I had plenty of time for my talk at the conference “Peak Oil: fact or fiction?” held in Barbastro (Spain) on May 4-7 2011. So, I could ramble a little on various subjects, from the entropy of complex systems to the stoic philosophy of Emperor Marcus Aurelius (above). Perhaps too many things but, in any case, here is a version written from memory where I tried to maintain the tone and the content of my talk.
1. Simple physics and complex systems
So, ladies and gentleman, first of all let me show you this apple (photo by Daniel Gomez)
Don’t worry; it doesn’t mean that this will be a very long talk! I brought this apple with me just because I wanted to tell you about Newton’s universal law of gravity. As we know, it seems to be true that he got the idea because he saw an apple falling from a tree (although it may not have fallen straight on his head!).
The fact that apples fall from tree – and that everything else that can fall, does – is an effect of the existence of relatively simple laws in the universe. Many things that we see around us are extremely complicated – or “complex”. Think of the solar system, for instance. There are many bodies of different sizes, moving in different trajectories. But there is a certain logic in it and the logic comes from a very simple law – Newton’s law – which can be expressed as follows:
Before Newton, for a long time scientists could only grumble something about “angels pushing” when asked about what caused planets to move. But if you know the law, you can describe not only the movement of the planets of the solar system, but all sort of bodies, including entire galaxies.
It is not rare to find an underlying simple law that generates complex systems. Think of fractals; Mandelbrot’s set, for instance. Fractals are not just mathematical entities, are common in nature, as well. Or think of models such a Feigenbaum’s bifurcations – they are the result of an extremely simple equation. These are examples of a class of systems that are relatively common in physics. Complex systems resulting from very simple laws. It is one of the beauties of physics that these systems exist.
2. Newton’s apple in economics
This graph emphasizes the “bell shaped” curve that production follows. Today, this curve is often know as “Hubbert’s curve” and the maximum in production is the “Hubbert peak”. You have surely heard to it. When referred to world oil production, people say “Peak Oil” and we heard that term mentioned many times at this conference.
3. The Hubbert law
As a last example, here are the data for something that is not by any means a mineral resource. It is the production of whale oil (and whale bone, used for stiffening ladies’ corsets). Even though whales do reproduce, they were hunted so fast that the cycle was the same as that of non renewable resources.
I think you see that there is a pattern; a logic; and this “bell shaped” curve does not appear just for oil, or energy resources. It is a very general pattern of production of non renewable resources (or slowly renewable ones, such as whales).
Before you interrupt me, I hasten to say that there are counter-examples, of course. Go see oil production in Saudi Arabia, for instance, and you will see no bell shaped curve. There are other examples. But the Saudis extract on very different assumptions than those of the commercial oil companies; short term profits are not their only objective. As I mentioned before, even for Newton’s idea, there were counter-examples; a feather for instance. Here, the concept is that, when governments or dictators, or the Gosplan (the Soviet planning agency), do not intervene in ordering people what to do, the actions of investors and operators will be based on reasonably objective evaluations of what is convenient to do in economic terms. That evaluation, in turn, must be based on physical factors – so a free market may be expected to be strongly affected by physical reality.
4. Entropy and economy
You can’t win
You can’t get even
You can’t quit the game
That is, of course, very simplified! There are even simpler versions. For instance, for economists it would be just a blank slide (sorry, I said no economist-bashing!). Before going on, let me tell you that this is a new idea that is moving forward nowadays– the idea of applying thermodynamics to the economy. More exactly, to apply “non equilibrium thermodynamics” (NET) to the economic system. It is a work in progress. So, what I’ll be telling you is still tentative, but I do believe that we are on the right track.
Now let me show you this image of a waterfall:
And now let me ask you a question: what makes water fall? You’ll say it is gravity; and that is correct. But there is a deeper factor here – this movement is eventually generated by the laws of thermodynamics. Nothing escapes thermodynamic laws. It is a question that I ask to my students, sometimes: how do you explain that water flows down in thermodynamic terms. It is difficult for them to find the answer right away, and yet they have studied thermodynamics. So, let me tell you; water flows down because of the second law – the entropy one.
You may remember from your studies that entropy is related to disorder. In some senses, it is true, but it is a definition that creates a lot of confusion. Think of entropy as heat dissipation. Then, everything that happens in the world is the result of some heat being dissipated – entropy tends to grow. When water falls from a high reservoir, some heat is created. The water at the bottom is slightly hotter than the water at the top – energy must be conserved, so it appears in the form of heat. Slowly, this heat is dissipated to the surroundings and that is what drives the system: entropy increase. The law of entropy is the law of change. Things move because entropy can increase – otherwise everything would stay frozen as it is. An equivalent way of saying that is that things happen because potentials tend to equalize. In the case of a waterfall, we have a gravitational potential difference (or “gradient”). With crude oil we have a chemical potential difference. There are other kinds of potentials, but let’s not go into that now.
Now, maybe it is not correct to say that something happens “because entropy must increase.” Probably, it is more correct to say that the universe behaves in a certain way and that it is convenient for us to describe this behavior with concepts such as “gravity”, “entropy” or “potentials.” These concepts are more useful than those involving angels pushing – or similar ones; such as the invisible hand…. sorry; no economist-bashing, I said. But, in practice, for these concepts to be useful I can’t just tell you, “the economy moves because entropy must increase”. It is true, but we need to go much more in detail. In order to do that, we need some kind of formalism where we can change the parameters of the system and see whether we can reproduce historical data, for instance Hubbert’s curve. That is what I’ll be doing; showing you how Hubbert’s idea can be derived from an interpretation that – ultimately – has to do with thermodynamics. But first let me introduce to you the method known as “system dynamics” which can be used to describe this kind of systems.
Let me show how system dynamics (SD) works by showing a description of a waterfall. Here, actually, it is about a bathtub, but the physics is the same.
5. A simple model of the economic system
Here, we have a very simple model that has three stocks: resources, the economy, and waste.
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:
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.
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:
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
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:
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.
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.
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 experiment 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.
From Marcus’ “Meditations” and from what I read about stoicism, I think I can summarize the basic idea as:
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.
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.