in a better way; here is how the three main stocks (resources, the economy, and waste) vary with time.

This is a very, very general behavior - it works for a variety of systems. It describes chemical reactions, epidemics, and even the explosion of a nuclear bomb. I also found that it can be applied to the collapse of empires. In a way, it is something like applying Newton's law to different systems - you can describe galaxies, planetary systems and spaceship trajectories, all with the same, simple law. Note that here, unlike the case of gravity, we don't have a physical "force" that pulls together the elements of the system; nothing that you could measure with a dynamometer. But there is a powerful entity that moves the system anyway: entropy.

Now, back to the case of an economic system, you see that the “engine” which is the economy, revs up until a certain time, then it slows down and it falters. Eventually, entropy wins. When all the resources have been transformed into waste, then entropy has been maximized. In the case of the world's economy, the transformation is mainly from fossil hydrocarbons (CxHy) to CO2 and, of course, the chemical potential of hydrocarbons is higher than that of CO2. The economy is an enormous, three stage chemical reaction.

We could modify the system taking into account many more effects – recycling waste for instance, but let me not go into that. Let's see, instead, is how the model describes Hubbert's curve which is the flow rate from the resources stock to the economy stock.

Qualitatively, you see that we do generate “bell shaped” curves. Here, the blue one ("production") is the one that should be compared to the historical production data for crude oil or other commodities. That is possible, but not sufficient to say that the model is good. What I think is a fundamental test for this model is whether it can fit at least TWO sets of data; if possible more. This is a hard test, as I found out working on that.

In practice, we often have good data for production, but for “the economy” it is much more difficult. Nevertheless, we'll see that we can find good “proxy” data for that. So, the model can be put to this hard test and it succeeds. We can test the model on small economic systems that we may assumed to be self-contained. Let me show you an example, whale oil in 19th century. We had already seen the production data earlier on. The question, then, is what could we take as data for "the economy," in this case related to that subsystem of the whole economy that was engaged in whaling at the time. Unfortunately, we don't have these data, but we can find a good "proxy" for the size of the whole industry in the size of the whaling fleet. And we see that it works:

There are other examples. Together with my coworker, Alessandro Lavacchi, we published a paper on this subject that shows how even this very simple model can be used to describe the exploitation of non-renewable resources. Here is just another example: crude oil production in the US 48 lower states - the quintessential "Hubbert curve".

Note that here we have used as “production” not the actual oil production, but the size of oil discoveries. That is because the main effort in oil production is discovery. Once you have found where the oil is, the development process is smooth – almost “automatic” – but it takes several years to go from the first successful find to actually producing something. And, as proxy for the effort of the oil industry we have the number of wildcats, that is of exploratory wells. Note how the industry made a big effort to find oil starting from the 1950s, but basically it couldn't find much. It is typical, as I said.

Now, to show you what the model can do, let's use it to extrapolate economic trends to the future. we could take as “production” the total world primary energy production and as “the economy” we use the world's GDP as a proxy. And here is the result. This is a calculation done together with Leigh Yaxley a few years ago.

As you see, the model predicts that the production of primary energy will peak in a few years from now and then will go down irreversibly. The size of the economy (measured in terms of GDP), curiously, will keep growing for a while; then it will peak and decline as well. Of course, you may be perplexed about these results if you see them as predictions. So, I think I'll spend a few moments discussing what exactly we aim to do with these models. One fundamental point is that we cannot make predictions of what will happen in decades from now. Maybe it makes sense to say that the world's primary energy production will peak in four years from now; that is because we have other models that tell us that. But about the world's GDP peaking in 2044, well, of course you have to take that as a guess. That doesn't mean that the model is useless. If you ask the right questions to the model, the model will give you useful answers. Otherwise, there holds the rule of "garbage in - garbage out." For instance, if you are asking, “How can the economy keep growing throughout 21st century” the model cannot tell you that.

So, from the model you can gain important insights in terms of trends. For instance, if you see the world's energy production going down and the GDP going up; then you might be very happy because you'll say that the economy is becoming “more efficient." But the model tells you that you are not being more efficient, you are simply using previously accumulated resources to keep the economy running. And, of course, you can do that only for a while.

But I do understand that this model is really very simplified. For instance, it does not include renewable resources and it is true that our economy is not completely based on non-renewable resources; even though most of it is. So, the question you may ask now is whether we can do something more detailed. How about adding to the model agriculture, recycling, renewable energy, etc.?

Sure. It can be done and – in fact – it has already been done long ago. The first time it was in 1971 in a work titled "World Dynamics" by Jay Forrester who, by the way, is the inventor of system dynamics. But let's examine here the more detailed study that was published one year later, in 1972. It was inspired by Forrester's work and I am sure you have heard of it. It is the “report to the Club of Rome” titled “The Limits to Growth” of 1972.

6. The Limits to Growth

Now, you may have heard that “The Limits to Growth” (let's call it "LTG") is an outdated work; that it was all a mistake, that they made wrong predictions and the like. Those are just urban legends. People tend to disbelieve what they don't like and that is why LTG was so widely rejected and even demonized. I wrote an entire book on the story of "LTG," it will be published next month, but let me not go into too many details. Let me just say that The Limits to Growth was a very advanced study for its times; it was not a mistake and its predictions were not wrong. In any case, these models are there to show you trends; not to give you exact dates for what will happen.

So, let's go into some details. Let me show you the structure of the first LTG model, called "World3". This is a scheme taken from the Italian 1972 edition:

Click here to enlarge

Of course, you can't understand anything here - and not just because the boxes are labelled in Italian. The reason why I am showing this image is to give you some idea of the structure of a complete SD world model. It looks like one of those puzzles that you find in the Sunday edition of your newspaper. This is a problem that I think we have with system dynamics. Most SD models look the same; at first sight you have no idea of what is being modeled: it could be a fish market, a nuclear plant or a hospital; it is still boxes all the way. There are SD software packages that allow you more graphic freedom; but let me not go into that. The point that I wanted to make is that this model - the "world3" model of "The Limits to Growth" it is not so different, in the end, from the simple model that I had been showing you before. All these models have something in common – the fluxes that go from one boxes to another are governed by thermodynamics. So we might think of a model like this one – the LTG one – as a big, multi-tiered fountain, more or less like this:

This is the Trevi fountain in Rome. It is complicated, as you see, but, in the end, there is a common force that runs the fountain: it is the gravitational potential that moves water down. So, the whole makes sense: there is a physical law that governs the flow of water. So, we could see the LTG model as an especially complicated fountain. We could go into details, but of course we don't want to do that now. Let's try, instead, to simplify the model and see if we can understand what it is about. Here is a graphic representation of the World3 model made by Magne Myrtveit a few years ago:

This is a simplified model; it doesn't reproduce all the features of the original. But it has the advantage of being "mind sized" - it is something that we can grasp and the use of images helps a lot; it is much better than boxes with some label on them. So, as you see, the model can be reduced to a small number of stocks. Here we see them: we have five main stocks; in alphabetic order we have agriculture, industrial capital, non renewable resources, population, and pollution,

Note that, again, this representation of the model does not show the thermodynamics behind. With the stocks arranged as they are in the figure, the potentials that move the system are not evident. Yet, they must be there. Nothing can move without a potential difference that pushes it. So, one thing that we'll have to do someday is to make these potentials visible in the representations of these models. But, as I said, I am telling you about a work in progress – there is plenty of work in this field that someone will have to do in the future.

Now, let's examine the model a little more closely. You recognize that there are three stocks which are just the same as those of the simpler model that I showed to you before. Here the stocks are given different names: mineral resources (the stock that was called "resources"), industrial capital ("the economy") and pollution ("waste"). Then, there are two more stocks; one is agriculture – intended as renewable resources and then there is population. These two new stocks are needed for more detail in the model and, of course, there are many more connections: now the model can describe such things as recycling and the effects of pollutions on the industrial capital. Note also that “renewable” resources may not be absolutely so. Soil is not renewable if it is overexploited – it is called erosion.

At this point, we may go to the results. I am showing to you the data from the first edition of LTG, back in 1972, the main results haven't changed much in simulations performed 30 years later with updated historical data. So, this is the output of the model for the best data available at the time; that was called the “standard run” (the graph is, again, from the Italian edition; the text is from the 2004 edition)

The labels in the plot are a little too small to be readable, but let me describe these results to you. First, the scale spans two centuries; starting in 1900 and arriving to 2100. We are about at the middle of the graph. Now, look at the “resources” curve (red). It has exactly the same shape as the one that we obtained with the simpler model, before. And the curves for industrial and agricultural production (green and brown), yes, they look very much like Hubbert curves, even though here they are not symmetric. This is due in part to the effect of pollution which adds to the effect of depletion. But it is not a very big change.

And then, of course, you see the pollution curve (dark green) – here a basic supposition is that pollution is not permanent - it is gradually re-absorbed by the ecosystem. So, the pollution curve goes up and then down, following with a time lag the behavior of industrial and agricultural production. Finally, there is population. It keeps growing even though agricultural production goes down; this is because people can still reproduce as long as there is at least some food. Actually, there is no direct proportionality in term of food availability and reproduction rate but, in any case, in the long run the lack of food takes its toll. Population starts going down too. What the graph shows is the total collapse of civilization – our civilization. It is thermodynamics doing its job; it is the way everything in the universe works.

You see that, according to this scenario, the start of the collapse of the industrial civilization might start, well, just about now. That might explain a few things about what is going on now in the world. But let me tell you that these simulations are not supposed to provide you with dates for specific events to occur – except in a very, very approximate way. As I said, these simulations tell you about trends, not about events. So, the model tells you that a collapse of the world's economy could start at some moment during the first few decades of the 21st century - maybe later, but in any case not in a remote future.

But there is more; much more. Here we go into something very interesting: it is that trends may change according to your assumptions. So, the “standard run” scenario tells you that civilization collapses mainly because of resource depletion. But we can change the initial assumptions and arrive to very different results. If you assume that we have more resources or - which is about the same - that pollution is more damaging than expected, then what brings civilization down is not resource depletion but the effect of pollution. This is, again, from the 1972 edition of "The Limits to Growth" - the results have not changed in more recent calculations.

Look at the pollution curve shooting up rapidly – it is a different path to arrive to the same result: collapse. In the end, thermodynamics must win. Of course, today we tend to see this “pollution” as something very specific: global warming caused by emissions of greenhouse gases.

So, you see, we are walking on a knife edge. We may be destroyed by climate change or by resource depletion (and possibly by both at the same time). From the most recent LTG simulations performed around 2004 it still seems that it is more likely that we will be destroyed by resource depletion – but we cannot really say. The data are too uncertain and in recent times we have seen a worrisome tendency for people to go for more and more “dirty” fuels (coal, tar sands and the like) and that increases pollution while it gives to you the illusion of having more resources. But the final result will be the same.

7. Facing Collapse (a view based on stoic philosophy)

So, here we are. You see, seeing these results in thermodynamic terms gives them a certain weight; a certain value of ancient prophecy – something that Cassandra herself might have uttered. She was not believed of course; just as today the authors of LTG have not been believed. But there are thermodynamic constraints to the system that we cannot dismiss - even though these limits may not appear in economics textbooks. The final result is collapse in a form or another. We cannot avoid it.

Not that we couldn't do something to soften the blow. What is collapse, after all? It is just rapid change; but things are changing all the time. A collapse is just a period in which things are changing faster than usual. It is like crashing a car into a wall: maybe you can't avoid it, but if you wear seat belts and you have an airbag you'll be much better off. Even more important is to see the wall as soon as possible and start braking. So, detecting the collapse in advance would permit us to go into mitigation strategies. It means managing collapse in such a way to transform into a "soft collapse"; even though not everyone might be happy about it. You are not happy when you car crashes into a wall, but if you come out of the wreck unscathed, well, it is a good thing.

This is the idea that we see very often discussed in meetings such as this one, today. We discuss about what we should do in order to avoid, or at least mitigate, the dark and dire things that depletion and climate change are bringing to us. We discuss plans, technological improvements, “sustainable development”, and many more ideas. The problem is that, outside this conference, nothing is being done and nobody seem to care about what the future has in store for us. It is worse than that, there are plenty of people out there who spend their time actively disparaging what science is telling us about the risks we are facing; global warming in particular. Unfortunately, if we deny thermodynamics we are destined to experience it on ourselves.

So, I am afraid that all the planning and all the “solutions” we have been discussing so earnestly in this conference will be leading to very little. So, what are we to do? Just keep quiet and brood? Well, that depends on you, but one thing I can tell you and it is that we might learn something more from history. See, collapses have already occurred for past civilizations – this much we know very well. And the question is what did they think, what did they do, when they saw their world collapsing around them. This is a fascinating question and we may try to answer it by looking at the civilization that is perhaps the most similar to ours and for which we have the most data. It is the Roman Empire.

I have already written something about the fall of the Roman Empire; I titled it “Peak Civilization”. I saw that it was a huge success in terms of readers. Indeed, you may have noticed that the Roman Empire is very popular nowadays. It is because it is not so difficult to understand that there are so many similarities between us and the Romans. Not everything, but a lot of things. In “Peak Civilization” I tried to apply system dynamics to the Roman Empire – that could not be made quantitative, of course, but in qualitative terms, yes, it works. The Romans were brought down by a combination of resource depletion and pollution. The same problems we are facing today.

So, what did the Romans do? Well, one thing that is clear is that they could do very little. They could never manage change; they were almost always overcome by change. Not that they didn't try; but it was difficult: the empire was too big and human efforts too puny in comparison. Even Emperors couldn't reverse the collapsing trend – no matter how hard they tried. Not even an emperor can beat thermodynamics. So, what did the Romans think about the situation? Did they get depressed? Hopeful? Resigned? Well, we can have some idea on what they were thinking from what they left to us in writing. And one thing that we may identify as their response to the situation was the philosophy that we call “Stoicism.”

Of course, this is not a presentation about philosophy, but I think I could conclude it with a note about this ancient philosophy because it might come useful to us, too. Stoicism was developed in Greece in a period when the Greek civilization was collapsing. Then the Romans picked it up and adapted it to their culture. Stoicism is a philosophy that permeates the Roman way of thinking, it also deeply influenced the Christian philosophy and we can still feel its influence in our world, today. The basic idea, as far as I can understand, is that you live in bad times, yes, but you maintain what we would call a "moral stance". We could say that Stoics thought that "virtue is its own reward" although, of course, there is much more than that in Stoicism.

So, when I was coming to Spain from Italy, I took with me a book written by Marcus Aurelius, a Roman Emperor who lived and ruled in mid-2nd century AD. It is titled “Meditations.” Perhaps it is not a great book, but surely it is an interesting one; mainly because it is a sort of manual on how to apply Stoicism to everyday life. Marcus had a very hard time during his reign. He had to fight almost all the time and he never had the time to write a treatise on philosophy. He just jotted down notes as he had a moment free from the battlefield. That is what the “Meditations” is; a book of snippets. From it, you can get a good idea of the personality of the Emperor. He was a good person - I'd say - who had seen much and experienced much. He had always tried to do his best, but he understood how puny are human efforts.

From Marcus' “Meditations” and from what I read about stoicism, I think I can summarize the basic idea as:

“You cannot win against entropy, but you must behave as if you could.”

Of course, Marcus didn't know about entropy, but he had very clear how the universe is in continuous flow. Things change and this is the only unchangeable truth. I think this is our destiny and what we have to do. Likely, we won't be able to save the world we know. Probably, we won't be able to avoid immense human suffering for the years to come. Yet, we must do our best to try and – who knows – what we'll be able to do might make a difference. I think this is the lesson that Marcus is telling to us, even from a gulf of time that spans almost two millennia. So, I leave you with some words from the book "Meditations" which maybe you can take as relevant for us today.

"Be master of yourself and view life as a man, as a human being, as a citizen and as a mortal. Among the truths you will do well to contemplate most frequently are these two: first, that things can never touch the soul, but stand inert outside it, so that disquiet can arise only from fancies within; and secondly, that all visible objects change in a moment, and will be no more. Think of the countless changes in which you yourself have had a part. The whole universe is change and life itself is but what you deem it." (translation by Maxwell Staniforth, 1962)


I would like to thank all of you for your attention and also the organizers of this conference, David Lafarga and Pilar Carrero, for all the work they did. I would also like to thank Daniel Gomez for driving me to Barbastro from Barcelona and for the photo of me at the conference, with the apple. Finally, thanks to Aglaia Gomez for her assistance in many things during and before the conference.

Source: Cassandra's Legacy

About the Author

Professor of Chemistry, Analyst