Of Collapses Large and Small

Bardi, Ugo

doi:10.1007/978-3-319-57207-9_3

Ugo Bardi⁹

Part of the book series: The Frontiers Collection ((FRONTCOLL))

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Abstract

This section of the book examines some fields where collapses often occur, listed in a very approximate order of complexity and lethality, with the idea of building up the understanding of what causes collapses by means of a series of practical examples. We start with the simplest case: that of the breakdown of everyday things, to arrive at what we may consider as the ultimate collapse: the death of Gaia, the Earth’s ecosystem. Each case examined offers the occasion for a discussion of the theory behind the collapse of complex systems. There doesn’t seem to exist a single theoretical framework that explains Seneca’s concept that “ruin is rapid,” but we may see a unifying factor in the “Maximum Entropy Production” principle. Whenever a system can find a way to go to its ruin, it will do so rapidly, as Seneca had already understood two thousand years ago.

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This section of the book examines some fields where collapses often occur, listed in a very approximate order of complexity and lethality, with the idea of building up the understanding of what causes collapses by means of a series of practical examples. We start with the simplest case: that of the breakdown of everyday things, to arrive at what we may consider as the ultimate collapse: the death of Gaia, the Earth’s ecosystem. Each case examined offers the occasion for a discussion of the theory behind the collapse of complex systems. There doesn’t seem to exist a single theoretical framework that explains Seneca’s concept that “ruin is rapid,” but we may see a unifying factor in the “Maximum Entropy Production” principle. Whenever a system can find a way to go to its ruin, it will do so rapidly, as Seneca had already understood two thousand years ago.

3.1 The Breakdown of Everyday Things

Ring the bells that still can ring Forget your perfect offering There is a crack in everything That’s how the light gets in.

Leonard Cohen, “Anthem”, 1992

3.1.1 Why Ships Don’t Have Square Windows

The 1997 “Titanic” movie includes the dramatic scene of the sinking of the ship , shown as it breaks in two before disappearing underwater. We can’t be sure that the Titanic actually broke down before sinking, we only know that, today, the ship is lying in two distinct pieces at the bottom of the ocean. But we know that ships can break down in that way when they are under stress, something that can tell us a lot of how fractures occur and of what kind of complex phenomenon they are.

In the 1978 book “Structures,” [35] James Gordon tells the story of a freighter sailing over the ocean and of how the cook of the ship noticed a crack that had appeared right in the floor of his kitchen. The cook went to see the Captain, who came, looked at the crack, shook his head, and then asked when would breakfast be ready. The cook remained worried. He had noticed that the crack was becoming a little longer every day, especially when the ship was sailing on rough seas. Being a methodical person, he took a can of red paint and a brush and he used it to mark on the floor exactly where the tip of the crack was on a given date. Gordon reports that

When the ship eventually broke down, the half which was salvaged and towed into port happened to be the side on which the cook had painted the dates and this <..> constitutes the best and most reliable record we have of the progress of a large crack of sub-critical length.

This story tells us, among other things, how treacherous fractures can be, a most egregious example of the “Seneca Effect” : sudden, destructive, and taking us by surprise. The captain of the freighter had been alerted that there was a crack in the ship but he didn’t know what it was and how dangerous it could have been. Evidently, he saw the crack as a small thing in a large ship and he couldn’t find a reason to be worried about it. We may imagine that, when the ship broke in two, the captain made the same face that a child makes when her balloon pops. Indeed, ruin can be rapid!

The collapse of engineered structures is relatively common. When it happens to large structures that move fast, that float, or that fly, often a lot of people get hurt and some may die. Fractures may cause especially disastrous results in the case of airplanes and probably the best-known case of accidents caused by structural failures is that of the Comet planes in the 1950s. It took some time for engineers to understand the reasons for these accidents, but eventually it became obvious that it was a design flaw.

Look at the image of the first prototype of the Comet plane , in Fig. 3.1. At first sight, it looks very modern with its sleek fuselage and its jet engines. Yet, if you look carefully, you will notice something unusual: large square windows with sharp-edged corners. That’s surprising because ships and planes are well-known for having round windows or, at least, windows with rounded edges, even though most people wouldn’t be able to tell why. But it is a well-established feature of engineering that openings in any structure tend to weaken it and that the weakening effect is smaller if the openings are round or with smooth edges. Yet, the designers of the Comet forgot that traditional wisdom. It may have been because they had the ambitious plan of creating an innovative airplane which was to be not only the fastest passenger plane ever built up to that time, but also a “panoramic plane” that would have afforded passengers a wide view of the outside. When engineers become ambitious, they may neglect the old wisdom that they may consider outdated. That was an especially bad idea in the case of the Comet planes which suffered from several structural problems in large part created by those square windows. The sharp edges generated weak points that were the main reason why several Comet planes exploded in mid-air.

The story of the Comet failures tells us how difficult it is to understand fracture even for engineers in a relatively modern age. Fracture is a typical non-linear phenomenon, while mechanical engineers are normally taught forms of “linear thinking” which assumes that there is always a proportionality between cause and effect. In other words, engineers expect materials to deform proportionally to the applied stress, which normally they do, except when they don’t. This is when fracture occurs and when people die as the result. Even today, we have plenty of stories of things that break down at the worst possible moment because of structural failures, often caused by bad design or poor maintenance. Small planes seem to be especially dangerous [36] with a history of mechanical failures of some components, such as leaky fuel tanks, helicopter blades snapping off, broken critical parts, and more. But mechanical failures remain a deadly problem in many fields.

The first scientist engaged in studying fracture was none other than Galileo Galilei, in the seventieth century. His work inaugurated a long series of studies on how things break. A first result of this effort has been the classification of the breaking down of things into two main categories: compressive failures and tensile failures. The compressive kind is normally the case of buildings: towers, homes, furniture, and the like, subjected to the stress caused by gravity. The tensile kind is the case of engineered structures such as planes, cars, ships, etc. The two cases are deeply different for many reasons. In this section, we will examine the trickiest and probably the most dangerous form of fracture: tensile fracture.

From the viewpoint of engineers, the only things that exist are those that can be measured. So, their approach to studying fracture often consists in measuring the effect of applying force (and hence energy) on things. A typical instrument used for this purpose is the “tensile stress machine” that you can find in various versions in the departments of mechanical engineering of most universities. It is normally a massive machine, endowed with two grips that take hold of the two extremes of an hourglass shaped specimen. The specimen is pulled apart with increasing force until it breaks apart, often making a typical banging noise. The deformation is slow, but the fracture is rapid; it is the “Seneca ruin” of the specimen.

During the process of testing , the machine records the extent of the deformation of the specimen as a function of the applied force. For small deformations, it is normal that these two parameters are directly proportional to each other. This is called “Hooke’s law” and the range for which the law holds is said to be the “elastic range.” In this domain, the deformation is completely reversible: if the applied force is removed, the object will return to its original shape, just like a rubber band does. This is how springs work and it is the principle on which dynamometers are based. Outside this range, materials may deform irreversibly: that is, they don’t return to the original shape when the load is removed. This is called the plastic range and it is typical of materials such as plastics or mild steel. As the stress is increased even more, eventually almost all kinds of materials will break down inside the testing machine. The force at which the break takes place, divided by the cross section of the specimen, is called the “ultimate tensile strength.” The force multiplied by the elongation is an energy, often defined as the “work of fracture” or “resilience” of the material. Another way of measuring the resilience of materials is by means of the “Charpy” test, where the specimen is hit by a heavy anvil. Nowadays, the term resilience is used a lot in social sciences but it has originated with these engineering procedures.

If there is the need to measure the energy of fracture, it means that we expect different results for different materials, as we also know from our everyday experience. So, here are some values of the Charpy resistance test for some common materials, taken from Gordon’s book “Structures” [35]. The energy is reported as joules per square meter, the area being that of the section of the standardized Charpy specimen.

Material	Energy of fracture (“resilience”), J/m²
Glass	3–10
Stone	3–40
Polyester	100
Nylon	1000
Bone	1000
Wood	10,000
Mild steel	100,000–1,000,000
Hard steel	10,000

Note the huge range of variation of the specific energy of fracture . What causes these large differences? The first idea that comes to mind is that they are caused by the different strengths of the chemical bonds in the atoms that compose the material. This is not wrong: eventually, all fractures are caused by atomic bonds being broken. But, in general, this idea just doesn’t work as a guide to understanding resilience. Just as an example, the atomic bonds in glass (silicon bonded to oxygen) are stronger than those in steel (iron bonded to iron). Yet, glass breaks much more easily than steel; as we all know. On this point, I may cite again James Gordon in his book “The New Science of Strong Materials” [37].

When the last war broke out, a very able young academic chemist came to work with me. He set to work straight away to make a stronger plastic. He explained to me that it must have stronger bonds and more of them than any previous material. Since he really was a very competent chemist, I expected it did. At any rate it took a long time to synthesize. When it was ready, we removed this war-winning product from the mould with excitement. It was about as strong as stale hard cheese.

So, you see how thinking of fracture in simple linear terms may lead you astray, a very general characteristic of complex systems. Instead, a big step forward in understanding fracture came when the British engineer Charles E. Inglis (1875–1952) started examining the volume of a material where there are no chemical bonds whatsoever: the empty space that forms a “crack” (Fig. 3.2).

In 1913, Inglis proposed a formula for the “stress concentration” at the edges of cracks. It turned out that the strain created by the crack is proportional to the length of the crack and inversely proportional to the sharpness of the crack (measured in terms of the radius of curvature of the tip, approximated as a sphere). Playing with Inglis’ formula, it is easy to see that a sharp crack can easily multiply the stress on a piece of material of an order of magnitude or more; increases by a factor of one thousand or more are perfectly possible. So, cracks are the main factor that determines what a material or a structure will do under stress.

A further factor that makes cracks important (and very dangerous) is that they don’t stay still. The windows of the Comets didn’t change in size with time but, in the story reported by James Gordon, the crack that had opened in the floor of the kitchen of the ship was expanding day by day. This is a phenomenon called “creep.” It leads to the weakening of the structure caused by repeatedly applied loads, especially when these loads are cyclical, a phenomenon defined as “fatigue.” Indeed, one of the major factors that led to the Comet disasters was the effect of the vibrations caused by the engines that had been embedded in the wings, close to the fuselage. Cracks had developed at the edges of some of the windows and they had propagated. The undetected progression of small cracks is one of the main reasons why fracture is such a treacherous phenomenon.

After the work of Inglis , engineers understood how important cracks are for the mechanical resistance of structures and a lot of work performed nowadays to make structures resilient can be defined as a “war on cracks.” In part, it involves designing structures without sharp corners and large openings. But design can do little to avoid the effect of the presence of microscopic cracks in the material. Dealing with these cracks and reducing their negative effects is a task for materials science rather than for mechanical engineering. Making completely “crack-free” materials is impossible, but engineers can create materials whose internal structure stops the propagation of cracks. It can be done in various ways, for instance using materials that are soft enough that they deform a little around the crack, thus blunting the edge and reducing the stress concentration. This is a straightforward application of the principle that Bertolt Brecht attributes to Lao Tsu, “hardness must lose the day.” Another effective way to stop cracks from propagating is to use composite materials. In this case, the interfaces between two different kinds of materials tend to acts as barriers against the propagation of cracks. A good example of how well the engineers learned their lesson is that of the Aloha flight 243 in 1988, when a Boeing 737 lost a major fraction of the hull in mid-air but, unlike the case of the Comets, it remained in one piece and the pilots could to land it safely with only one fatality. A triumph of aircraft engineering.

Today, in large part as the result of Inglis’ work , planes, ships and all sort of human-made structures subjected to tensile stress are much safer than they used to be. But there is much more about fracture that makes it an excellent case for understanding the general behavior of complex systems and of why fracture, when it happens, follows Seneca’s concept that “ruin is rapid.” To understand this point, we need to go into what makes physical and chemical transformations happen: it is the realm of the principles of thermodynamics.

3.1.1.1 Energy and Entropy

The dwarf Regin is said to have welded together the two halves of Sigurd’s sword, Gram, that had been broken by Odin, the God. But Regin could restore the sword only by using magic; in the real world, fracture is normally irreversible. As in the story of Humpty-Dumpty, broken things are always difficult to be put back together and a broken sword that was welded back together will always be a poor weapon. The principle doesn’t only apply to breaking things. It is a general observation that the universe tends to move in a certain direction and that reversing its motion is not easy; sometimes it is just impossible. Modern science can quantify this tendency. Of the two main principles of thermodynamics, the first tells us that energy must be conserved but not that systems should move in one or in another direction. But the second principle tells us that, in an isolated system, entropy must always increase in all transformations. That provides a tendency for things to move in a certain direction.

A problem, here, is that the concept of entropy has been explained in the wrong way to generations of students who then explained it in the same wrong way to the subsequent generations. So, many of us were told that entropy is the same thing as “disorder” as it is commonly defined and that seems to explain what causes the clutter that’s typical of most people’s desks. But that’s not what entropy is and this definition causes a lot of problems. For instance, you might argue that a broken piece of metal is more disordered than one that’s still whole, but that would tell you little or nothing about the mechanism of fracture. The story is further complicated by the fact that we are often told that systems tend to move spontaneously from high-energy states to low-energy states. But thermodynamics tells us that entropy, not energy, must change in spontaneous processes. So, how’s that? Again, a remarkable confusion.

Admittedly, it is a complicated story to explain and, here, let me just say that the correct definition of the second principle is that all systems tend to reach their most probable state; which is not the same thing as “disorder”. Then, the second law tells you that entropy always tends to increase in those processes that occur in isolated systems, that is, systems that do not exchange energy with the outside. The only truly isolated system is the whole universe and so, in practice, chemical and physical processes are normally described in terms of entities called “energy potentials” which depend on both the internal entropy change and the internal energy change. That is, when dealing with these potentials, you don’t have to worry about what happens to the whole universe; which is indeed a bit cumbersome. It can be demonstrated on the basis of the second law of thermodynamics that high-energy potentials tend to be turned into low-energy potentials, dissipating their energy in the form of heat. This is equivalent to saying that entropy must always increase in the universe.

Energy potentials are entities which have a certain “potential” to do something. A simple example is a falling body: its gravitational potential diminishes with lower heights and the fall is spontaneous because it agrees with the second principle of thermodynamics and heat is dissipated when the body bumps into something, stopping its fall. When a solid breaks down, there is some potential being reduced and it is not difficult to understand what it is: it is the energy potential stored in the stressed chemical bonds. When these bonds return to their natural length, they dissipate heat in the form of atomic vibrations. The laws of thermodynamics are satisfied: when the conditions are right, fracture is a spontaneous process. Note that energy potentials are often referred to simply as “energy” and that causes most of the confusion deriving from the statement that “energy must diminish in a transformation”. Energy is always conserved; an energy potential is not.

At this point, we enter the fascinating subject of “non-equilibrium thermodynamics”, a subfield of general thermodynamics that tries to describe how systems dissipate the available potentials or, equivalently, create entropy at the maximum possible rate. This is called the principle of maximum entropy production or MEP [2, 38–40]. It is an area still being explored, and it includes ideas and concepts that haven’t reached the accepted status of “laws,” but we have here the basic thermodynamic reasons for collapses; a more rigorous way of expressing Seneca’s concept that “ruin is rapid.”

The business of lowering—or dissipating—energy potentials in non-equilibrium systems is often described in terms of “dissipative structures,” a concept proposed by Ilya Prigogine in 1978 [41]. It is a very general concept that includes human beings, hurricanes, and the vortexes in a boiling pot of water. All these systems keep dissipating potential energy as long as energy flows into them. If the flow remains constant, the system tends to reach a condition called “homeostasis,” that is, it maintains nearly constant parameters for long periods of time. Try a little experiment with your bathtub: the little vortex that you normally see forming when you open the sink is a dissipative structure. It makes water flow down faster. Now, if you disturb the vortex with a hand, you may make it disappear. But, if you then leave the water in peace, the vortex rapidly reforms; this is homeostasis. The Earth’s ecosystem is a homeostatic system that has been dissipating the sun’s energy potential for almost four billion years. A human being can remain in homeostasis (alive) as long as she has a chemical potential to dissipate in the form of food—otherwise, she is in a condition of thermodynamic equilibrium (dead).

From these considerations, we can say that fracture obeys the laws of equilibrium thermodynamics in the sense that it maximizes entropy. It also obeys the laws of non-equilibrium thermodynamics since it provides a fast pathway for dissipating entropy. This behavior of fractures is very general and it is akin to many other phenomena that we call “collapses” that will be faster, larger, more destructive, the larger the potentials being involved. Explosive storage sites, nuclear plants, high voltage transformers, high-speed vehicles; they are all examples of systems that store a lot of potential energy in various forms. So, thermodynamics tells us what we should be worried about, but not the details of what exactly happens during the collapse. Here, the fracture of solid bodies can tell us a lot about the general features of these mechanisms, as we’ll see in the next section.

3.1.2 Why Balloons Pop

When I teach mechanical fracture to my students, I start by showing them an inflated party balloon. Then I make it pop with a pin. Then I ask them, ‘now explain to me what happened in terms of the physics and the chemistry you know’. They can’t normally do it. It is not because they are not smart or not prepared enough, but because the kind of science they have been taught is “linear” science, the kind of view that assumes that things change gradually as the result of applied forces. This kind of linear approach won’t explain fracture, a typical non-linear (also termed “critical”) phenomenon that takes place all of a sudden and with a drastic change of the parameters of the system. It is a behavior that results from the discontinuous nature of matter; made of atoms linked together by chemical bonds. Solids are special cases of “networks” and we’ll see in the next chapter that collapses are a typical characteristic of networks of all kinds, not just of solids.

Fracture means that chemical bonds are being broken. But just breaking bonds does not cause a fracture; for that, we need to see a lot of bonds breaking down, all together, and all in the same region: we need to see a true avalanche of bonds breaking. This is a behavior that we call a “collective” phenomenon, something that doesn’t just involve a small section of the object, but that carries on to involve most of it. How that happens is a fascinating story that was told for the first time by Alan Arnold Griffith (1893–1963).

Let’s consider an object that has a well-defined, crystalline atomic structure, meaning that the atoms are arranged in an ordered lattice. Now, if you pull the object apart, a little, you pull the atoms a little farther away from each other and, as a consequence, you put some extra energy in the chemical bonds. The more you pull the object apart, the more energy gets stored in the deformed bonds, at least as long as the atoms don’t move too far from their original lattice positions. In this way, you have created a “potential;” the displaced atoms would tend to return to their original positions, releasing the stored energy. But that, by itself, won’t cause a fracture . If you think of a simple solid, say, a piece of pure copper, all the atoms in it are the same and all the bonds are the same. Then, if all the bonds are stretched in the same way, in principle, you could stretch the metal lattice all the way until it vaporizes when all the bonds break together at the same moment. But, of course, that doesn’t happen. For most structural materials (copper, steel, aluminum, ceramics, etc.) the maximum possible stretching is about 1%, often much less than that. Try to stretch a solid more than that and then—bang!—it breaks apart (that doesn’t hold for rubber bands, but they are not crystalline solids). Why is that? It is because, at the point of fracture, the non-linear phenomena typical of complex systems kick in.

In order to have a fracture , you need to separate at least two sections of whatever is being broken, and that means creating two surfaces that didn’t exist before. Creating these surfaces can be seen as a chemical reaction since it implies breaking chemical bonds. And here we have the problem: breaking chemical bonds requires energy. In other words, it requires increasing the internal potential of the system and, as we saw earlier on, that’s not a spontaneous phenomenon. The solid doesn’t really “want” to create a fracture surface because that means going against the natural tendency of physical systems to dissipate internal potentials. So, how is it that the fracture occurs? It is because the energy potential dissipation game is not played just with the fracture surface, but with the whole solid. When the solid breaks apart, it will release all the elastic energy stored in the deformed chemical bonds inside it. If the algebraic sum of the two phenomena generates an overall potential dissipation, the fracture will be spontaneous.

This is the essence of the Griffith mechanism : part of the elastic energy stored in the volume of the solid is released even before fracture because the two halves of the solid can be pulled away a little from each other. The longer the crack, the more elastic energy is released, so this goes downhill (thermodynamically speaking). But, up to a certain length of the crack, the dissipated energy is not sufficiently large to compensate the energy needed to create a longer crack. But, when the crack reaches a certain “critical” length, expanding it releases more energy from the volume than it takes to expand the crack. That’s the tipping point of fracture and it explains why it is sudden and explosive: the process feeds on itself, becoming faster as it proceeds. The longer the crack, the more energy is released, it is what we call “enhancing feedback,” we’ll see this concept in more detail later on. The end result is the Seneca effect applied to materials science!

Another insight that we can gain from the Griffith fracture theory is that there is no “equation of fracture.” The theory tells us how long a crack must be in order to cause a certain structure to break (Fig. 3.3). But it tells us nothing about how exactly the fracture will develop, how fast the crack will propagate, and in which direction. In general, we lack simple mathematical tools able to describe the rapid and sudden changes that we call critical phenomena. That doesn’t mean we can’t study fracture at the atomic level. We can do so by using a method called “molecular dynamics,” which takes into account the motion of each atom. In Fig. 3.4, you can see one such simulation of a fracture (courtesy of Dr. Zei). You can see how the breakdown starts with single atoms losing contact with each other at the two sides of the crack. It is like atoms were telling to each other “I can’t hold it anymore, now it is your turn” and this is the way the crack propagates, eventually causing the fracture.

So, we can now answer the question that I pose to my students: why do balloons pop when punctured? Griffith’s theory explains it perfectly well: the hole made in the balloon when puncturing is the crack. The elastic energy applied to the structure comes from having inflated the balloon which, of course, requires energy! If this hole is larger than the critical crack length, and only in that case, then the balloon will explode, suddenly releasing the elastic energy stored when it was inflated. The larger the pressure, the smaller the hole needs to be. At the limit, the balloon will pop by itself, even without puncturing it, because there are some micro-cracks already present in the rubber. The fate of a punctured balloon is a good description of the destiny that befell the Comet planes, whose fuselage can be seen as an inflated balloon because the passenger cabin was pressurized. The windows were the cracks, big enough to cause it to burst. Note also that if the balloon is only weakly inflated, then puncturing it will not make it pop, but just deflate slowly. And that’s why the Comet would burst to pieces only at high altitudes: the strain increased with the increasing pressure difference between the pressurized cabin and the exterior.

Griffith’s theory is by now almost a century old, but it has withstood the test of time and remains the center of our modern understanding of the fracture phenomenon. Of course, there have been many more studies that have expanded the theory using more sophisticated theoretical tools [42]. In time, the theory was expanded to describe phase transitions in solid materials and, in general, in all the systems that can be defined as “networks” [43]. The theory shows to us how an everyday phenomenon such as the breakdown of objects turns out to be subtle and complicated. It illustrates some of the elements that are common to all complex systems: non-linear phenomena, maximum entropy production, networking, and that typical characteristic that makes complex systems always ready to surprise us: their unpredictable and sudden switch from one state to another in what I termed in this book the “Seneca Effect.” Within some limits, these characteristics can be observed also in apparently unrelated systems: social, economic, and biological systems, being part of the general thermodynamic laws that govern the universe [44]. Of course, human beings in a socioeconomic system are not the same thing as atoms in a crystalline solid, but we will see in the following that these systems all share some rules and tendencies.

3.2 Avalanches

“The wise speak only of what they know”

J.R.R. Tolkien, “The Two Towers”

3.2.1 The Fall of the Great Towers

Pharaoh Sneferu (also known as Snefru or Snofru) reigned during the Old Kingdom of Egypt, around the mid-third millennium BCE. He attempted to build at least three large pyramids, none of which turned out to be so impressive and successful as the three, better known pyramids of Giza, that include the largest of all, the “great pyramid” built by Sneferu’s son, Cheops. The story of these three pyramids is told in detail by Kurt Mendelssohn in his 1974 book “The Riddle of the Pyramids” where he put forward a plausible theory that explains what went wrong [45]. Mendelsshon’s theory remains somewhat controversial, today, but it does provide interesting insights on the problems involved with building large buildings, at the time of the Egyptians as in ours.

The clue to the whole story is the Meidum Pyramid, shown in Fig. 3.5. If you don’t know that this structure was supposed to be a pyramid, you may not recognize it as such. But the rubble that surrounds it tells us what happened: this building collapsed, probably midway during construction. We remember the Egyptians as great pyramid builders and they were but, evidently, they too made mistakes and sometimes disaster ensued. But they were perseverant: the great age of pyramid building in Egypt started about one century before Sneferu , with the first large pyramid built under the direction of the architect Imhotep at the time of pharaoh Djoser ca. 2670 BC. It still exists today and it is known as the “step pyramid.” The name describes it nicely: it is made of six giant stone steps, one over the other. There may have been other stepped pyramids that Djoser or others before him attempted to build, but they were never completed or crumbled down and disappeared from history. Then, with the new dynasty founded by Sneferu , there came a change of pace. The architects of the new pharaoh promised him something bigger and way more impressive than anything built before: smooth pyramids that would look like single polished stones.

When these ideas were being put into practice, it seems that there existed already a pyramid at Meidum in the form of a relatively small stepped pyramid. So, the architects decided to expand this old structure into a larger, smooth pyramid. It was a nice idea but, as it often happens, it carried unexpected problems. One was that the outer layers of the new pyramid were not well anchored to the older structure. These new layers were also standing on sand, rather than on rock, as the old structure was. Finally, the stones used for the new construction were not well squared and didn’t fit very well with each other. As the builders were to learn later, that’s not the way to build a pyramid. At some point, perhaps during construction or shortly after completion, the outer walls started sliding down and collapsed, taking with them part of the earlier stepped structure. The result was the mass of rubble that we can still see today surrounding the remnants of the central nucleus that took the shape of a tower. It must have been a spectacular collapse; surely fast and unexpected. It may even have buried the people who were involved in building the pyramid or, hopefully, they had sufficient time to run to safety. In any case, it is a good example of a “Seneca Collapse,” in the sense of having been rapid.

Neither of the other two pyramids that Pharaoh Sneferu built escaped troubles. One of them is known today as the “Bent Pyramid,” and, as the name says, it is a curious and ungainly structure. The builders had started to build it at the same angle that was later to be used for the large pyramids at Giza. But, midway in the process, they changed the angle to a much less steep one. The result is disconcerting rather than impressive. The other is known as the “Red Pyramid.” It is surely a large pile of stones, but the low angle at which it was built makes it not as remotely impressive as the later pyramids at Giza (Fig. 3.6).

Mendelsshon hypothesi [45] starts, first of all, with the fact that, a pyramid needs less and less workers as it grows because the upper layers are smaller than the lower ones. So, in order not to leave workers idle, it is likely that there would have been more than a single pyramid construction site open at any given time. Then, it is also likely that the construction of each pyramid benefited from the experience gained with the others and each construction site would try to avoid the mistakes made in the others. Perhaps the sites were also competing against each other for building the largest and tallest pyramid. But competition may generate haste and that may lead to mistakes, even big ones. Let’s assume that the Meidum pyramid was the most advanced in its construction when the disaster struck. At that moment, the other construction sites may have been midway to completion or just starting. So, the bent pyramid may have been the result of the news of the Meidum collapse arriving when the pyramid was already half-built. At that moment, the architects devised an emergency plan to avoid another collapse; they built the rest of the pyramid at a lower, and safer, angle (Fig. 3.6). An even more drastic decision was taken in the case of the red pyramid, built from the beginning at a low angle (Fig. 3.7).

This is, it must be said, just a theory. We can’t discount the possibility that the Egyptians built the bent pyramid because they liked it to be bent and the Red pyramid because they thought it was a good idea to build it the way they did. Still, Mendelsshon’s ideas sound very plausible. We don’t know if Pharaoh Sneferu was happy about these pyramids, none of which, probably, turned out to be what he really wanted. But he had to content himself with what he could get. It was left to Sneferu’s son, Khufu (also known as Cheops), to build the first “true” pyramid that we can still admire today in Giza, together with two more that were built in later times.

An interesting point about the story of the Meidum pyramid is that we know about it only from its remnants (Fig. 3.8). Nowhere do we find written records about the collapse; yet it was an event that must have reverberated all over Egypt and, perhaps, over the whole of North Africa and the Middle East . Perhaps the legend of the Tower of Babel originates from that ancient collapse ? We cannot say, but we can perhaps propose that the very silence surrounding these events shows the dismay of the builders. This is a very general point: it has to do with the difficulty we have in understanding the behavior of complex systems. We have another example of this problem with the fall of the World Trade Center buildings in New York, during the attacks of September 11, 2001. The Twin Towers, two truly magnificent buildings, rapidly collapsed in a heap just like a house of cards. For many people it must have been seemed unlikely, perhaps even impossible, that the collapse could take place just because two puny airplanes had hit the towers. A consequence of this perception was the appearance of the “controlled demolition” theory; the idea that the fall of the towers was the result of the presence of a series of explosive charges hidden inside the buildings, detonated one after the other in such a way to bring down the towers one floor at a time. The legend remains among the most popular ones that we can find nowadays on the Web [46] and it is unbelievable how much psychic energy is dissipated to discuss how the towers should have fallen according to various hypotheses and theories. From a systemic viewpoint, however, the rapid fall of the towers looks in agreement with the studies performed by the National Institute of Standards and Technology (NIST) [47]. The buildings fell as the result of a typical, feedback enhanced, chain reaction generated by the weakening of the steel beams invested by the fire generated by the hitting airplanes. The planes were not the “cause” of the fall, they were just the trigger that started the avalanche.

Maybe a “controlled demolition” theory could have been proposed also for the fall of the Meidum pyramid, at the time of Pharaoh Sneferu. For sure, the collapse must have been fast, probably very fast, and that must have been surprising for those who had a chance of witnessing it (and of surviving it). Of course, at that time, explosives didn’t exist, but could it be that the Pharaoh’s enemies had rigged the structure in such a way to cause its rapid ruin? We cannot rule out that Pharaoh Sneferu thought exactly that and then he proceeded to behead a good number of political opponents under the accusation of sabotage. But what happened with the Meidum pyramid was much simpler. Maybe a small earthquake, maybe a gust of wind, maybe a storm, or maybe just a worker sneezing. It doesn’t matter; one stone started rolling down and then the whole structure followed. It is just an example of how a small forcing can cause a chain reaction and how, later on, people only see the final effect and can’t convince themselves that the whole thing collapsed so much because of such a small cause. Again, the Seneca collapse is part of the normal way the universe works. But there is a difference between the case of the Meidum Pyramid and that of the Twin Towers of New York, In the latter case, we can be 100% sure that it was a conspiracy. Someone must have planned the attacks against the WTC in secrecy before carrying them out, and this is the very definition of “conspiracy.” But the laws of physics remain valid even for conspiracies.

3.2.1.1 The Physics of the Hourglass

It takes very little effort to create avalanches; the snow piled up on the side of a mountain is unstable, it may start moving as the result of an event as small as a loud voice or the clapping of someone’s hands. And the same is true for the land or stones accumulated on a steep slope: for instance, in 1966, the collapse of a pile of coal mining debris at Aberfan, in Wales, killed 116 children and 28 adults in a school that had been erected nearby.

What makes all these events similar is that they are collective phenomena . They are events that involve a network of elements that interact with each other. One stone, alone, does not cause an avalanche, but a pile of stones, as in a pyramid, does. It is the same phenomenon that brings down a house of cards and, in nuclear physics, creates a nuclear detonation by means of the mechanism called “chain reaction .” It is a very general phenomenon; the more it goes on, the more it grows. It doesn’t just include collapsing buildings, but often takes place with everything that can break down, crash, crumble, go deliquescent, explode, and more ways that things may collapse in the real world. It is the “Seneca Collapse” everywhere.

Everyone knows that avalanches are a normal occurrence in the world, but can they be predicted? One would need some kind of “avalanche theory,” possibly producing an “avalanche equation” that would tell us exactly when and where the avalanche should take place, how large it should be, and how fast it should move. But there is no such equation. Geologists know a lot about landslides of all kinds; but mostly they rely on tabulated data, general knowledge, and careful measurements of the movement of masses of earth and rock. But no measurement can tell when exactly the rapid phase of an avalanche will take place. A good example of the problem, here, is the landslide that caused the 1963 Vaiont disaster, in Italy [48], when a massive landslide caused the basin of a hydroelectric dam to overflow and the resulting wave killed nearly two thousand people. Geologists knew that the area was in danger of landslides, but they couldn’t quantify the risk in terms of size and timing. The same is true about earthquakes, a phenomenon we can see as a kind of avalanche; there is no such a thing as an “earthquake equation” that can predict where and when an earthquake will take place.

We have here a general observation: we are dealing with complex, non-linear, collective phenomena and only in a few cases, such as in the “Ising model” of magnetic lattices, is it possible to find an explicit equation that describes the evolution of the system. But we can describe the behavior of complex systems by means of computer simulations. A modern study of these phenomena is the “sandpile model” created by Bak, Tang, and Wiesenfeld [49] and popularized by Bak in his 1996 book “How Nature Works” [50]. In this model, the behavior of an idealized sandpile, also described as an hourglass, is simulated in terms of a concept called “self-organized criticality” (SOC) and applied to a variety of systems where collective behavior could be observed, from earthquakes to the human brain.

Bak and his coworkers were not thinking of Egyptian pyramids or of modern buildings collapsing when developing their concept of self-organized criticality. Rather, they had started from an abstract model of coupled oscillators. But with time, they discovered that their mathematical model could be applied to a rich variety of physical phenomena and that most of them, although not all, involved those rapid events that we call “catastrophes,” including the crumbling down of buildings. Surely, the Meidum pyramid before it collapsed could be seen as a giant sandpile, although it was never conceived as an hourglass!

A typical sandpile/hourglass model can be visualized as a square grid, a chessboard, where each square is supposed to contain from 0 to 4 grains of sand. At each step of the calculation, the computer adds one extra grain of sand to a square chosen at random, providing a simplified description of what happens inside an hourglass. In the model, when a square happens to contain 4 grains, it collapses, spilling its grains of sand evenly among the four nearest neighbor squares. It may be that one or more of these nearby squares contained 3 grains of sand, so that, with the addition of one further grain, they collapse as well, spilling their grains to nearby squares. The process may go on, involving several squares, while those grains which exit the grid are considered lost. The number of squares involved in the process defines the size of the avalanche. Large and small avalanches keep occurring as the simulation moves on. As one would expect, large avalanches (involving a large number of squares) are rarer than small avalanches. What’s surprising, however, is that there exists a linear relation that links the number of avalanches to their size in terms of a “log-log” plot; that is when you plot the number of avalanches as a function of their size (this is called also a “Pareto law” from the ninetieth century Swiss economist Vilfredo Pareto) [51] (Fig. 3.9).

When you see a straight line on a log-log plot, it may be referred to as “Zipf’s law ,” “Pareto’s law,” or “power-law” (also “1/f noise” ). All these names refer to similar phenomena, also described as “scale-free” or “fractal” phenomena and, occasionally as “fat tail” distributions. It is appropriate to clarify here what the different names mean.

Zipf’s law is the simplest way to study these phenomena: it consists in ordering the magnitudes of the events in a numbered list and then plotting the logarithm of the size as a function of the rank in the list. George Kingsley Zipf (1902–1950) was a linguistics professor at Harvard who used this method to study the frequency of the use of words in English and in other languages. He was surprised, probably, to find that the rank of the use of a word is linearly proportional to the logarithm of the frequency of its use. It was later found that the log-rank plot works for a variety of phenomena.
A “power-law” is the term used when some entity is found to be proportional to a parameter elevated an exponent that’s not necessarily an integer. This law is typically written as f(x) = ax ^-k. This is the law that holds for the avalanche model by Bak et al. [50], where f(x) is the frequency of the avalanche and x is their size.
The term “Pareto’s distribution” refers to Vilfredo Pareto, 1848–1923. Pareto worked in terms of “cumulative distributions,” that is the probability of events larger than a certain threshold (“x₀”). One of the fields that he studied was the income distribution in the economy [51]. In this case, we can write that the fraction of people having an income larger than “x” as F(x) = 1—(k/x)α where x is the variable, k is the lower bound of the data (larger than zero) and α is called the “shape parameter.” For x smaller than k, then F(x) is zero. The Pareto distribution implies a power-law and, as a result, the two terms are often used interchangeably. Note that the Pareto distribution is often referred to as the “80/20 rule” that says, for instance, that 20% of the people hold 80% of the wealth of a country. Or maybe that 20% of the workers produce 80% of the output of a company. This is just an approximate way to note the unbalanced distribution of this kind of statistics.
The concept of “1/f noise” is a little more complicated. It has to do with phenomena that vary as a function of time. The record of one such phenomenon may be referred to as a “spectrum,” and it may be periodic and regular (say, a sine wave) or not. When the spectrum is irregular, you can still analyze it by means of a procedure called “Fourier analysis” that decomposes it into a number of discrete sinusoidal waves; this is usually called a “power spectrum.” It means that any irregular signal can be described in terms of the sum of a number of periodic signals with different frequencies and intensities. You can plot the intensities of the different frequencies as a function of frequencies and, in some cases, you’ll find that the power density is proportional to the reciprocal of the frequency, that is to 1/f. Sometimes, the “f” in the formula is elevated to an exponent different than one, but it is still referred as 1/f. A “1/f noise” is another case of power-law, just expressed in different terms.

Bak and his coworkers proposed that real avalanches would generally follow a power-law . As you may imagine, many laboratories in the world soon started experimenting with real sandpiles. Some initial results were negative but, later on, the power-law was observed in experiments with rice grains [52]. Over time, it was proposed that the concept of self- organized criticality describes a wealth of real world phenomena. Actually, the power-laws that define self-organized criticality were known much before the SOC model was proposed, even though they were not recognized for what they are. As we are dealing with sudden collapses, a good example is that of earthquakes. It has been known for a long time that not only large earthquakes are less probable than small earthquakes (and fortunately so!), but that there exists a well-defined relationship between size and frequency.

Here is a table showing these data, as reported by the USGS for a 47-year period [53].

MS	Earthquakes per year
8.5–8.9	0.3
8.0–8.4	1.1
7.5–7.9	3.1
7.0–7.4	15
6.5–6.9	56
6.0–6.4	210

Now, the “Ms” (magnitude ) was defined by Richter in the 1930s as the base 10 logarithm of the maximum amplitude registered on a seismograph, corrected for the distance from the epicenter and other factors. So, the Ms values are already the logarithm of an intensity and now let’s plot these data also taking the logarithm of the frequency, that is their number per year.

There is a regularity in the earthquake phenomenon, at least in the range of these data (Fig. 3.10). The linear relation between frequency and size indicates a power-law; something that was well known in geology under the name of the “Gutenberg-Richter” law, much before the development of the theory of self-organized complexity. Among other things, the Gutenberg-Richter law tells us that there is no such thing as a typical earthquake size. The probability of an earthquake of a certain size decreases regularly with increasing sizes. Note that if the size distribution had been a Gaussian curve, as it is for many other phenomena, the probability of large events would be much smaller than for a power law. For this reason, the term “fat tail” is often used to describe these distributions. It means that the probability of events at the tail of the distribution is larger than, typically, an exponential or Gaussian distribution.

The existence of a power law in describing the frequency of earthquakes tells us that there exists a certain degree of organization among the elements of the system that are correlated to each other; they must a network of connected elements. This agrees with what we know of the Earth’s crust, which is an ensemble of giant continental plates interacting with each other. Most earthquakes are the result of the release of the energy accumulating in the form of elastic energy stored at “faults”, regions where the plates slide against each other. The sliding process is not smooth and the energy is released in bursts; much like, in solids, fractures release in a single burst the energy accumulated in strained chemical bonds. These faults are large areas of connected elements and it is not surprising that the result is a mathematical relation that links their size with the frequency of their suddenly sliding against each other.

It seems that we know a lot about earthquakes and we do: we can reasonably predict the probability of an event of a certain size. We also know where the plates slide against each other and that tells us in which geographical region earthquakes are most probable. One well-known example is the St. Andreas fault where the North American plate slides against the Pacific plate, a line that goes through California. That makes that region especially earthquake-prone and the Californians know that: they are waiting for “the big one” to strike; a major event that could have apocalyptic consequences. But we cannot say when exactly it will arrive; this is a general problem with all seismic regions in the world. That may be seen as an insult to human ingenuity and some people seem to have understood it exactly in this way. For instance, in Italy in 2014, a tribunal sentenced a group of geologists to six years in jail for not having alerted in advance the inhabitants of the city of L’Aquila about the possibility of an earthquake before the one that struck the city 2009 and that killed more than three hundred persons [54]. It may be that the behavior of these geologists was a little cavalier since they had explicitly told the inhabitants of the city that there was nothing to be worried about. Nevertheless, the sentence that had found them guilty had no justification on the basis of what science knows about earthquakes . Correctly, the sentence was reversed in 2015 and the geologists were cleared of all accusations.

So, even with all our knowledge about critical phenomena, the best that we can do in terms of defending ourselves from earthquakes is to build structures that can withstand them without being damaged. If you live, or have lived, in Japan, you know that it is a fact of life that the building where you work or live will start shaking at least a few times per year. Most of these earthquakes are totally harmless because buildings in Japan, and in particular high-rise buildings, are designed to be “earthquake proof”, at least within some limits. But the probability of an earthquake intensity that falls outside the safety limits is not zero. As recently as 1995, the Great Hanshin Earthquake, also known as the “Kobe earthquake,” caused more than 6000 victims in Japan, seriously damaging more than 400,000 buildings. Another disastrous event took place in 2011 when the nuclear plant at Fukushima, in Northern Japan, was heavily damaged by the tsunami caused by an earthquake. The builders had assumed that waves higher than six meters were so unlikely as to not be worth planning for. But they should have taken into account that the Pareto distribution puts no upper limit to the size of an event, it only makes it less and less in probable. So, in 2011, the wall was hit by waves that reached 13–15 m of height; these waves couldn’t possibly be contained and the damage they caused resulted in the disastrous meltdown of three of the six reactors of the plant. The conclusion that we can obtain from these concepts is that large events that are seen as unexpected catastrophes are, in reality, just the extreme part of a sequence of non-catastrophic or less catastrophic events . These events have sometimes been called “gray swans” or “black swans” by Nassim Taleb [55].

Note also that power-laws cannot hold for the whole range of the possible values of the parameters of the system. For one thing, if the law were to stretch all the way down to increasingly small events, the result would be an infinite number of microscopic events. For instance, it is well-known that the size of cities follows a version of the Pareto law called “Zipf’s law ” in which the log of the number of inhabitants generates a straight line when plotted against the city rank. That is, cities are listed in order of their size and ranked accordingly to their position in the list. But, of course, a city of less than one inhabitant is not possible. The same is true for other phenomena, such as oil fields [56]. If the power-law distribution were true for all sizes, there would be an infinite number of small oil fields and that might imply infinite oil; which is obviously not possible.

On the other side of the Power law distribution , that of the very large events, there is another effect that was noted for the first time by Laherrere and Sornette and termed “the king effect;” a large deviation from the distribution for some events/sizes that are unexpectedly large [57]. Later, Sornette used the term “Dragon King” for these events [58, 59]. An example of this effect is the position of Paris in the distribution of the sizes of French cities. Paris is, much larger than the power law distribution would indicate. It is the true “king” of French cities.

Let me now summarize what we have been discussing. A certain kind of collapse can be described in terms of the model called “self-organized complexity” and the result is that, in several cases, the size of collapses follows a law, called the “Pareto Law” or “power-law” that relates it to their frequencies. True catastrophes are often extreme events in this distribution. We can never predict when a catastrophe will strike, but the study of the properties of their distribution can at least give us some idea of their probability as a function of their size. This approach can provide some defense if one knows how to deal with the data and what precautions must be taken. That’s not possible for all phenomena: if you are hit by a meteorite while walking along a street, that’s a really unpredictable event: there are no proven cases in the recorded human history of anyone having ever been killed by a falling meteorite. But it is so rare that you are justified if you take no precaution about its occurrence. On the other hand, if you live in a seismic zone and your home or office doesn’t have precautions against earthquakes, then you can’t complain if you end up buried under the rubble. Taking precautions against random events is not prevented by the fact that they are random. It is both wise and mandatory!

3.2.2 Networks

Networks are an important concept in understanding the behavior of systems formed of many elements connected to each other. Only networks can show the phenomenon we call collapse: no network, no avalanche. A large number of stones can create an avalanche, but a single stone cannot. In the same way, a single molecule cannot collapse, but a solid formed of many connected atoms or molecules can. This is a very general property of complex systems.

Networks are entities formed of “nodes ” connected by “links.” They are often represented in the form of a “graph,” a static model of the network; a little like a photograph is a static representation of a real human being. Entities such as an Egyptian pyramid , a sandpile, a cluster of Facebook friends, and a crystalline solid can all be seen as networks (Fig. 3.11). In a pyramid, the nodes of the network are stones and the links are the gravitational forces that make one stone weighing on another. The sandpile described in the self-organized criticality model [50] is a two-dimensional network where each square is a node connected to the nearby nodes by the rules that determine the propagation of an avalanche. In a Facebook network, each person is a node and the links are the condition of “friendship” that Facebook provides. In a crystalline solid, atoms are the nodes and chemical bonds are the links. So, there exists an enormous variety of possible networks, virtual and real.

A network is said to be “fully connected” when every node is directly connected to every other node. On the other extreme, there is the possibility that the network is fragmented into clusters without a pathway to link one to another. A network is said to be “connected” when there exists a pathway that links every node to every other node by jumping from one node to the other. This property is sometimes described as part of the story of the “six degrees of separation” which proposes that every one of us can reach everyone else in the world (say, the president of the United States) by jumping on no more than six connections among friends and acquaintances. This is an approximation, but it hints at another concept, that of “small world networks, ” where the average distance between two randomly chosen nodes (the number of steps required to go from one to the other) grows proportionally to the logarithm of the number of nodes in the network. Other networks are called “scale-free” a term that refers to a class of networks that exhibit a power-law degree distribution in the number of links. That is, nodes with a large number of links are rarer than nodes with a small number and the probability distribution of having a certain number of links follows a power-law. The mechanism that creates these networks is said to be “preferential attachment,” that is, a new node is more likely to form to a node that already has many. This is also termed “the rich get richer” and it is a qualitative description of a well-known phenomenon of everyday life [60].

When considering networks, collapse can be defined as a rapid rearrangement of the links . This rearrangement may involve the formation of new links, the breakdown of old ones, the partial loss of connectivity of the network, even the complete loss of all the links and the disappearance of the network. In most cases, this kind of phenomena can be termed as “phase transitions;” best known at the atomic and molecular level. For most of us, atoms and molecules are something you learn about in a chemistry class in high school, part of a series of notions that involve long lists of compounds and abstruse rules of nomenclature. Indeed, chemistry can be boring and it seems to be perceived as such by most people who are forced to study it. But much of the boredom of a chemistry class comes because it deals mainly with small molecules; they may vibrate, emit or absorb photons, react with each other, and more, but they are not networks and they don’t show the variety of surprising and interesting behaviors of complex systems. They are just too small for that.

But single molecules can show a complex behavior if they are large enough to form a network. This is the case of proteins which are formed of a long chain of molecules (“amino acids”). The chain “folds” on itself as if it were a woolen ball. The weak bonds among different sections of the protein chain form a network of nodes and links that can be rearranged. Because of this feature, proteins show at least one of the typical characteristics of complex systems : phase transitions. You may have heard of the Creutzfeldt–Jakob disease, the prion disease, amyloidosis, and others. These are called “proteopathies” and, in many cases, they are the result of a change in the folding structure of some protein in the human body. In this transition, the protein is not destroyed, its chemical bonds are not broken, it doesn’t change its chemical composition. What changes is only the way the chains of atoms that compose it rearrange the weak links that keep the protein folded in a certain way. That may destroy the functional characteristic of the protein within the organism that contains it. The results can be disastrous because, in some cases, the collapse is self-propagating; that is, it is driven by an enhanced feedback effect. A single misfolded protein can cause other proteins to misfold as well, generating a chain reaction that destroys the functional capability of a large number of proteins in the organism. People may die because of this effect.

Solid materials normally contain many more atoms or molecules than any protein and they, too, can be seen as networks. Whereas a protein is a linear chain of nodes, a solid is a three-dimensional network where each node is connected to its nearest neighbors by chemical bonds. There are many ways for atoms and molecules to arrange themselves in a network; the most common one is a “crystalline solid” where the nodes are arranged in the kind of network that we call “lattice.” Typically, an atom in a metallic lattice is directly connected to 12 nearby atoms, although different numbers of connections are possible in other kinds of solids. Solids may be stable and, in most cases, we want them to be. But solids can also show complex behavior: they can break apart in two or more pieces, as we saw in the section on fracture, but they can also change their internal structure by rearranging the way atoms are bonded to each other. In this case, the change can be as radical as involving the destruction of the network, with the solid undergoing melting or sublimation. But the solid can also undergo a radical change while remaining a solid in a phenomenon called solid-solid phase transition. You may have heard the term “Martensite.” It indicates a specific arrangement, or phase, of the iron atoms in a crystalline iron phase that also contains carbon. The Martensite phase generates a very hard solid, much harder than other phases that iron atoms can form; so it is an essential component of steel. The spectacular process of quenching red-hot steel in cold water is specifically aimed at generating the phase transition that transforms the soft phase called Ferrite into the hard one called Martensite . The two lattices, Martensite and ferrite, may both exist at the same time inside an object made of iron, but there is no intermediate atomic arrangement. It is an example of a collective phenomenon because it involves a large fraction, perhaps all, of the atoms in the lattice.

In virtual networks, phase transitions occur according to similar rules as those valid for a solid lattice, although in a virtual network there are no physical limits to how many links a node can have nor to the distance that separates two connected nodes. For instance, the Internet includes “hyperconnected” or “hyperlinked” nodes such as, say, CNN news, having many more links to other web pages than, say, an average blog kept by a single person. The number of links, is by the way, one of the criteria used by search engines to rank Internet pages. Then, the connections of a virtual node don’t need to be limited to near neighbors in space but can be long-range. For instance, your Facebook friends are likely to be people close to you in space, maybe living in the same city. But nothing prevents you from having as friends people living on the other side of the world.

In general, we may define as “collapse” certain phase transitions that take place in a network and, in particular, when a connected network becomes disconnected—as it happens in the case of the fracture of a solid or its melting or sublimation. In analogy with the case of regular lattices, we can examine the collapse in generic virtual networks by taking into account each node and each link in an approach similar to that of molecular dynamics for crystalline lattices. In this approach, each node may decide to leave the network when the number of links it has goes below a minimum number. In a sense, we can take each link as a chemical bond and imagine that nodes “sublimate” when they are no longer connected to the rest of the network by a minimum number of bonds. We may also see the situation as similar to that of Conway’s “game of life” [61] that deals with cells in a square network. Each cell can be “alive” or “dead” and it can change from one state to the other depending on the number of neighbors it has. Too many neighbors, or too few, make the cell die, but the right number may create a new, live cell. This phenomenon is general and not necessarily linked to a square grid as it is in this specific game. Since the disappearance of one node from the network causes the disappearance of at least one link, and normally more than one, it can generate an enhancing feedback and an avalanche of lost links that generates a collapse.

This kind of study is a hot topic in modern network science . For instance, in a recent paper by Yu et al. [62], networks are studied in terms of the “KQ-cascade model,” where K stands for the number of links and Q for the number of neighbors. The study assumes that each node makes a risk/benefit calculation for maintaining links with other nodes and may decide to break off and leave the network when either the number of connections it has becomes too low or when it has lost more than a certain proportion of its neighbors. This kind of behavior may lead to an avalanche of broken links and leaving nodes that generate an enhancing feedback. The result may be the crash of the network and its breakdown into two or more smaller networks. These crashes take a clear “Seneca shape” in a phenomenon that looks like fracture in solids. This is just an example of a vast effort that involves many researchers and many kinds of networks. Note also that these results are valid for relatively simple networks, while many real-world networks are multilayered structures, “networks of networks” (NON) whose behavior is more complex, but can be studied as well [63].

Another kind of approach to study networks and their behavior is based on the concept of “Catastrophe theory,” developed in the 1970s by the French mathematician René Thom [64]. In turn, Thom’s ideas were based on the earlier work by Alexander Lyapunov on the stability of differential equations. The catastrophe theory is quite complex but it can be described in a relatively simple manner if we consider only two parameters of the network. One, that we may call “x,” is the state of the system, a property that we may understand as the size of the connected network. When the network undergoes a phase transition, it becomes disconnected and x must abruptly become smaller. We may assume that the value of “x” depends on some conditions or parameters that we may indicate, for instance, as “a” and “b”, representing some property of the network. These parameters may vary as the result of external perturbations, the number of links and their strength, or other parameters. This variation affects the network in a strongly non-linear manner, as shown in Fig. 3.12.

Note how in a certain region of the graph the dependency of the network state on the a parameter is strongly non-linear: for some values of a, there are two possible states of the network parameter, x. So, network state may abruptly snap from one state to the other going through a well-defined tipping point. It is what we called a phase transition which may also be seen as a Seneca collapse. An Egyptian pyramid can exist as standing or collapsed, a piece of metal can be intact or broken, a human society may form a single kingdom or several feudal reigns fighting each other, and many other cases are possible.

The catastrophe theory developed by Thom is very abstract and nowadays it seems to have lost much of its earlier popularity owing to the difficulty of applying it to real-world systems. But in recent times, researchers have found that there appears to exist ways to use it in a form in which the network parameter, x, can be described as depending on a universal parameter, called “βeff,” that, for networks, plays the same role that temperature plays in physical systems [65]. This parameter may allow us to determine beforehand the collapse point of a specific network. That is, it describes how far the system can be perturbed before a phase transition takes place. It is a very interesting idea, but it must also be said that the βeff parameter is equivalent to temperature only in a very abstract kind of way. Temperatures can be measured for any material object without knowing anything about its structure and composition. On the contrary, to determine the βeff parameter, one needs an in-depth knowledge of the internal structure of the network and of the various relationships that link the nodes to each other. Nevertheless, this result illustrates how network theory is a rapidly developing field.

In some cases, the collapse of virtual networks can show the typical “Seneca shape.” You can clearly see it in the case of the crash and the disappearance of the social network called “Friendster” in that started in 2009 and was complete by around 2013–2014 (Fig. 3.13).

The collapse of Friendster was studied in some recent papers that confirm the feedback-based mechanism of the collapse [66, 62]. As people started leaving the network, other people found themselves having too few contacts to be worth staying, and so they left too. The result was a rapid disappearance of the network population. If you look at the Friendster site, today, you’ll find a note that says “Friendster is taking a break.” It is a rather optimistic statement, but also a good illustration of Seneca’s concept that “ruin is rapid.”

3.3 Financial Avalanches

Money, it’s a gas

Grab that cash with both hands and make a stash Money, so they say

Is the root of all evil today.

Pink Floyd, “The Dark Side of the Moon”, 1973

3.3.1 Babylon Revisited

Scott Fitzgerald, the author of The Great Gatsby, left to us a poignant description of Paris in the early 1930s. Titled Babylon Revisited (1931), the story is about an American citizen returning to Paris during the Great Depression, after having lived there during the bright and prosperous “crazy years” (also known as the “roaring twenties”). During that golden age, the American expats in Paris had formed a thriving community dedicated to the good life and to all sorts of pleasures, including the kind of sexual pastimes that gave the city the nickname of “Babylon.” That golden world evaporated in a short time when the money that had generated it disappeared with the great financial crisis of 1929. The Paris that the protagonist of Babylon Revisited sees is a shadow of its former glory; a good example of the ruin that so easily hits people and things. Here is how Fitzgerald describes the city as seen by the eyes of the protagonist of the story.

He was not really disappointed to find Paris was so empty. But the stillness in the Ritz bar was strange and portentous. It was not an American bar any more–he felt polite in it, and not as if he owned it. It had gone back into France. He felt the stillness from the moment he got out of the taxi and saw the doorman, usually in a frenzy of activity at this hour, gossiping with a chasseur by the servants’ entrance….

Zelli’s was closed, the bleak and sinister cheap hotels surrounding it were dark; up in the Rue Blanche there was more light and a local, colloquial French crowd. The Poet’s Cave had disappeared, but the two great mouths of the Café of Heaven and the Café of Hell still yawned–even devoured, as he watched, the meager contents of a tourist bus–a German, a Japanese, and an American couple who glanced at him with frightened eyes.

So much for the effort and ingenuity of Montmartre. All the catering to vice and waste was on an utterly childish scale, and he suddenly realized the meaning of the word “dissipate”–to dissipate into thin air; to make nothing out of something. In the little hours of the night every move from place to place was an enormous human jump, an increase of paying for the privilege of slower and slower motion.

(Scott Fitzgerald, Babylon Revisited, 1931)

This story shows how major changes and collapses can be triggered by apparently minor causes. Before the great financial crash of 1929 , a considerable number of Americans could travel to Paris to be wined and dined, and more than that. One year after the crash, the Americans were gone. And yet, nothing physical had disappeared, there had been no hurricane, no tsunami, no earthquake. Paris was the same, the Americans were the same, the ships that transported them to France were the same, the caves of the Parisian bars were still stocked with Champagne as before, and the Parisian prostitutes, the “filles de joie,” were still waiting for customers in the back roads of the city. What had disappeared was the non-physical entity that we call “money.” And it had disappeared not in its physical form of chunks of metal or paper bills. What had disappeared was a purely virtual entity: numbers written in the reports of financial institutions.

The stock market crash of 1929 is probably the best-known among a long series of financial crashes in history, but there have been many more. Perhaps the first recorded financial collapse in history is the third century CE currency collapse that resulted from the depletion of the Spanish silver and gold mines and that sent the Roman Empire on its way to oblivion. There may have been earlier monetary collapses, just as there were earlier empires, but the records are blurred and we cannot say for sure. But, in our age, we know that financial crashes are common, even though our civilization seems to have survived all those that took place during the past two centuries or so.

The latest major financial collapse is that of the “subprime” market crash of 2008. As we learned later on, the term “subprime” meant mortgages that were offered by financial institutions to customers whose ability to repay their debt was considered substandard. These mortgages were risky for the financial institutions that provided them, but offered attractive rates of return. So, they were dispersed among other financial instruments in such a way that their possible default was supposed to be unable to cause major damage. But, evidently, something went wrong with the idea. Starting in 2007, the US housing market saw a rapid decline in home prices, a trend that was later described as the bursting of the “housing bubble.” The collapse may have been triggered by the rise of oil prices that had reached $100 per barrel on January 2008. It led to a cascade of mortgage delinquencies and foreclosures and the devaluation of housing-related securities. It was a major disaster, with several major financial institutions collapsing in September 2008 with significant disruption in the flow of credit to businesses and consumers and the onset of a severe global recession. For many people, it meant just one thing: before the collapse they used to own a home; afterward, they didn’t own it anymore.

The mortgage crisis of 2008 was interpreted in various ways, but we can see it as a classic example of a “Seneca Collapse” in the sense that the fall of the housing market was much faster than its previous growth (Fig. 3.14). It was also a good example of how a relatively small perturbation can generate an avalanche of effects that cause the whole system to collapse. The propagation of the subprime crack was rapid and unexpected. The percentage of subprime mortgages defaults had remained around 8% in the US for a long time, but it rose rapidly to 20% from 2004 to 2006, reaching a maximum of 23.5% and with much higher ratios in some regions of the U.S. [67]. Just as the propagation of a small crack in the hull of a plane can make it explode in mid-air, the subprime lending was the crack that expanded and that sent the whole global financial system careening down to a disastrous crash.

The 2008 crash was similar to many others, including the one of 1929, in the sense that nothing physical had happened. The homes affected by the collapse were not hit by a hurricane or an earthquake. After the crash, they were still standing as before, intact, except in some cases when the owners purposefully damaged their homes as an act of revenge against the banks. In other cases, the banks themselves or the city authorities arranged for the demolition of houses that had no more market value. In some instances, banks decided not to foreclose the mortgages because they saw no value in the property they would be gaining possession of. So, homeowners maintained the property of valueless homes, but they were still supposed to pay property taxes. This was the case of the “zombie titles,” still haunting many people in the US, today [68]. But, in the great majority of cases, the only difference was that the former owners had become tenants of the new owners, the banks.

The financial crisis of 2008 is just one of the many cases illustrating how financial bubbles grow and then burst, usually with ruinous results. It is a typical phenomenon that starts with people investing in something they believe is valuable. The problem is that, just as beauty is in the eye of the beholder, the perception of the value of a something may have little to do with its actual value. In some cases, the commodity doesn’t even exist: what’s overvalued is a purely financial scheme that’s supposed to create riches out of nothing. We call these cases “Ponzi schemes” from the name of Charles Ponzi who used them with some success (for himself only, of course) in the 1920s. The Ponzi scheme is nothing more sophisticated than taking the money from later investors to pay the early ones. It works only as long as the number of investors grows, and for this reason it is called also a “pyramid scheme” to indicate that the small number of people on the top profit from the large number of people at the bottom. Just as stone pyramids may collapse because of the force of gravity, financial pyramids tend to collapse because of financial forces. The difference is that a stone pyramid may keep standing for thousands of years while a financial pyramid doesn’t normally last for more than a few years.

These financial scams seem to be remarkably common and plenty of people may fall for them. A good example is the “airplane game” that was popular in the US and in Europe in the late 1980s . The idea was so silly that you wonder how anyone could even remotely consider it: someone drew a rough sketch of a plane on a piece of paper and invited other people to “board the plane” as passengers, in exchange for a fee. You paid real money to enter the game and you would be paid back handsomely when opting-out after having lured in other passengers, or so the gamers hoped. At the beginning, it seems that some people managed to make money in this way and for a short time the game became a diffuse social phenomenon. But, in the real world, nothing can grow forever and the airplane game went into a tailspin and crashed, leaving its passengers a little poorer and—perhaps—a little wiser.

If people can fall for such an obvious Ponzi scheme as the airplane game, you may imagine how the fascination for technological gadgetry makes people fall for some pretended innovation that’s described as able to change the world. This kind of scam falls in the “snake oil” category. In recent times, it has been most often related to energy production with endless schemes for creating energy out of nothing or by means of some mysterious phenomenon, unknown to official science. These wonderful inventions are often described in terms of suitably portentous and high-sounding language that normally includes the term “quantum” and, in a diffuse subcategory, the term “cold fusion” (or the more resounding term “Low Energy Nuclear Reactions,” LENR ) [69]. Often, the inventor doubles down his claims, maintaining that he is the victim of a conspiracy contrived by the scientific establishment, the oil companies, the powers that be, and/or the Gnomes of Zurich.

Even when an invention is not a scientific scam, it still needs to have the features that will make it successful in the market. It needs to be compatible with production at a reasonable cost, it needs to have a market and, more than anything, it needs a reliable financial backing during the various stages of its development and marketing. Technological innovation is a very complex and difficult field and making money by developing a better mousetrap is far from being guaranteed, even assuming that it can really catch mice. High technology is a typical example of a field where excessive enthusiasm can easily lead to the financial version of the Seneca ruin.

It seems clear that all financial collapses have something in common. It doesn’t matter if they are purely financial scams, or if they are connected to some real-world commodity. The link in all these phenomena is money. There is something specific to money that makes it capable of creating these roller-coaster cycles of growth and collapse. It is the mirage of monetary gains that leads people to make wrong choices that then lead to even more wrong choices. It is the typical case of something that feeds itself to reach a certain degree of complexity, then to crash down in a financial avalanche that, like real avalanches, leaves in its wake only ruin and pain. It seems to be the way our world is, but there is much more to be learned in this field.

3.3.1.1 But What Is this “Money” Anyway?

The mother of all questions in economics is “what is money?” What is this wonderful entity that, as Karl Marx noted in 1844, “can turn the ugly into the handsome?” You might think that the nature of money should be something well-known, today, after almost two centuries of work of economists, but the subject is still debated. Overall, we can say that there are two main views of money in economics. The first sees it as a “commodity,” that is something that has at least a certain physical, real-world consistency. It may be gold or silver, whereas in ancient times it might have been oxen, seashells, shark teeth, or whatever was handy and not too bulky. This view may go back all the way to Aristotle and it is sometimes referred to as the “metallist” theory of money. The other view sees money as a purely virtual entity: a measure of the exchange value of real commodities . This assessment may go back all the way back to Plato but it gained ground in economics only in relatively recent times with the diffusion of paper money. This view is often termed the “chartalist” theory of money. Its modern version originates with the British economist Mitchell-Innes [70] and the German economists Knapp [71]. The debate among chartalists and metallists is still ongoing, but it is easy to note that money is becoming more and more a purely virtual entity; especially since when, in 1971, President Richard Nixon abolished the gold convertibility of dollars (that, anyway, had been purely theoretical for most of our recent history). To say nothing about the recent appearance of “Bitcoin.” If that is not virtual money, what is?

So, what, exactly, is the chartalist idea? It comes from the Latin “charta,” a term that originally indicated the papyrus plant and that later came to indicate sheets or rolls on which people could write texts. Chartalism, then, emphasizes the idea that money doesn’t necessarily need to be linked to metals or other commodities. Money is nothing material, it is not a commodity but just a record that describes what some people owe to others; that is debt.

Debt is something very old and the fact of being “indebted” to someone for a favor of some kind must go back to Paleolithic times when our ancestors exchanged goods and services by a mechanism that we can still see in societies where “gift-giving” is practiced. This idea can be seen as an informal account of what you owe to others and what you are owed to by others, even though it is normally much more complicated than this. Exchanging gifts is regulated not just by their material value but by a tangle of social and human factors that may make gift-giving an extremely delicate and complex task for both the giver and the received: a mistake may result in social rejection or worse. But, with societies becoming larger, the subtle network of relations and obligations ceased to be the only area where goods and services were exchanged. People needed to deal with perfect strangers whose capability of reciprocating the gift they had received could be reasonably doubted. And, of course, governments wanted people to pay taxes, and that was a completely different story: not an exchange of gifts, but an imposition. The result was the need of keeping track of who exactly owed what to whom and it was the start of the diffusion of the concept of “money.” It was in the Middle East, during the third millennium BCE, that we see the appearance of commercial contracts written on clay tablets. These contracts stipulated that, say, someone agreed to pay a sheep to someone else on some specific date. Then, the contract could be given to another person, and it was as if that person had been given a sheep. These obligations were, within some limits, tradeable. They were a form of “money.”

The problem with contracts written on clay was that their value depended on the existence of some form of authority that could enforce them in case someone tried to cheat. In times where the typical political entity was the city-state, the consequence was that they had value only in the city were these contracts had been issued. So, a contract signed in Uruk, in Mesopotamia, had probably little or no value in the city of Eridu, not far away but ruled by a different Lugal (king). That made long-range commerce difficult since it could only be based on bartering for goods. So, in time, metal-based “commodity money” started to appear with the development of mining and metallurgic technologies, approximately during the third millennium BCE. Metals have both practical and decorative purpose but it is likely that, from the beginning, they were used as stores of value to be exchanged for goods that were bulkier and more difficult to transport. In time, gold and silver started to become the most important tools for long-distance commerce, while copper was normally relegated to a minor role as local currency for small transactions. In these ancient times, there was no such thing as “coinage;” precious metals were kept in the form of bullion and weighed at every exchange. In the Middle East, that was normally performed in temples, possibly invoking the locally worshiped deity as a guarantee of honest weighing. This method of managing currency lasted for at least two millennia. In the gospels, we still find a trace of this role of temples when we read of the money exchangers whom Jesus chased away from the temple of Jerusalem. In Greek, these money changers were termed “trapezitai” from the Greek word meaning “table,” in the sense that they performed their activity on small tables. The modern term of “bankers” derives from the Italian (or French) term that still means “small table.”

A revolution in the concept of money took place during the mid-first millennium BCE when in Lydia, the Western part of Anatolia, someone developed a way to produce standardized metal disks, all of the same weight; that is, coins. King Croesus, the last Lydian King, is commonly credited for having introduced this idea, mainly as the result of the need to pay his soldiers involved in the ongoing conflict against the larger Persian empire. It seems that the invention of coinage helped King Croesus a lot in gaining a long-lasting fame in history, but little to avoid the Lydian kingdom’s destiny of being defeated and absorbed by the Persian Empire. But the idea of coinage was so good that the Persians quickly copied it with their “Daric,” a silver coin that they used to pay their own soldiers to expand their empire. That was a successful strategy until the Persians clashed with an empire in the making, the Athenian one, that was just as good, and perhaps better, at minting coins from the silver mines it controlled in Attica. The defeat of the Persians at the hands of the Athenians at the battle of Salamis in 480 BC put an end forever to the expansion of the Persian Empire, but not to the growth of other empires. The technology of coinage rapidly spread all over the world and many events of ancient history can be seen as the result of the struggle for the control of mines of precious metals that created empires and destroyed them when the mines were exhausted. Still today, the term “soldier” comes from the Latin word “solidus,” a coin of the late Roman Empire.

Over the centuries, money has been penetrating more and more into the fabric of society. A century ago, many people in the countryside, even in the Western World, still lived a life where money was scarcely used; what counted most was a man’s word and his reputation. But, with time, money in its various modern forms started pervading all aspects of life and the situation is still rapidly evolving. Everything is becoming monetized, one way or another, and people seem to be more and more convinced that every problem can be solved by throwing money at it. And not only is society becoming more monetized, but money is becoming more virtual, with coins and banknotes gradually disappearing, replaced by the ubiquitous debit and credit cards. But how can such an incorporeal entity have so much effect on our lives? Of course, there exists a wide-ranging discussion and an enormous amount of written material on this subject. But, as we have been examining the dynamics of complex systems, we may try a stab at seeing money in the context of what we have been discussing so far: complex systems and networks.

Let’s describe money in its social context : an economic system composed of “agents;” people, firms, and institutions who own different amounts of money; also in its negative form called “debt.” Each agent is a node in a large network where interactions take place among nodes in the form that we call “transactions.” People move money from one node to another in exchange for goods and services. Of course, as we all know, money is not equally distributed among agents and that’s an essential feature of the system: some agents are rich, and some poor. But how exactly is money distributed? That is, how rich are the rich and how poor are the poor? Surprisingly, this is not well known. One problem is that, normally, people do not publicly disclose their net worth. Besides, a lot of assets are not easily quantifiable in monetary terms: jewelry, real estate, antiques, and similar things. What we can quantify, instead, is income. Governments tend to tax income rather than wealth and, therefore, they go to great lengths in order to quantify their tax base. So, the income data for many countries are made public by their respective tax agencies (the Internal Revenue Service, IRS, in the US). Income is not exactly proportional to wealth, but examining the income distribution can give us at least some idea of how wealth is distributed in society.

The measurement of the distribution of income is traditionally reported in terms of the “Gini Coefficient,” invented by the Italian sociologist Corrado Gini in 1912. To understand how the Gini is determined, imagine a country where perfect income equality has been obtained, that is where everyone has the same income as everyone else. Now, imagine drawing a graph where you have on the x-axis the people, numbered one by one in any order you like. On the y-axis, you place the cumulative fraction of the wealth owned by the people on the corresponding point of the axis. In this peculiar kind of society, the first 10% of the population will hold 10% of the wealth (or, more exactly, of the income); the same will be true for the first 30%, for the 50%, or for any fraction. The result will be a straight line in the x-y graph.

But, of course, that’s not the way things are in the real world. Suppose that now we order the population on the x-axis in order of wealth, as measured in terms of income. We place first the poorest people and then move along the axis until we have the wealthiest people on the extreme right. The curve will start low and keep low for a certain fraction of the x-axis since the poor own a small share of the total. But, as we move to the right, the curve will start rising up with the rich people appearing in the graph. The result is something like the graph in Fig. 3.15.

From Fig. 3.15, we can define the Gini coefficient as a ratio of areas in the form of A/(A+B). In other words, the Gini coefficient it is larger the larger the “A” area is. Obviously, the larger the Gini coefficient, the larger the income inequality. The case of perfect equality has Gini = 0 since the area of A is equal to zero. The opposite case would be when only one person owns all the wealth while all the others own nothing. This condition would generate a Gini coefficient equal to 1. Both conditions are obviously improbable and coefficients measured for different countries range, typically, from 0.2 to 0.7 (sometimes given in percentiles, that is from 20 to 70). Some countries are less egalitarian than others: for instance, South-American countries have normally high Gini coefficients, with Brazil perhaps at the top with around 0.6. On the opposite side, European countries are rather egalitarian, with income coefficients in the range from 0.2 to 0.4, especially low in Scandinavian countries. About the United States, it had seen a trend toward lower inequality that started in the ninetieth century and that accelerated after the end of the second world war, thus making the US trend similar to that of most European countries. But the trend changed direction in the 1960s–1970s, to arrive today at values of the Gini coefficient between 0.4 and 0.5, typical of South American countries. This phenomenon is part of the series of economic changes in the US economy that was termed “The Great U-Turn” when it was noted for the first time by Bluestone and Harrison [72]. You can see it in Fig. 3.16.

There is no general agreement on what happened to the US society that caused such a change in the trend of the income distribution. What we know is that a lot of money flew away from the pockets of middle-class people to end up it in the pockets of the wealthy. As you may imagine, we have here another one of those problems where the large number of explanations provided is an indication that nobody really knows how to answer the question. For instance, there is no lack of conspiracy theories that propose that the rich formed a secret cabal where their leaders collected in a smoke-filled room to devise a plan to steal from the poor and give to the rich. Recently, I proposed that the “U-Turn” may be related to the peak in oil production that took place in the US in 1970 [73]. At that moment, the US started a rapid increase in the imports of crude oil from overseas. The result was that the money that the Americans spent on foreign oil returned as investments in the US financial system, but from there it never found its way to the pockets of middle-class people. But I am the first to say that it is just a hypothesis.

A limitation with these measurements is that the Gini coefficient integrates all the data to give us just a single number and that tells us little of how exactly wealth is distributed among people. We know that, in most cases, the distribution approximates what was defined as the “Lorenz curve” that looks like it is depicted in Fig. 3.17. But, in principle, the same Gini coefficient could be originated by different distributions: a few filthy rich people would have the same effect of many “just rich” people. This issue was studied for the first time by Vilfredo Pareto (1848–1923); his results are reported in a paper published in 1898 [51]. The set of data that Pareto was working on was limited but he found clear evidence that the distribution of income followed a power-law, at least approximately (this is incidentally, the first cases where clear evidence of a power-law was found; the reason why these distributions are given the name of “Pareto laws). This concept is often expressed in terms of the so-called “80/20” law that says that 20% of the people own 80% of the wealth. This is an approximation but it captures the essence of Pareto’s discovery.

Because of this early study by Pareto, today the standard wisdom in economics is that the income distribution always follows a Pareto law. But, surprisingly, it turns out that things have changed from Pareto’s times. A series of studies by Yakovenko and his coworkers provided different results [74, 75]. The Pareto distribution was observed only for the income of a small fraction of very rich people, whereas the lower income part of the curve showed an exponentially declining distribution. An exponential distribution was also found for the wealth of the different countries of the world. All that doesn’t change the fact that the rich are few and the poor many, but an exponential distribution goes down toward zero faster than a Pareto distribution. An exponential curve means that the distribution of incomes is, in a certain sense, more balanced as it implies that the number of rich people is smaller. But when the Pareto law takes hold of the curve, it bends the distribution in such a way to create a relatively large number of ultra-rich people: billionaires, some of whom are well on their way to becoming “trillionaires.”

How can we explain the existence of these exponential income distributions ? We may start from the “Boltzmann Game” developed by Michalek and Hanson as an operational game to teach statistical thermodynamics to their students [76]. It doesn’t seem that they had in mind simulating an economic system; rather, their game was developed as a way to make the concept of entropy easier to understand. But the game can also be seen as a small-scale economic simulation. It is played by a group of students who interact at random, in couples, playing each time a game of “paper, rock, and scissors” against each other. Each student is supposed to start the game with one dollar or with a token representing one dollar (if they start with more than one token each, the results don’t change, but it takes more time for the distribution to stabilize). At each interaction, the winner takes a dollar from the loser if the loser has at least one dollar (negative wealth, or “debt,” is not allowed in the game). After a certain number of interactions, the game reaches a condition of approximate stability; homeostasis. At this point, some students turn out to have amassed several coins: they have become the rich, while most of them have zero coins, they have become the poor. The interesting thing is that the distribution of wealth resulting from the game turns out to be the same predicted by the “Boltzmann-Gibbs” distribution that was developed to describe the entropy of atomic systems. In mathematical form, it is given by an exponentially decaying function. In other words, the probability of someone having a certain level of wealth is proportional to “e” (the base of the natural logarithms) raised to a factor proportional to the wealth itself. It is exactly what Yakovenko and his coworkers found for the largest part of the real-world income distribution.

This distribution is not more favored than other distributions in terms of being more stable or being actively preferred by the players of the game. It is more probable because it can be attained in many different ways. To explain this point, imagine you want absolute equality in the game. There is only one configuration of the group that has this property: when each student has exactly one coin. Now, think of a situation in which one student has zero coins and another one has two, while all the others have one. There are many possible ways in which the group can have this characteristic, depending on who has the extra coin and who misses one coin. If you calculate the number of configurations for each possible distribution, it turns out that the exponential one has the largest number, so it is the one that you would expect to see most frequently. The game maximizes the entropy, just as the Boltzmann- Gibbs distribution predicts. Entropy rules in this game, as it does in the real world.

Yakovenko’s results for the real economy are the same as those obtained by the Boltzmann game and he summarizes the results he found with the statement “Money, it is a gas,” taken from a song by Pink Floyd, meaning that money follows the same distribution as that shown by the kinetic energy of gas molecules. This is not exact because real gases follow a similar, but different, distribution: it is called the “Maxwell-Boltzmann” distribution and the most probable state for a gas molecule is to have a larger than zero energy. That is a consequence of money and a physical gas being different things, in particular, income being a scalar while the momentum of a gas molecule is a vector. But note that when we consider the income of families, rather than of individuals, Yakovenko and coworkers find that the distribution shows a peak as you would expect from everyday experience. In most societies, the most probable state for a family is to be poor, but not to have exactly zero income.

It is already hugely interesting to find that thermodynamics can describe the distribution of income in the real world, but there is more. As mentioned before, Yakovenko and his coworkers found that the Boltzmann- Gibbs distribution does not hold for the whole population, but only for about 97% of the total. The richer 3% of the population, instead, follow a different statistic, a power-law. That this difference exists is confirmed by the data that Forbes has been publishing about the net worth of the world’s billionaires since 1987, a number that has reached the level of some 2000 persons by now. This set of data is especially interesting because it is not about income but actual wealth. Measuring this parameter can only be done by directly asking the rich of the world how rich they are [77]. We might have doubted that they would tell the truth, but, apparently, they did since the wealth distribution of billionaires was found to follow a “power- law” (or a Pareto distribution) [78], in agreement with Yakovenko’s results.

The rich, apparently, can even defy entropy by following a wealth distribution that ignores its effects. But what exactly makes a person rich or poor? An interesting feature of the thermodynamic distribution model of incomes is that being rich or poor is purely casual; the rock-paper-scissors is not a game of skill (nor is the second principle of thermodynamics!). Certainly, in real life, skill and grit count in one’s career, but it is also true that most rich people are the offspring or rich families [79]. As you may imagine, the idea that wealth is inherited rather than earned is not popular with the rich but, for some reason, they seem to be the ones who are most active in dodging and opposing inheritance laws [80].

Still, that doesn’t explain why the rich seem to live in a world of their own in which thermodynamics laws don’t seem to apply. Perhaps we can find an answer noting that power-laws tend to appear when we look at the evolution of highly networked systems, that is, where each node is connected to several other nodes. The Boltzmann-Gibbs statistics may be seen to apply to a “fully connected” network in the sense that each molecule can interact with any other molecule. But it is also true that, at any given moment, a molecule interacts with no other molecule or, at best, with just one in the kind of interaction that, in physics, is called “pairwise.” In a gas, molecules bump into each other and then they leave after having exchanged some kinetic energy; these pairwise interactions don’t affect other molecules and so don’t generate feedback effects. And, as it is well-known, there do not exist phase transitions in the gas phase; only solids (and, rarely, liquids) show phase transitions as the result of feedback effects Something similar holds for the kind of economic interactions that most of us are involved with: we get our salary or our income from an employer and we spend it buying things in stores, and we pay our taxes to the government, too. These are, mostly, pairwise interactions, just like molecules in a gas and it is not surprising that the resulting distribution is the same. The rich, apparently, are much more networked than the poor and their many connections make them able to find and exploit many more opportunities for making money than us, mere middle-class people. So, they don’t really play the Boltzmann game, but something totally different. Whether this observation can explain the observed income distribution remains to be proven, but it is an indication of how important networking factors are in our world.

There remains the question of why the income distribution was so different in the late 1800s, at the time of Pareto, than it is now. What happened that shifted the distribution from a purely Pareto law to a mix of Pareto and exponential? On this point, I may propose an explanation that considers the gradual monetization of society that took place over the past century or so. It may well be that most people who had an income in the ninetieth century were highly networked people, like today’s rich people. Today, salaried people engaged mostly in pairwise economic transactions may have become much more common. So, it may be that over time there has been a sort of financial phase transition where some money “sublimated” from the rich to move to the poor, an interpretation that is consistent with the trend for lower inequality that has been the rule during the past century or so. As times change and the trend is reversed, the rich may regain their former 100% of the distribution, leaving the poor totally moneyless; maybe as a result of the “negative interest rates” that seem to be fashionable today. But that, for the time being, is destined to remain pure speculation.

It is said that Scott Fitzgerald said, once, “The rich are different from you and me” or “The rich are different from us.” To which Ernest Hemingway replied: “Yes, they have more money." But, maybe, Fitzgerald had hit on something that only much later the physicist Yakovenko would prove: the difference between the rich and the poor is not just the amount of money they have. It is in how they are networked.

3.3.1.2 Why Financial Collapses?

Let’s go back to the subject we approached at the beginning of this chapter: the question of financial collapses. Does the thermodynamic model of income distribution tell us something about that? For one thing, the Boltzmann-Gibbs distribution doesn’t generate collapses. When no debt is involved, either one has some money or has none; so, nobody can go bankrupt [74]. In these conditions, the model could describe a very simple society where not much money is around, maybe one of those small “transition” communities that make use of local money, often distributed for free when it is introduced, and so it does not involve debt. But, in the real world, things are different.

To explain bankruptcy , the thermodynamic income model needs to be expanded to take into account the possibility of negative wealth (i.e., debt). Once that is done, the Boltzmann-Gibbs model no longer produces a stable wealth distribution [75]. Yakovenko and his coworkers found that the new distribution has no upper or lower boundaries: there is no limit to how much one can be rich, nor there is a limit to one’s debt. As the model runs, wealth and debt tend to keep increasing forever. The can do that in a theoretical model but, in the real world, there exist bankruptcy laws that aim at preventing people from accumulating infinite debt or even just debt that they can’t reasonably be assumed to be able to repay. Here, the bankruptcies of rich people and of middle-class people are, again part of different worlds. When a middle-class person goes bankrupt, we don’t see the kind of enhancing feedback that leads to avalanches: a person or a family may lose their money and their home, but that doesn’t normally cause their friends or their relatives to suffer the same destiny. That makes sense: as we saw, middle-class people are mostly engaged in pairwise monetary interactions. So, the disappearance of a single customer in the kind of market where middle-class people do their shopping will normally have little or no effect.

But things change when bankruptcy affects rich people or large companies and institutions. One problem, here, is that while we know something about how wealth is distributed, we know nearly nothing about debt. Does it follow a Pareto law? At present, we lack data on this point. It may be likely that, in the same way that there exist a small number of people who are hugely rich, there also exist a small number who are hugely indebted, maybe following a Pareto distribution just like the super-rich do on the other side of the financial spectrum. Then, we would expect that these highly networked people and institutions would tend to create large financial avalanches when they crash. Large, heavily networked structures or persons don’t normally fail just because of the strict application of the bankruptcy laws. As we saw in the previous section, the collapse of the subprime market and, earlier on, the market crash of 1929, were collective phenomena where investors tried to get back their money from financial institutions that they didn’t trust anymore and found that they couldn’t. As a result, when governments rush in to save the situation they seem to be more interested in saving the large institutions (those termed “too big to fail”) rather than helping the middle-class people who risk losing their homes. That seems to be what has been happening in the world in recent times. Again, we see how important the network factor is in creating collapses.

To summarize, the financial market is a networked structure and, as we saw in the previous section, networked structures are subjected to the kind of reinforcing feedback that leads to the kind of phase transitions that we call “collapses.” The financial world can collapse in various ways, and it may be interesting to describe the different kinds of disasters that can take place. So, let’s try to defined a brief taxonomy of collapses in an approximate order of their increasing catastrophic character :

1.
Black Elephants [81]. These are the “known unknowns,” to use a term attributed to Donald Rumsfeld. They are the elephant in the room that you know is there, but you choose to ignore, or whose size cannot be correctly evaluated and that may lead to various disasters. Black elephants can cause collapses, being a case of “information concealment” as described by Sornette and Chernov in their book “Man-made catastrophes” [82]. Many financial disasters arise from information concealment, including the tendency of people to invest in obvious financial or technological scams.
2.
Gray Swans [55] These are large events, but still part of a Pareto distribution, defined as “consequential but low probability events” [83]. Most vagaries of the markets, including many collapses, fall within this distribution. Note that Taleb, and a lot of the literature on this subject, sometimes mix the definition of gray swans with that of black swans. Gray Swans are not predictable as single events, but their frequency can be determined and, consequently, precautions can be taken. So, when a gray swan creates a financial collapse (market crash) or a physical one (e.g. an earthquake) the resulting damage can be in large part attributed to the failure of having taken adequate precautions in advance.
3.
Dragon Kings [58, 59]. These events are physically part of the events that form a Pareto distribution, but are outliers in terms of their large size (example: the size of Paris compared to that of the other French cities). These events/entities are difficult to predict: if Paris didn’t exist, you probably wouldn’t be able to even imagine that such a large city could exist in France. For what we know, none of the recent financial collapses fall in the category of Dragon King, but that doesn’t mean a future one could be so large and so bad that it would defy the known distribution. A Dragon King is basically unpredictable and precautions against it can hardly be taken. At least, however, their existence can be conceived on the basis of known trends.
4.
Black Swans [55]. Events that are physically and statistically outside the distribution: the “unknown unknowns” according to Donald Rumsfeld. Taleb defines the worst financial crashes as Black Swans, in the sense that they defy the current knowledge and market theories. The same can be said of terror attack such as the one carried out on Sep 11, 2001 or—maybe—the hypothetical landing of hostile aliens on the lawn of the White House in Washington D.C: In general, this is the worst possible kind of disasters because they come in forms that are totally unpredictable.

From these considerations, we see that collapses are not a bug but a feature of the universe, a rule that applies also to markets. When we have networked systems in a state of self-organized criticality [50], such as in the case of the financial market, periodic collapses are unavoidable. The result is a lot of damage for everybody, not just for the rich and for the large financial institutions. Money may be virtual, but people need material things, food, energy, and more, to survive. And the way our society is structured, they also need money to obtain them. Large financial collapses destroy the purely virtual entity that is “money,” but they also destroy the capability of the system to supply people with the goods and the services they need. We have already seen an ominous signal with the 2008 financial collapse that caused the near-collapse of the world’s international commercial system. The ruin that such an event could have caused to humankind is nearly unimaginable but, fortunately, the system managed to recover. But how long can we keep playing the money game before the whole thing falls apart, as it is normal that these systems do, in a single, huge, Seneca collapse? This is impossible to say, but I may perhaps cite Lao Tsu in the Tao Te Ching, “A house filled with gold and jade cannot be defended.”

3.4 Famines

What shall we do for timber? The last of the wood is down,

……

There’s no holly nor hazel nor ash here But pastures of rock and stone

The crown of the forest is withered And the last of its game is gone.

From Kings, Lords and Commons, by Frank O’Connor (1903–1966) (reported in [84]).

3.4.1 Malthus Was an Optimist

In 1729, Jonathan Swift wrote an article titled A Modest Proposal in which he ironically discussed the idea of having the Irish eat their babies in order to reduce poverty, eliminate beggars, and avoid famines. Swift is still famous today mainly as an author of children books, while the corrosive irony of his work has been mostly ignored and forgotten. But that could hardly happen for A Modest Proposal, whose stark denunciation of the terrible conditions of poverty in Ireland is still unsettling for the modern reader. And note that Swift couldn’t probably imagine that the problem of hunger would become much worse in Ireland. Today, famines in Ireland are mostly remembered in terms of the “Great Famine” (in Irish the “An Gorta Mór,” the Great Hunger) that started in 1845, more than a century after that Swift had denounced the famine problem in Ireland. The Great Famine caused about one million victims in a few years. Then, over about a decade, poor nutrition, sickness and emigration led the population of Ireland to be reduced from more than eight million people to little more than four million. The data are somewhat uncertain, but they show how abrupt the collapse was; another case of a “Seneca Collapse” with a rapid decline that follows a slow growth (Fig. 3.18).

There are several examples of large famines in history. The memory of these events goes back to Biblical times with the story of the “seven lean cows” that the Egyptian Pharaoh dreamed of and which the Jewish prophet Joseph interpreted as seven years of famine. Similar forms of the same legend were common all over the Middle East, an indication that famines must have been common throughout the history of humankind from the beginning of agriculture [85]. Yet, we have scant quantitative data on historical famines, if we have any. That’s not surprising: during a major famine, people have other worries than recording demographic trends and mortality rates. Even for modern famines, the data are rarely complete and reliable. Famines often strike poor countries where demographic records are missing and in some cases, the data are clouded by political interpretations that attribute the famine to supernatural, and sometimes human, agents. So, the great Irish famine of 1845 remains among the best-known ones although, even in this case, detailed data are often missing and there is no lack of teleological and ideological explanations for it.

We know that the immediate cause for the An Gorta Mór disaster was the “potato blight” (Phytophthora infestans), a parasite that killed the potato crops. From the viewpoint of the parasite, the environment of Ireland was a perfectly connected system, a network that allowed it to spread and grow in an avalanche. Once a potato field was infected, the neighboring ones were easy targets. The result was a typical feedback-driven growth mechanism. And it is not surprising that the power of the enhancing feedback led to rapid ruin for the Irish agriculture. The potato harvest failed, and the Irish peasants followed the ruin of their crops, starving and dying in great numbers. But, if the immediate cause of the Great Famine is clear, there remains for us to understand what had led Ireland to become so vulnerable. The parasite also struck other European regions at the same time, but nowhere with such devastating results. It is a story that needs to be examined in detail.

The Great Famine was not an isolated case in Ireland’s history and we should rather be discussing Irish famines , of which there were several in the period that goes from the early eighteenth century to the late ninetieth century. Swift’s work was inspired by a series of famines that struck Ireland in the eighteenth century [87], but these were minor events in comparison to what happened in later times. The famine of 1740–1741 is referred to as “Bliain an Áir,” the Year of Slaughter [86]. With nearly 40% of the population exterminated as the direct result of lack of food, this famine was even worse, in relative terms, than the better known Great Famine of 1845. So, for at least a couple of centuries, Ireland was recurrently struck by famines of various intensity; the last one recorded having taken place in 1879 and taking the name of the “mini-famine” or “an Gorta Beag.” These famines don’t seem to be related to a common cause. If the Great Famine was caused by a parasitic infestation, the one in 1740 was related to the cold and rainy weather that reduced agricultural yield, in turn probably caused by a volcanic eruption in Kamchatka [88]. Other famines may have been caused by other parasitic infestations or climatic instabilities, or their combination. But the search for their proximate causes tells us little about the basic question: what had caused Ireland to become so vulnerable?

A common interpretation of the Irish famines, and in particular of the Great Famine of 1845, is based on overpopulation. This is sometimes called the “Malthusian” interpretation . Thomas Malthus (1766–1834) remains today both widely known and widely misunderstood for his book “An essay on Population” (1798) [89] that caused him to be described in our times as nothing more than a doom-and-gloom prophet; merely the bearer of news of catastrophes to come. But are Malthus’ ideas relevant for the Irish famines? In part, yes, but not in the simplistic terms in which these ideas are often described. A point that’s often missed about Malthus is that he simply didn’t have the concept of “overshoot and collapse” that’s common nowadays and that was applied to socio-economic systems only in the 1960s with the work of Jay Forrester [90]. What Malthus had in mind was that the human population would keep expanding until it reached the maximum allowed by the capacity the land to produce food. Then, it would stay there, limited by epidemics and malnutrition. Malthus couldn’t conceive that it would go way over that limit and then collapse well below it. But what happened in Ireland was exactly that: the population collapsed to nearly half its maximum level. Besides, if there was such a thing as a “Malthusian limit” for Ireland’s population, why did catastrophic famines occur for population levels as different as about three million in 1740 and eight million in 1845? What was, then, the Malthusian limit? Three million or eight million? And note that Ireland was not more densely populated than other European countries at that time; in many cases, it was the opposite [91].

The problem of explaining the Irish famines is difficult enough that, as usual, it has generated a conspiracy theory that involves the evil English as the culprit, accused of having exploited the parasite in order to get rid of at least some of their hated Irish neighbors. For sure, the English of that time didn’t have a good opinion of the Irish, as you can read, for instance, in the work of the eighteenth century Anglo-Irish landlord Jonah Barrington [95] where the Irish are described as both evil and stupid, some sort of lowly trolls of the land. For this reason, you sometimes see the term of “Irish holocaust” applied to the famine. At times, you can even read that Malthus in person was the culprit [92], even though he was gone more than 10 years before the Great Famine started. Painting Malthus as evil, in addition to being wrong, seems to have become common nowadays, but it is a great injustice done to him. In the many texts he wrote it is perfectly possible to find parts that we find objectionable today, especially in his description of “primitive” people whom he calls “wretched.” In this respect, Malthus was a man of his times since that was the prevalent opinion of Europeans regarding non-Europeans (and maybe, in some cases, still is today [93]). Apart from that, Malthus’ writings are clearly the work of a compassionate man who saw a future that he didn’t like but that he felt was his duty to describe. Surely, there is no justification in criticizing him for things that he never said, as can be done by cutting and pasting fragments of his work and interpreting them out of context. For instance, Joel Mokyr in his otherwise excellent book titled Why Ireland Starved [91] reports this sentence from a letter that Malthus wrote to his friend, David Ricardo,

The land in Ireland is infinitely more peopled than in England; and to give full effect to the natural resources of the country, a great part of the population should be swept from the soil.

Clearly, this sentence gives the impression that Malthus was advocating the extermination of the Irish. But the actual sentence that Malthus wrote reads, rather (emphasis added) [94]:

The land in Ireland is infinitely more peopled than in England; and to give full effect to the natural resources of the country, a great part of the population should be swept from the soil into large manufacturing and commercial Towns.

I can’t think that Mokyr truncated this phrase himself but, at least, he was careless in reporting something that he read somewhere without worrying too much about verifying the original source. In any case, you see that Malthus wasn’t proposing to kill anyone; rather, he was proposing the industrialization of Ireland in order to create prosperity in the country.

Nevertheless, legends easily spread on the web and the truncated sentence reported by Mokyr can be found, repeated over and over, as a demonstration that Malthus was proposing the extermination of the poor and that he convinced the English government that it was a good idea to do exactly that with the Irish. But Malthus never said anything like that and, about the English government, surely it was careless and inefficient in dealing with the Irish famine, so much that claiming that it was evil may not be totally farfetched. But it is surely too much to conclude from these data that the members of the British government collected in a smoke-filled room in London to plan the extermination of their unruly and overprolific Irish subjects. The mismanagement of the Irish famines is best explained by incompetence rather than evil intentions, another example of how difficult it is, even in modern times, to understand the behavior of complex systems without resorting to teleological arguments.

There remains the question of why Ireland was so badly struck while other European regions , even more densely populated, were not. It is because famines aren’t just a question of overpopulation: no, the problem is much more complex. We need to take into account many more factors than just population and agricultural production; we need to consider the whole economic system. If we do that for Ireland at the time of the famines, Malthus and Mokyr turn out to be in agreement with each other, since they both note how poor Ireland was. That doesn’t mean that the Irish were starving all the time. On the contrary, Irish farmers were often reported to be in good health and in good physical shape, better than their English neighbors; not surprising considering the working conditions of the British miners and factory workers. But poverty in Ireland was the unavoidable result of the economy being nearly completely rural. Ireland didn’t have an industrial and commercial system comparable to the one that the neighboring England did. That was the result of two factors: the first that Ireland didn’t have the coal resources that England had and which England used to start the industrial revolution. The second that Ireland couldn’t match England in military terms. After the conquest by the English army led by Oliver Cromwell (1649–1653), Ireland had become part of the possessions of the British Crown. It was never formally considered a colony but it was managed as such. England, clearly, had no interest in seeing Ireland developing an industrial and commercial base that would have made the Irish able to compete with their English masters and, perhaps, able to rebel against them.

So, Ireland remained a rural country well into the ninetieth century . It was mainly inhabited by “cotters,” small farmers who lived in simple cabins and rented one-two acres of land on which they cultivated enough potatoes to feed the whole family, normally paying the rent in labor. Such small plots of land were sufficient even for the large Irish families of those times, a small miracle created by the agricultural wonder of the time: the potato. It had been first introduced to Ireland as a garden crop, probably as early as in sixteenth century. By the late seventeenth century, potato cultivation had become widespread, but only as supplementary food while the main food of the Irish remained grain. In the eighteenth century, the potato started becoming the staple food of the poor [96]. In good times, the potato harvest in Ireland was reported to have been so abundant that the excess had to be thrown away; an action that, incidentally, invited another, later, teleological explanation of the famine, one that attributed it to the wrath of God against His excessively profligate children. But the yields of potato cultivation were amazing and there we have no reason to disbelieve the calculation made in 1834 by Reverend James S. Blacker (reported in Porteir [97]) showing that, by cultivating potatoes, Ireland could have sustained a population of 17 million people. In theory.

But theory is not the same thing as reality. It may well be that, theoretically, Ireland could have sustained a much larger population than it ever did but, in the real world, nothing ever works as perfectly as it does in theory. The problem, here, is one that’s often overlooked in these discussions: famines are not just a question of food production, they are a question of food supply; something different and much more complex. It is not enough to be able to produce crops; there must also be ways to distribute the food to the people who need it, ways to compensate for local productivity losses, ways to store the food, ways to avoid reliance on a single crop. But the Irish economy was so poorly networked that it just couldn’t do that.

The main problem was that the commercial infrastructure of Ireland was terribly underdeveloped, as Malthus himself had noted. Cotters cultivated potatoes and used them to feed their family; they didn’t need money to buy them. The other fundamental commodity they needed was fuel for their stoves and that they extracted themselves from peat reserves that were widespread and abundant. Again, they didn’t need money to buy fuel. Finally, they normally paid for the rent of their plots in labor rather than in cash. So, the Irish peasants could theoretically survive even without any money. Quite possibly, they would rarely, if ever, see any significant amount of cash in their lives. In a sense, they were still living in the early stages of the Holocene, when money had not been invented yet.

But a non-monetized economy is not the mythical “age of barter” of which you are told in the Economics 101 class. In the case of a failure of their crops, the cotters of Ireland had no money to pay for food produced somewhere else, and nothing to barter for it, either. So, local, small scale famines may have been more common than the large famines reported in history books. Sir Jonah Barrington tells us about the Irish peasants, “The only three kinds of death they consider as natural are–dying quietly in their own cabins, being hanged about the assize-time, or starving when the potato crop is deficient.” [95].

Ireland’s economy was so poorly capitalized that it didn’t even have a sizable fishing industry. The Irish fishing fleet of the ninetieth century was still based on the kind of boats called “Currachs” or “Curraghs,” a version of the Welsh “coracle.” These boats were made of a wooden frame covered with rawhide; fishermen were probably unable to afford to buy the wood that would have permitted them to build stronger boats. The curraghs are reported to have been seaworthy vessels, perfectly able to sail in the rough Atlantic waters. But they were not suitable for the kind of large-scale fishing that would have been needed to make a difference in terms of food supply. Apparently, the Irish fishing industry was so inefficient that, at the time of the Great Famine, most fishermen preferred to pawn their boats to buy food rather than attempting to obtain it by fishing [98].

The poor commercial system of Ireland made the loss of crops a practically unsolvable problem even when it was not affecting the whole island. During the Great Famine, the North-Eastern regions of Ireland were less affected than the South-Western ones. But if the people of, say, Connacht were starving, they had no way to buy food from the people of Ulster who may have had a surplus. The English landlords who controlled food production in Ireland would reasonably (in a purely commercial sense) prefer to export their excess food to England, where it could be paid in hard currency rather than giving it to the poor in Western Ireland, who had no way to pay for it. Even if they had wanted to send food to famine-stricken Western Ireland, the transportation system was poor. At the time of the Great Famine, there were only 70 miles of railroad track in the whole country, mainly in the Eastern region and no usable commercial shipping docks on the rugged coast of the Western districts. It is curious to note that this feature of the coast of Ireland is the result of the “isostatic rebound” of the island that took place after the end of the last ice age, some 12,000 years ago. Freed from enormous weight of the ice that had covered it, the island slowly rose up, creating the high coastline that we see today and which makes it difficult to build harbors. The Irish of the time of the Great Famine couldn’t know that their plight was caused, in part, by this ancient geological phenomenon.

So, famines were not the result of Ireland being overpopulated in a literal (and wrong) interpretation of Malthus’ ideas. In principle, the agricultural system of Ireland could have produced more than enough food for even the highest levels of populations ever reported on the island. But this theoretical supply was subjected to wide oscillations and distributing it was a difficult problem. Times of scarcity led to famines and times of overabundance led to a further problem: population growth. Since in good times food was abundant, for the Irish it must have seemed possible, perhaps even obvious, that their children would be able to find space for their own plot of land. People married young and families tended to be numerous and that lead to rapid population growth. In retrospect, it is obvious that this high natality was leading Ireland toward disaster, but it was only after the Great Famine of 1845 that the Irish understood the problem and greatly reduced their birth rates.

The misperception of the population problem on the part of the Irish people was also a consequence of deforestation, another plague of Ireland in those times. We don’t have to think that at the times of Cromwell’s conquest Ireland was still covered with the lush forests of the time of the mythical hero Cuchulain. But the data reported by Michael Williams in his Deforesting the Earth [99] show that Ireland in the seventeenth century still maintained about 12% of the land covered with trees, significantly more than most European countries of that time. These forests were an important economic asset during the eighteenth and ninetieth century: timber was exported, while charcoal was made from shrubs and used for producing iron. The Irish iron industry couldn’t compete with the English one in terms of manufacturing heavy equipment and machinery, but Ireland had enough iron ore to keep the forges running, smelting iron for local uses and for export. The attitude of the English landlords of the time with regards to forests may be well summarized by a line that Jonah Barrington wrote in his Recollections [95], “trees are stumps provided by nature for the repayment of debt.”

We don’t have detailed data on the extent of deforestation in Ireland before the great famine; apparently, nobody would keep such a record at that time. But we can learn from Eileen McCracken [84] that, for instance, the Irish exports of timber went from more than 170,000 cubic feet in the mid-seventeenth century to nearly zero in 1770 (p. 113). Timber imports, conversely, grew nearly 20-fold from 1711 to 1790. Evidently, in the eighteenth century, Ireland was being rapidly deforested. We also learn from McCracken’s book that the Irish iron production died out in late eighteenth century, most likely because there was no more wood for making the charcoal necessary to smelt iron ore. The only quantitative data we have on the actual deforestation trends are from the extent of wood acreage on sale advertised in newspapers, again as reported by Eileen McCracken. The data can be plotted as shown in (Fig. 3.19).

We may reasonably assume that the wood acreage on sale is proportional to the deforestation rate and, therefore, we see one more confirmation that Ireland was being rapidly deforested in the mid-eighteenth century. According to McCracken, at the beginning of the ninetieth century, no more (and probably much less) than 1% of the Irish land was still covered with trees. The situation was noted by Arthur Young, an English writer, who reported in 1776 in his Tour of Ireland that “the greatest part of the kingdom exhibits a naked, bleak, dreary view for want of wood.”

These data tell us something about the devastation that was wrecked on the Irish land. Not only were the trees cut, but native animal species were exterminated without regret. The last wolf of Ireland is reported to have been shot in 1770. Even squirrels and deer went extinct, to be reintroduced only in the twentieth century. The same destiny was reserved for the “woodkernes,” dispossessed Irish people who had taken to the woods and lived by expedients and banditry. We may be tempted to see these forest dwellers as romantic freedom fighters, an Irish version of Robin Hood and his merry companions. But the woodkernes were never sung as sylvan heroes; rather, they were lumped together with the wolves and exterminated as outlaws. They are reported to be still existing up to the end of the eighteenth century 100 (p. 60 of The Montgomery Manuscript 100). But, just as it is difficult for us to imagine Robin Hood without the forest of Sherwood, the Irish woodkernes couldn’t exist without the Irish forests and no mention is made of them anymore in later times.

So, deforestation in Ireland operated as a diabolical machine that freed space for cultivations and that generated population growth. Eventually, that could have led Ireland to reach its “Malthusian Limit” once all the forests were cut and all the lands were occupied by the potato cultivations. But this theoretical limit was never reached; the practical limit of population growth is dynamic, not static as Malthus thought. What was reached was the “resilience limit” of the land, the capability of the system to adapt to local disruptions of the food supply. This limit was reached more than once, starting with the early eighteenth century, when the population was around three million, that is around 20% of the 17 million people that Blacker had calculated as the upper limit (the true Malthusian Limit) to the island’s population [97]. At the time of the Great Famine in 1845, the Irish population was still less than half of the theoretical limit, but that was more than enough for generating a disaster. One more case of that “rapid ruin” that Seneca mentioned.

3.4.1.1 The Land of the Rising Sun

Godzilla is the quintessential monster of Japanese science fiction movies. It’s an ugly and gigantic creature, the fantasy incarnation of the fear of the atomic holocaust that for the Japanese is something all too real after the nuclear bombing of the cities of Hiroshima and Nagasaki, in 1945 . Even before these terrible events, Japan was a land known for its frequent natural disasters: earthquakes, tsunamis, and volcanic eruptions; tragedies that continue to occur to this day. Still, these spectacular disasters seem to have had little or no effect on Japan’s population in history. In particular, the Japanese seem to have been able to avoid the disastrous population collapses that were caused by famines and that were common in Ireland and in other countries during pre-industrial times. We can see in Fig. 3.20 how the Japanese population remained constant during the roughly 150 years of the duration of the Edo period (1603–1868), the same period that saw a succession of tragic famines in Ireland [101]. Not that famines were unknown in Japan during the Edo Period; several are reported in the records of the time. But they appear to have been mainly local and limited in extent.

So, Japan escaped the boom and bust cycles of many other pre-modern human civilizations and managed to create a stable and relatively prosperous society. Of course, that doesn’t mean that Edo Japan was Paradise on Earth. It was a tightly regulated society where individual freedom and individual rights were unknown concepts. Social inequality was also very pronounced and political power was concentrated in the hands of a small number of wealthy landlords. Still, we can learn a lot from ancient Japan on how to create a society that doesn’t overexploit its resources and maintains the natural wealth of its territory. The Japanese interpretation of the concept of sustainability made it possible for them to develop a remarkably sophisticated society. The skills of the Japanese craftsmen are still legendary today, while Japan attained achievements in poetry and figurative art that are a cultural heritage of all humankind: from Hokusai’s prints to Basho’s sophisticated poetry. In comparison, it is truly heartbreaking to note how the cultural treasures that Ireland had produced during its long history were destroyed by the greed and the carelessness of the foreign rulers of Ireland.

So, how could the Japanese attain sustainability whereas Ireland couldn’t? It is, of course, a complex question, but I can list here the main factors that differentiated Japan and Ireland during the ninetieth century.

1.
Japan had a strong national government. Ireland was governed by a different country.
2.
Japan had a well-developed commercial system and a national currency. Ireland had neither.
3.
Japan was isolated, practicing no commerce with other countries. Ireland was integrated with the British worldwide commercial system.
4.
Japan is a country of steep mountain ranges and low coastline. Ireland is mainly flat, with high coastlines.

About the first point, governments are not normally benevolent organizations but they have no interest in seeing their subjects going through population booms and busts. They encourage population growth only when they see it as an asset against an external enemy but that was not the case of Japan during the Edo period; a peaceful country that had no need of cannon fodder. The presence of a strong national government and the economic isolation of the country also affected the management of the Japanese forests. Since Japan didn’t export anything, there was no interest in producing more timber than was locally needed. In addition, in a mountainous (and rainy) land such as Japan, unrestrained cutting of the forest would rapidly generate disastrous erosion phenomena that would damage agriculture. That’s an immediate economic damage for the landlords and the Japanese government enacted truly draconian measures to protect forests: the unauthorized cutting of trees could be punished by death. It was a successful policy and it is reported that nearly three-quarters of the Japanese territory were covered with forests during pre-modern period. That not only saved the Japanese forests, but it had the side effect that the availability of timber made it possible to build large fishing and commercial boats. Japan also had better ports than Ireland because of its flat coastline. Geology had been favorable to the Japanese archipelago that had never been covered with an ice-sheet during the last ice age and that had not undergone the process of isostatic rebound that had generated the high coastline of Ireland. The availability of good harbors led to a well-developed fishing industry that could even engage in whaling, a traditional activity whose origins in Japan go back to the times of the first emperors. Fishing remained a precious source of protein for the Japanese population over the whole Edo period and it remains so even today. Whale meat is not eaten anymore in significant amounts in Japan, but an old generation of Japanese still remembers how common it was after the second world war.

Another advantage of Japan over Ireland was its well-developed national commerce . Japan was a mountainous country, but that didn’t prevent the Japanese from building roads and the harbors were exploited for transporting all sorts of bulky goods. Edo Japan was a throbbing economic machine and we can still see that on the Japanese prints of the time: We can still see snapshots of the bustling commercial activity taking place along the Tokaido road; one of the “five roads” that linked the cities of the central island of Japan. The Japanese archipelago stretched over a wide range of latitudes, generating a variety of local climates and conditions and that favored the production of different agricultural crops. The Japanese never fell into the monoculture trap; they produced rice, wheat, barley, buckwheat, and millet. This differentiation made agriculture resilient to shocks due to pestilences and climatic variations. The Japanese monetary system was also well developed. It was sometimes based on rice but, mainly, it was based on precious metal coins that were, initially, made using locally mined silver and gold. As the mines were depleted at the beginning of the ninetieth century, the Japanese government forbade the export of precious metals and succeeded at maintaining a good supply of currency and hence at keeping the commercial system running.

The most important lesson that we can learn from Edo Japan is how it managed to maintain a stable population . For us, having in mind the population explosion of humankind in the ninetieth and twentieth century, the stability of the Japanese population may seem surprising. We tend to think that people, normally, tend to reproduce “like rabbits” and that human populations always tend to grow unless kept in check by wars, famines, and pestilence; just like Malthus had proposed. But the Edo period in Japan is a direct confutation of Malthus’ theory: the Japanese avoided the Malthusian trap by keeping birthrates low by means of contraception (even though, occasionally, they had to recur to infanticide [102]). How could they do that while the Irish couldn’t? Maybe it was a question of religion. The Irish were Catholic, while the Japanese were Buddhist and, traditionally, these religions had different views about contraception and family size. But that doesn’t seem to be a good explanation. The Irish were Catholic at the time of the great famine and they remained Catholic afterward but birthrates in Ireland dropped dramatically. The Japanese practiced Buddhism during the Edo period, when birthrates were low and continued practicing it after the second world war when birthrates dramatically shot up. So, there is no real correlation between religious beliefs and birthrates.

It seems that we need a different explanation for the low birthrates of Edo Japan and we can probably find it in what we know about the reproductive strategies among living creatures. In all animal species, parents have a choice (not necessarily a conscious one) of how to employ their limited resources. One strategy consists of in having as many offspring as possible, knowing that they will have to fend for themselves and hoping that at least some of them will survive. This is called the "r-strategy", also known as the "rabbit strategy”. The other strategy consists of investing in a small number of children and caring for them in such a way to maximize their chances of reaching adulthood. This is called the "K- strategy" or the "Elephant strategy". The choice of the reproductive strategy depends on the situation. Let me cite directly from Figueredo et al. [103]

......all things being equal, species living in unstable (e.g., fluctuation in food availability) and unpredictable (e.g. high predation) environments tend to evolve clusters of “r- selected” traits associated with high reproductive rates, low parental investment, and relatively short intergeneration times. In contrast, species living in stable and predictable environmental conditions tend to evolve clusters of “K-selected” traits associated with low reproductive rates, high parental investment, and long intergeneration times.

Humans, clearly, behave more like elephants than like rabbits. The number of children that a human female can give birth to is limited, and it is normally a good strategy for her to maximize the survival chances of fewer children, rather than trying to have as many as possible. So, for most of humankind’s history, a family or a single woman would examine their environment and make an estimate of what chances their (or her) children have to survive and reach adulthood. In conditions of limited resources and strong competition, it makes sense for parents to maximize the health and fitness of their children by having a small number of them and caring for them as much as possible. This seems to be what happened in Japan during the Edo period: facing a situation of limited resources, people decided to limit the number of their children, applying the "K-strategy."

The opposite is true for periods of abundant resources and scarce competition. When the economy is growing, families may well project this growth to the future and estimate that their children will have plenty of opportunities. In this case, it makes sense to have a large number of them; that is, to apply the "r-strategy". This phenomenon is clearly visible in the demographic data after the drastic population reductions caused by epidemics or wars. After these events, the number of births tends to increase and the population reaches again, and often surpasses, the previous records. We shouldn’t think that families consciously seek to affect the population of their society, but they can probably see the open slots (homes, land, jobs, etc.) left by the disaster and they correctly reason that their offspring will be able to profit from these opportunities. It may well be that the tragic famines of ancient Ireland were the result of the misperception of future opportunities that arose from the cycles of boom and bust of the Irish agriculture. On the contrary, the Japanese of the Edo period lived in a nearly zero-growth economy and they perceived the need to have few children in order to give them the best opportunities for the future. It was a successful strategy for one and a half century.

If we examine the current population trends of the world’s population in view of these considerations, we see that we are living in a society that looks more like ninetieth century Ireland than Edo Japan. The dramatic growth of the world’s population during the past 1–2 centuries is the result of the increasing consumption of fossil fuels that generated an abundance never experienced before by humankind except, perhaps, when our hunter-gatherer ancestors entered the previously uninhabited American continent. Everywhere, people reacted by filling up what they saw as opportunities for their children. Japan, too, built up its economy on its national coal resources and experienced a burst of rapid population growth. By 1910, the Japanese population had reached 50 million people, twice that of the Edo period. It kept climbing with the transition from a coal based economy to an oil-based one, reaching the current value of about 127 million people (2015), five times larger than it was during the Edo period. But, with the second half of the twentieth century, economic growth slowed down and the Japanese started to perceive that the world was rapidly filling up. The result was the "demographic transition," in Japan, occurring also in many Western countries. This transition is normally explained as directly related to increasing wealth, but that we may also see as the result of a perception of the future that was seen as less rosy than before. Today, Japan has one of the lowest birthrates in the world and its population has started declining. We don’t know what the future trend will be for the rest of the world, but it is happening in many countries, for instance in Italy [104].

We may conclude that humans are intelligent creatures and that, within some limits , they choose how many children to have in such a way as to maximize their survival probabilities. The human population tends to grow in a condition of economic growth, but it tends to stabilize by itself in static economic conditions. So, if we could stabilize the world’s economic system, avoiding major wars and the need for cannon fodder, then the human population may well stabilize by itself, without any need for a top-down intervention by governments to force a reduction in birthrates; something that most people correctly consider as a nasty idea to be avoided. Unfortunately, we don’t know if this stabilization will be possible at all or even fast enough to avoid the overshoot condition that would generate the return of the periodic collapses that have been troubling human populations throughout their history. And if we can’t attain a stabilization, the Seneca collapse of the world’s population may be just around the corner.

3.4.1.2 Famines to Come

Is the age of the great famines over? Maybe that’s the case, since there has not been a major famine in the world since the 1980s (Fig. 3.21). Nearly 40 years without famines may not be enough to say that the problem is gone forever, but it is still a remarkable achievement for humankind considering that periodic famines have been common in history from the beginning of agriculture, some 10,000 years ago. The disappearance of famines is often attributed to the effect of the “Green Revolution,” a series of technologies developed during the second half of the twentieth century that greatly improved agricultural yields. But this cannot be the only factor; as I mentioned earlier about the case of Ireland, the question of famines is not about food production but about food supply: it is useless to produce abundant food if it can’t be distributed to those who need it. So, the current world situation may be due in large part to an improvement of the capacity of storing and distributing food, even though it is also true that agricultural yields have been steadily improving during the past decades.

We can find the roots of the world situation in terms of food supply in the development of the system called “Globalization” . Today, the whole world is connected by means of a commercial system mainly based on maritime transportation. Bulk carriers transport grain, coal, oil and other bulk commodities, while container ships carry all kinds of goods over long distances on the sea. Once arrived at the harbor of destination, the containers are transferred to local hubs, moved to nearby areas by means of large trucks, and finally distributed to retail shops everywhere by small trucks. All this is made possible by the existence of a control element in the system: the globalized financial system. The integration of the regional economies into a large worldwide system has made it possible for anyone to purchase food from anywhere in the world. In this way, the consequences of local reductions of food production have been minimized.

Even people who are too poor to buy food at market prices can survive because food relief organizations ship food all over the world and distribute it for free or at low prices. There exist today 27 such worldwide organizations [105] whose budget is in part provided by private donors and in part by governments. Among these, the “World Food Program,” (WFP) a branch of the United Nations, is probably the world’s largest organization dedicated to promoting food security. The WFP reports on its website ( www.wfp.org/ ) to have had a budget of 4.38 billion dollars in 2014, to have distributed 3.5 million tons of food worldwide, and to have provided food relief for more than 97 million people.

There is certainly a strong humanitarian element in the work of the food relief agencies , but it is also true that their purposes are economic and political as well. The system was created in the 1950s in the US with the explicit purpose of preventing communism from spreading to poor countries (apparently, the idea was to pay people to not become communists!). In time, the system has evolved into something that benefits large agribusiness producers who, otherwise, would have serious problems in dealing with their excess production. One of its negative side effects has been to make many poor countries totally dependent on foreign aid, while impoverishing farmers and destroying local agriculture [106]. In addition, the problem of hunger has not been really solved. The United Nations Food and Agriculture Organization (FAO) estimates that about 800 million people were suffering from chronic undernourishment in 2014–2016 and that about half of the world’s human population is suffering from occasional periods of hunger [107]. Of the remaining half, many are not being nourished in a balanced and healthy way because obesity and type II diabetes are rampant diseases.

All that should not detract from the success of a stupendous food supply system which had never existed before in the history of humankind and of which we should be proud. If the system could be made to keep operating for a long time in the future, we might imagine that the world’s population could follow the same trend that of the Japanese population during the Edo period. That is, it could go through a demographic transition that would reduce birthrates and reach a stable level, compatible with the available food supply. It is a trend that we are already seeing in many rich countries of the West, where the population is stabilizing or even decreasing. The result could be a world population reaching a peak perhaps at around 9–10 billion people by the end of the century and remaining stable afterward, maybe even declining. Then, there would be no population bomb and periodic famines would remain a thing of the past. In such case, we would never see a Seneca collapse of the world population.

Unlikely? Perhaps, but not impossible, either. After all, a resilient system such as the Roman Annona lasted for almost a half millennium before collapsing. So, why couldn’t the modern global Annona last for comparable periods? The problem is that, unfortunately, our food system has elements of fragility that the ancient Roman system didn’t have. The Roman sailing ships that carried grain over the Mediterranean Sea didn’t need fossil fuels, but the modern container ships and bulk carriers do. Also, the trucks that transport food on land use diesel fuel, but also need fossil hydrocarbons for the rubber of the tires and for the asphalt of the roads. In modern agriculture, fossil fuels are needed for almost the whole production process. They are used for the machinery used in the fields, to manufacture fertilizers and pesticides, to extract mineral fertilizers and to transport them from mines to the fields. By the 1970s, Carol and John Steinhart estimated that the food supply system in the U.S. utilized 12.8% of the total energy consumed in the country [108]. In 1994, the food system was estimated to consume 17% of the total [109]. Today, it is probably even more. These are huge amounts of energy, utilized not just for producing food, but for storing, packaging, and distributing it. Take away the fossil fuels, and the system immediately grinds to a halt. Yet, we need to wean ourselves from fossil fuels to fight climate change and, even if we don’t do anything about that, depletion will take care of doing it for us. The problem affects the whole food production system. No fossil fuels, no food.

To these already huge problems, we may add the negative effects that climate change may have on agriculture in the form of droughts and the disruption of stable weather patterns. Think of how important the yearly monsoon is for the Indian agriculture and imagine what would happen if it were to disappear or even simply be reduced in intensity. An ever more serious threat the sea level rise. At present, the trend is on the order of 1–2 mm per year and that doesn’t seem to be worrisome. But this is a typical case of the Seneca Trap: you see gradual ongoing changes, but you don’t see the abrupt disaster looming a little farther ahead. Here, the melting of the world’s glaciers could become so rapid, even abrupt, that the sea level rise could make most of the world’s harbors unusable [111]. In this case, the stupendous globalized system that ships food everywhere wouldn’t work anymore. The ensuing disaster is barely imaginable.

Can we think of technological solutions to take care of these problems? In principle, yes. It is possible to imagine that every single fossil technology in the food supply system could be replaced with an equivalent renewable one [110]. Diesel powered tractors could be replaced with electrically powered ones that wouldn’t necessarily need bulky and expensive batteries by getting the energy they need from aerial wires; a technology that was tested already in the 1930s. Artificial fertilizers could be produced without the need of fossil energy , for instance, nitrates could be produced using renewable-produced hydrogen as feedstock, rather than using methane as it is done today. Other mineral fertilizers, such as phosphates, could still be extracted using electrically powered equipment, even though depletion would force farmers to use smaller and smaller amount and to recycle them efficiently. There also exist ways to produce pesticides starting from biological precursors, rather than fossil ones. Then, ways to transport food worldwide could be found, even though the bulk carriers of today would have to be scrapped and replaced with something smaller and less polluting, maybe a new era of sailing ships is coming. And floating harbors could be imagined to cope with the rising sea level. Of course, the costs of all this is huge, but it is not an impossible transition if it were realized in parallel with the introduction of new forms of agriculture that would be more respectful to the fertile soil and rely less on artificial fertilizers and pesticides. Much work is being done in this field and new forms of agriculture, for instance permaculture, have been proposed and are being tested.

Unfortunately, even if all the technical problems to a sustainable agriculture could be solved, there is a subtler and possibly more dangerous problem with maintaining the food supply system: the control of the system. We saw in an earlier chapter how the Roman Empire may have been doomed because of a loss of control of their financial system. Something similar could happen today to the global food supply system; controlled as it is by the world’s financial system. The problem is that, today, food is shipped worldwide because someone is paying for it. Take away the ability to pay and the whole system disappears; another case of a Seneca Collapse. We saw what happened with the financial crisis of 2008, when the world’s commercial system nearly came to a grinding halt and it is not farfetched to think that this might happen again, perhaps in an even more disastrous form. More ominously, the world’s food relief agencies exist because shipping food for free to the poor of the world is generally considered a good thing to do in the West. But, with the Communist threat gone, the powers that rule the world may well decide that it is more convenient for them to deal with the poor by using drones to bomb them to smithereens. Without arriving at such extremes, the food relief agencies need public money and they might easily be de-financed in our times of tight government budgets. Eventually, it is perfectly conceivable to return to a worldwide situation of war and conflicts where it could again become fashionable to win wars by starving one’s enemies, as it was common in the past.

For the past 30 years or so, the world food supply system has managed to cope with an increasing world population. It has done that by a combination of technological progress and adaptation. Today, it is under heavy strain and we can only hope that it will be possible to avoid a Seneca collapse of the world supply system. If it happens, that would probably have as a consequence the largest and most disastrous famines ever experienced in human history.

3.5 Depletion

Coal, in truth, stands not beside but entirely above all other commodities. It is the material energy of the country–the universal aid–the factor in everything we do. With coal almost any feat is possible or easy; without it we are thrown back into the laborious poverty of early times.

William Stanley Jevons, The Coal Question, 1865

3.5.1 The Shortest-Lived Empire in History

On June 10, 1940 , Italy declared war on the United Kingdom. It was a startling development in the relations of two nations that had not been fighting against each other from the time when Queen Boudicca led the Britons against the invading Roman legions, in 60 or 61 CE. In modern times, the British had discovered that they loved the Italian culture and art, the Italian climate, and the fact that, unlike in Britain , homosexuality was not illegal in Italy. As a result, the British had been flocking to Italy from the time when the “Grand Tour” had become fashionable, during the eighteenth century. You may read the 1908 novel by E. M. Forster, A Room with a View, to understand the peculiar relationship that existed between Italy and Britain around the beginning of the twentieth century, with the British becoming “Italianized” in their love for Italian culture, and the Italians becoming “Anglicized,” acquiring uses and traditions brought by the British visitors. But all this friendship and reciprocal love was thrown away in a single stroke in 1940 by a war that lasted for four years and involved all the horrors of modern war, including reciprocal aerial bombing. Not everyone remembers today that the Italian air force had participated in the Battle of Britain together with the German air force, supplying a small but not insignificant number of bombers. The British retaliated with their own bombing campaign that left the Italian cities mostly in ruins.

What had happened that had turned an old friendship into so much enmity? It was a manifestation of the awesome power of fossil fuels that generate wars almost as if they have an evil mind of their own. It is a story that starts in the eighteenth century, when Britain was engaged in the difficult but rewarding task of conquering the whole world; it was the time of iron men and wooden ships. The military strength of the powers of the time depended on a crucial commodity : wood. It was used to make ships, but also to make the charcoal that was needed for smelting iron and make weapons. Wood was so important that supplying enough of it for the military needs of a country would put its forests at risk. Cutting too many trees could easily lead to soil erosion and to desertification; a destiny that had already destroyed more than one Empire in the past. One of the first cases was that of the Athenian Empire of the times of Pericles and Thucydides while, closer to our times, it was the Spanish empire that was to succumb to deforestation and soil erosion after having peaked at some point during the sixteenth or the seventeenth century. But, in the eighteenth century, Britain escaped that destiny by using something that the earlier empires didn’t have: coal.

Coal was abundant in England and that was the origin of the British power . Coal built the British industry, the British prosperity, and the British empire, the first global empire in history. With coal, the British didn’t have to worry about deforestation and they always had plenty of resources for their industry. Coal also ushered in the age of iron ships that replaced the old wooden ships and ruled the waves for Britannia. But British coal could also be exported. It was too bulky and heavy to be transported on land over long distances, but there was no such limit for moving it on the sea by means of sailing “coaler” ships. So, British coal could create an industrial economy even in countries that had no coal. That set a geographical limit to industrialization: above a certain latitude, the climate was wet enough that it was possible to use waterways to distribute coal inland. Below a certain latitude, the climate was too hot and too dry to build waterways: coal could be brought to harbors but could not be distributed inland. That made it impossible to build a modern economic and military power. Those countries that were located below the “waterway line,” for instance those in North Africa, had little or no hope of escaping the destiny of becoming colonies of the burgeoning European Empires.

The Italian peninsula was in a special geographic position with respect to the waterway line: it was cut in half by it. So, Northern Italy had waterways and could industrialize by importing British coal. That led to an increasing economic wealth and military power of the Northern Italian regions. Intellectuals in Southern Italy had noted the situation and complained bitterly about it [112], but couldn’t change the laws of geography. Eventually, Piedmont, in the North, exploited its economic and military superiority to take over the whole peninsula by defeating the Kingdom of Naples that ruled most of Southern Italy. Britain played a direct role in these events by supporting the Piedmont-sponsored adventure of General Garibaldi who led an army of volunteers landing in Sicily in 1860. Garibaldi’s army defeated the Neapolitan army in a series of battles and, eventually, consigned Southern Italy to the king of Piedmont, who then proclaimed himself “King of Italy.”

Britain supported the birth of Italy as a unified country in part for idealistic reasons but also for practical ones: a unified Italy was a strategic ally of Britain in the Mediterranean region. For Italy, the alliance with Britain was also an advantage, since it provided the country not only with the coal needed for its industry but also with the military backing that was necessary to stand up to France, a theoretically friendly country but also a much more powerful one. The British-Italian alliance was solid and long-lasting. During the hard challenge of the First World War, Britain and Italy turned the Mediterranean Sea into a lake for the Allied Powers. In 1917, when the Italian army was routed by the Austrians, the British sent troops to Italy to help the Italians to stop the Austrian advance.

Everything seemed to go well in the best of worlds until, in the 1920s , something went wrong and the Italians started to complain that Britain wasn’t supplying them with the coal they needed. D.H. Lawrence, in his Sea and Sardinia (1921) tells us that the coal problem and the evil English machinations were among the main subjects of conversation among Italians at the time. In the press, the British were often accused of being jealous of the growing Italian power and Britain started to be referred to as the “Perfidious Albion,” an Anglophobic term that goes back to Medieval times. In Britain, instead, the Italian resentment against Britain was consistently misjudged; nobody seemed to believe that it could become so entrenched and strong that it would eventually lead to war.

Had the people in power at the time understood the depletion issue , maybe something could have been done to avoid the clash that was coming. But they didn’t, and that may have been unavoidable: mineral depletion is a subtle problem. It is because it is so gradual; there never comes a moment when the mineral industry “runs out” of a resource. What happens is that the best resources, those that are pure, concentrated, and easy to extract, disappear. And what’s left are the resources which are dirty, dispersed, and more expensive to extract, process, and purify. At some point, the cost of production becomes so high that the task is not profitable anymore. Then, extraction must slow down or even stop, even though there remain theoretically extractable resources underground. This is a concept that’s especially hard for politicians to understand since their mindset makes them tend to look for yes/no answers to their questions. Facing problems with the supply of a mineral resource, politicians would ask their experts, “is there still coal (or oil, or whatever) left to be extracted?” And the only answer that can be given to this specific question is “yes.” At this point, the politicians would conclude that if coal (or oil, or whatever) is not extracted, it is because of machinations by the unions, laziness of the workers, enemy sabotage, or something like that. But there are no simple answers to complex problems, and reality has its own way to assert itself, even though politicians may not understand it.

So, the question about coal depletion had been answered long before the symptoms started to appear in Britain. It was an intuition by William Stanley Jevons, who was not only the first to recognize the depletion problem, but also the first to try to estimate its consequences. In 1865, he wrote The Coal Question, where he sketched out the future history of British coal. He lacked the mathematical tools that would have allowed him to make quantitative extrapolations, but he correctly estimated that coal production in Britain could not last for much more than a century. Indeed, a century after Jevons had published his book, the British coal production was in terminal decline. Today, Britain still produces some coal but the last deep pit mine closed in 2015 [113] and the time when Britain will produce no more coal cannot be too far away in the future (Fig. 3.22).

Because of the ongoing gradual depletion, by the 1920s the British coal production had reached its maximum historical value and couldn’t increase anymore. Probably as a consequence, the British coal industry experienced a series of strikes and general turmoil that created strong oscillations in its output and that had repercussions for Britain’s capability to export coal. It was also the root cause of wave of rage that swept Italy at that time. The Italians couldn’t understand that Britain was not withholding coal because the British hated Italy, but because coal production in Britain had reached the limits imposed by depletion, as Jevons had correctly predicted almost a century before. Unfortunately, the real problem was never recognized, and that had political consequences.

The first of these consequences was the Italian invasion of Ethiopia , in 1935. At first sight, this ill-conceived venture doesn’t seem to have had anything to do with the coal supply problems that Italy was experiencing. But, in reality, coal was behind everything that happened in those years. Without the abundant coal supply that had been available in earlier times, economic growth had stopped in Italy and the people were becoming angry. The government was afraid it could become the target of that anger and thought that it was a good idea to direct it against a country that seemed to be an easy military target, Ethiopia. The adventure was presented to Italians as a way to find a “place in the sun” (“un posto al sole”) for their growing population; a way to recreate the ancient and glorious Roman Empire and, more than that, as a slap in the face against those perfidious British people who were withholding the coal that Italy justly deserved. The idea was to show them that Italy could build its own Empire. Most Italians seemed to believe in this propaganda campaign and they rallied around the flag, supporting the war.

In military terms, Ethiopia turned out to be a weak opponent as the Italian government had hoped. The Ethiopians put up a spirited resistance, but they were rapidly overwhelmed by the more modern weaponry fielded by the Italians and the victorious Ethiopian campaign led to the dubious honor for the king of Italy to take upon himself the title of “Emperor of Ethiopia.” That was duly exploited by government propaganda and that made Mussolini’s government hugely popular in Italy. But the war was also a colossal strategic mistake. There were reasons why Ethiopia in the 1930s was one of the very few non-European regions of the world that had not been colonized by European powers; the main one being that it was so poor, with no mineral resources of note. In Italy, people may have believed in the government’s propaganda that described Ethiopia as a place where Italian farmers could settle. But, in the real world, it made no sense to send people from Italy to a country that was already populated to the maximum level that the local resources could support. So, the conquest of Ethiopia turned out to be not only a military disaster for Ethiopia but also an economic disaster for Italy, placing a tremendous burden on the state’s finances. It is reported that, by the late 1930s, almost 25% of the Italian government’s budget was dedicated to bearing the costs of the military occupation of the overseas colonies [114]. That may well have been the reason why Italy arrived so unprepared and so militarily weak at the start of the second world war.

By conquering Ethiopia , Italians had thought that they would gain an empire and, in a limited sense, they did. But they forgot that there was already an empire in the world at that time. The British Empire was not only much more powerful than the tiny Italian Empire but also it didn’t take so lightly Italy’s attempt to become a rival power. So, in 1936 Britain enacted a coal embargo, stopping all exports to Italy. That dealt a severe blow to the Italian economy, equivalent to the “oil embargo” enacted by the OPEC countries against the West in the 1970s. The Italian people couldn’t understand the reasons for what was happening; they felt that the honor of the nation had been stained and they reacted furiously. Still today, in Italy, you can find stone slabs in the squares of town that commemorate how the Italian people had surged to respond to the challenge of the sanctions. If nothing else, this story shows how economic sanctions usually obtain results opposite to the intended ones, often leading to war. One of the results of the reaction against the British blockade was a series of measures taken by the Italian government, collectively called "autarchy,” designed to make the Italian economy run without the need of importing mineral commodities. But ideas such as making shoes out of cardboard, clothes out of fiberglass, and running cars on nitroglycerin were mainly propaganda and never really worked. The attempt to develop new coal mines in Italy met with even less success. The Sulcis mine in Sardinia was the main domestic source of coal, but it was a toy mine in comparison with the British and German mines of the time. At most, during some particularly favorable periods, the Sardinian mines could produce about 10% of Italy’s coal consumption between the two world wars [115].

The ultimate consequences of the coal embargo were exactly the opposite of what the British had hoped. Instead of bowing down to Britain, the Italian government preferred to befriend the other world power capable of supplying coal to Italy. In the following Fig. 3.23, we see what was going on: by the late 1930s, Italy had managed to replace British coal with German coal, but that had a political cost that had to be paid, one day or another. The events played out as if following a prophecy written down long before.

A contemporary source, Ridolfo Mazzucconi, reports that

England ordered, with a quick action, the suspension of the shipping of German coal directed to Italy from Rotterdam. As a compensation, England offered to replace Germany in coal shipping. But this service was subordinate to conditions such that accepting them would mean to be tied to the British political interests and grievously damage our war preparations. The Fascist government responded with suitable roughness; and German coal, which couldn’t come anymore by sea, found its most comfortable and short road via the Brenner pass. This matter of coal was a healthy and clarifying crisis of the political horizon. On March 9 and 10 (1940) Ribbentrop was in Rome and the visit gave rise to a clear and precise statement. The axis was intact. The alliance of Germany and Italy was continuing. A few days later, on the 18th, Mussolini and Hitler met for the first time at the Brenner pass and then even the blind were forced to see and the dim witted to understand.

Ridolfo Mazzucconi, from Almanacco della Donna Italiana 1941, translation by the author.

The war started and, without national sources of coal, Mussolini’s Italy had no more chance against a coalition of coal-producing powers than Saddam Hussein’s Iraq had in 2003 against the United States. We all know the resulting disaster: Italy was not just defeated, but thoroughly humiliated. In the end, the Italian Empire enjoyed the only notable record of having been, perhaps, the shortest-lasting empire in history: about five years. And it collapsed in a little more than one year (talk of Seneca collapses!). It was, perhaps, the first case of social and political collapse caused by the depletion of fossil carbon resources, an ominous hint of what may happen to the modern Global Empire in the future.

3.5.2 Tiffany’s Fallacy

At the public debates that deal with energy, it is common to hear statements such as “oil will last for 50 years at the current rate of production.” You can also hear that “we still have one thousand years of coal.” (Donald Trump stated exactly that during the US presidential campaign of 2016). When these statements are uttered, you can sometimes hear the sigh of relief of the audience, the more pronounced the surer the speaker appears to be. Instead, the people who are worried about climate may react with a gasp of disappointment. Both these reactions are understandable if these assessments of long duration of fossil fuels were to correspond to what we can expect for the future. But can we, really?

The essence of propaganda, as we all know, is not in telling lies but in presenting only one aspect of the truth. That holds true also for the depletion debate. Saying that a certain resource will last for decades, centuries, or even longer is not a lie but it is not the truth, either. These numbers are based on just one aspect of the problem and on highly simplified assumptions. It is the concept of “reserves to production ratio” (R/P) that gives you a duration in years of the resource, supposing that the size of the reserves is known and that extraction will continue at the current rates. Normally, the results of these estimates have a comfortable ring to it. According to the 2016 BP report (www.BP.com), the global R/P ratio for crude oil calculated for “proven reserves” is about 50 years; that for natural gas is about the same. Coal is reported to have an R/P ratio of more than a hundred years. If the “possible reserves” are added to the “proven reserves,” coal turns out to have an R/P ratio of the order one thousand years or even more and that’s probably the origin of Mr. Trump’s recent statement.

What most people understand from these data is that, when it comes to oil, there is nothing to be worried about for at least 50 years and, by then, it will be someone else’s problem. And, if we really have a thousand years of coal, then what’s the fuss about? If the Germans could produce gasoline out of coal during World War II, surely we can do the same today and with that we can happily keep driving our SUVs for a long time, if not forever. Add to this the fact that the R/P ratio has been increasing over the years and you understand the reasons for a rather well-known statement by Peter Odell who said in 2001 that we are “running into oil” rather than running out of it [116]. In this view, extracting a mineral resource is like eating a pie: as you have some pie left, you can keep eating. This peculiar pie that’s crude oil even has the characteristic that it becomes bigger as you eat it!

If that sounds to you too good to be true, you are right ; the optimistic vision that sees oil resources as a pie also firmly places the pie the sky. To raise a nagging question, let me cite a report that appeared in 2016 on Bloomberg (not exactly a den of Cassandras), titled Oil Discoveries at a 70-year low [117]. The data show that, during the past few decades, the amount of oil discovered is way below the amount produced. In other words, the new discoveries are not sufficient to counter the depletion of the old wells, a fact that had been noted many times even before the Bloomberg article and that continues to this day, with 2016 hitting an all-time low in terms of oil discoveries. So, if we really have 50 years of proved reserves, where are they? If we can’t find them, clearly, we are not by any means “running into oil” as Odell said.

Is this a conspiracy of the oil companies to keep oil prices high ? If that were the case, these mighty powers seem to have been especially inept at the task because the past few years have seen oil prices collapsing. But the crude oil world is rife with conspiracy theories; including the one that says that oil is “abiotic,” that is, it is continuously formed in enormous quantities as the result of inorganic processes occurring in the depths of the Earth; a “fact” that everyone would know were it not for the conspiracy of the oil companies. That’s just one of the many legends pervading the Internet (for a detailed discussion of the issue of “abiotic oil” see an article by Höök et al. [118]). These legends, as many others, are just more examples of our teleological approach to problems that consists in finding evil human agents for explaining them.

But there is no cabal, no hoax, no conspiracy in the estimates of oil resources. The problem is that using the R/P data to assess the future of mineral resources is misleading. I call this approach “Tiffany’s fallacy”. Perhaps you remember the 1961 movie Breakfast at Tiffany’s that featured the character played by Audrey Hepburn having breakfast while looking at the jewels on display in Tiffany’s windows. There is plenty of gold on the other side of the glass, but it would be a fallacy to assume that one is rich just because of that. To get that gold, one must pay for it (or use illegal and dangerous methods to get it). That’s the problem with the industry estimates of “proven resources.” These resources probably exist, but it takes money (and a lot of it) to find them, extract them, and process them. So, minerals are nothing like a pie that you can eat as long as there is some of it left. They are more like the jewels on the other side of the glass windows of Tiffany’s shop ; you may have them only if you have the money to pay for them. You may decide that you don’t need jewels and so you don’t have to buy them. But the world’s industrial system cannot survive without a constant influx of mineral commodities. Can the costs of mining remain affordable forever?

The question of paying for the costs of mining is not just a financial question. Money is an ephemeral entity that can be created by means of all sorts of financial tricks, but it takes material resources to extract minerals: drills, trucks, rigs, and every sort of equipment, including transportation and, of course, people able to use all of it. When we deal with energy producing minerals, such as oil, we can quantify the physical resources needed for their production in terms of the concept of “net energy,” first developed by Howard Odum in the 1970s [125]. It is defined as the difference between the energy obtained and the energy spent in any process. The net energy of extraction must be larger than zero for the process to be worth doing; in other words, you have to get more energy than you spend. It is the same problem that living creatures face: for a lion, hunting a gazelle makes sense only if the energy obtained from eating the gazelle is larger than the energy spent running after it. Another way to express the same concept is in terms of “EROI” or “EROEI”, which stands for “energy return on energy invested”, introduced by Charles Hall [26] as the ratio of the energy obtained to the energy spent. Obviously, the EROEI associated to the exploitation of an energy mineral, such as oil, must be larger than one if the task is to be worth doing. Today, the EROEI of crude oil is estimated at around 10–20 [126, 127]. It means that if you invest the energy of one barrel of oil to explore/drill/produce oil, you can get back the equivalent of 10–20 barrels. The EROEI of oil was much larger a century ago, on the order of 50 and perhaps more. But as oil is extracted and burned, there is less and less of it. And since the “easy” oil (close the surface, for instance) is extracted first, it follows that the EROEI of oil tends to go down with time. The EROEI of fossil fuels is a fundamental indicator of depletion and it has been steadily going down during the past decades; an indication of big troubles to come.

These considerations hold not just for energy producing minerals , but for all mineral resources for which the same phenomenon of increasing need of energy for extraction takes place. For example, a Californian 49er could find enough pure gold nuggets to make a living from of his activity and, sometimes, to get rich. In terms of energy, mining cost him very little: mainly the energy of the food that he needed to eat. Today the gold mining industry may extract gold from ores that contain less than one part per million (1 ppm) of it. Although it normally exploits higher ore grades. This concentration is still about three orders of magnitude larger than it is on the average in the Earth’s crust, but extracting gold from these low-grade ores is a completely different proposition than it was at the time of the 49ers. It requires lifting large amounts of rock, crushing it to a powder, treating it with expensive and highly-polluting reactants such as mercury or cyanide, and, finally, recovering the gold; a series of processes requiring enormous amounts of energy. The same considerations hold for most other mineral commodities, even though we can’t even dream of extracting them from such low concentration ores as it is possible with gold. For copper, for instance, extraction is not economically possible for a concentration smaller than about 0.5% (5000 ppm) [128].

In practice, producers find that the cost of extraction becomes higher and higher as a mineral resource is exploited, so they must raise prices if they want to keep making a profit. Prices are affected by market oscillations, technological developments, and scale factors, so that it is difficult to detect a clear increasing trend, even in the long run [121]. But the trend is clear for some critically important resources, such as crude oil, at least if the short-term oscillations are discounted (which is never done in the media and in the political debate). So, facing higher prices, customers may decide that they will use a different resource, or use less of it. This is called “demand destruction” and it is often accompanied by a crash in market prices, as it was recently observed for crude oil. At this point, the industry finds itself unable to make a profit with the resources it manages. Because of the shortage of capital, the expenses for exploring for new resources are slashed down and the number of new discoveries diminishes. If demand destruction continues for a long time, it may happen that the low prices will downgrade ores into deposits; what was once considered a resource ceases to be it. Eventually, production must start a downward trend that becomes unstoppable. This is what’s happening, or will soon happen, with several mineral resources worldwide. It is a completely different picture than the rosy one generated by looking at the R/P ratios. The problem with the ratio is that neither R nor P are constant over time and R tends to diminish with demand destruction. That makes the ratio an overoptimistic way to predict the future of mineral resources.

So, where are these trends leading us? We need some kind of model that could tell us what trajectory is normally followed by the production of a mineral resource. I already mentioned the work by Jevons [129] who was the first to look at the depletion issue in modern terms. Much later, in 1956, a quantitative hypothesis on the production cycle of mineral resources was proposed by Marion King Hubbert with his “bell-shaped” curve that correctly described the cycle of oil production in the US for a half century, until the turmoil of shale oil generated a new cycle [130] (Fig. 3.24).

Hubbert ideas were generally abandoned during the period of optimism that followed the oil crisis of the late 1970s, but they were rediscovered and picked up again by the “peak oil movement” starting with the late 1990s. Mainly, it was the work of the British geologist Colin Campbell who popularized these ideas and coined the term “peak oil” to indicate the moment in which world oil production would reach its historical maximum and start on an irreversible decline. In recent times, the concept of peak oil seems to have become unfashionable, mainly as a result of the low prices of the past few years that have been generally interpreted as an indication of abundance. It is a bad misperception of the situation: the low prices indicate, instead, the demand destruction phase that precedes the start of the irreversible decline of the industry. But misinterpretations are common when dealing with prophecies of doom, especially when the predicted doom is approaching. It was the same for the scenarios of “The Limits to Growth,” that were popular for a certain time when they were proposed, in 1972, but then were widely disbelieved and they are still disbelieved today, just as we seem to be arriving at the economic turning point that the study had predicted for around the second decade of the twenty-first century [131].

We will see later how the Hubbert curve can be generated by a dynamic model that sees the oil extraction industry as a complex system dominated by feedback effects. It is a special case of a more general dynamic model that describes the trends of exploitation of all natural resources, not just the non-renewable mineral ones. Even though it can correctly describe some historical case, the Hubbert curve should be seen as a trend, not a law of physics, and surely not a prophecy. It is not always observed, but it tends to appear under certain conditions. Specifically, it appears when an industry (1) exploits a non-renewable or slowly renewable resource, (2) operates in a free, or nearly free, market and (3) re-invests an approximately constant fraction of the profits into exploration and production. If these conditions are satisfied, then the result is the typical “bell-shaped” production curve, also known as the Hubbert curve. But that’s not always the case: political interventions can completely change the curve, just as the vagaries of the financial market can. Financial intervention may lead to a temporary inversion of the Hubbert trend, as it happened in the United States with the shale oil bubble that started in the early 2000s, creating a second cycle of extraction. Several production trends in various regions of the world can be explained as multiple Hubbert cycles, generated by changing economic and political factors [132]. Nevertheless, the Hubbert curve remains a strong factor that drives the extraction cycle of all mineral resources.

The Hubbert curve, as it is normally described, is symmetric. That is, growth and decline occur at the same speed and the curve doesn’t show a “Seneca” shape. Symmetric curves have been observed in several cases for the production of crude oil in various regions of the world, but not always. There are also several cases in which the decline of an oil producing region has been slower than the growth [134]: we could call this the “anti-Seneca” shape. This can be explained in terms of the effect of financial factors in the exploitation of the resource. When an oil field or an entire region starts declining, investments are often increased to contrast the trend. The field may be “rejuvenated” by applying various technologies to keep extracting from aging wells or by optimizing the efficiency of production. We could say that it is a way of throwing good money after the bad or, more exactly, good resources after the bad. Nevertheless the result is normally a slower decline than the simple Hubbert curve would predict.

The opposite shape, the Seneca shape , for the oil production curve is also possible, although it has rarely been observed at the regional level so far. A fundamental point here is that the production of oil and other energy resources is normally measured in units of volume or weight. But this measurement does not tell us the net energy that production makes available for society. As the more profitable resources are extracted and burned, more and more energy is necessary to produce a certain amount of energy, and that means a smaller amount of energy available for society. The idea that this phenomenon would produce a “Seneca shaped” curve was proposed perhaps for the first time by Nate Hagens in a post published in 2006 on “The Oil Drum” [135]. That post contained a qualitative representation of the Seneca Curve as applied to the exploitation of an energy resource. In recent times, several analysts (for instance, by Antonio Turiel [136] and Gail Tverberg [137]) have proposed that the world’s oil (or energy) production is poised for going down a steep cliff as a result of the diminishing net energy yield (Fig. 3.25).

But it is unlikely that this Seneca collapse will be the direct result of the declining EROEI of fossil fuels. At present, the oil industry is already in deep trouble even though the EROEI of extraction remains on values that are still large, most likely over 10. As it often occurs, the system may be vulnerable not so much from depletion but to a loss of control. We have already seen several examples of the prevalence of financial factors in generating collapses that occur much before the physical problems involved with the system become serious in themselves. The mining industry is part of the world’s commercial system, and, for this reason, it is vulnerable to financial crashes such as the one we saw in 2008. The various sectors that compose the mining industry are networked with each other, too and if one sector goes down, it will bring down others. For instance, if oil production declines, that will make less and less diesel fuel available for the machines that extract coal and other minerals. If coal extraction declines, it will be more difficult to produce the steel necessary for the drilling equipment used by the oil industry. All that, in turn, will make it more difficult to extract copper and steel, which are used to make the machines necessary to extract other mineral resources. So, the Seneca cliff may come to fossil fuel production more as the result of financially triggered economic factors than as the direct result of declining EROEI.

But financial factors are not the only problem with the tipping point of the production of a major economic resource such as oil, political ones may be even worse. Regional peaks have often occurred in correspondence with considerable social and political turmoil, especially if the economy of the region is strongly dependent on the revenues obtained from the extraction of the resource. That may have been the case in the Soviet Union, when it collapsed as a political system as it reached its oil production peak [133] even though this point is obviously debatable. Another case is the peaking of the oil production in Iran, which corresponded to the popular revolution that ousted the Shah. Surely, as the world’s oil production (intended as “all liquids,” not just crude or “conventional” oil) is close to peaking, we are seeing plenty of political turmoil in the world. A new world war, or even a regional war in a major oil production region, may generate a destructive Seneca Cliff that will affect the whole world’s energy production system. Such an event would be obviously disastrous, especially for the poor, not only for the disruption of the power generating system, but also for many other uses - transport, agriculture, steel, cement, aluminium that would be negatively affected. Solutions could be found for all these problems, but not easily.

3.5.2.1 Thanatia and the Mineral Eschatology

If we were to bring the current worldwide trend of ore grade decline to its logical conclusion [139] we would have to move to progressively lower concentrations in the mineral deposits we exploit, until we reach that region where deposits don’t exist anymore (called the “mineralogical barrier” [140, 141]). Eventually we would have to mine the undifferentiated crust and that would mean using what I called the “universal mining machine” [139], a hypothetical device that processes ordinary rock, separating it into its elemental components to produce all the elements of the periodic table. From a physical viewpoint, it is not impossible: we have technologies that could do exactly that. But rare elements are present in such tiny concentrations in ordinary rock that such a machine is simply unthinkable as a practical way to mine anything. To produce amounts of minerals comparable to the current production, processing the huge masses of crust required would need orders of magnitude more energy than what we can muster today and which are unlikely to be available in the future. Another problem, maybe even worse, is that the pollution created by giant, lumbering universal mining machines would be simply beyond imagination. Think of processing amounts of rocks hundreds or thousands of times higher than the amounts we process today and imagine, if you can, turning the Earth into a single, giant quarry that would leave little space, if any, to human beings to live.

This problem is the result of humankind having engaged in the exploitation of something—ores—that we can see as the detritus left over by for millions or even billions of years of geological processes in the Earth’s crust. In biology, the creatures that live on detritus are termed “detritivores” and their destiny is an ignominious demise when they run out of food. That may be our destiny as well, avoidable only if we could find new sources of exploitable minerals. Unfortunately, that seems to be nearly impossible and most of the proposals in this sense have a certain ring of “science fiction” to them. Some people speak about mining the moon and the asteroids, but they forget that ores are the result of tectonic processes that occur at or near the surface of the Earth’s continental crust. As far as we know, these processes never occurred on the Moon or on the asteroids, so we don’t expect to find ores to mine there. Perhaps, tectonic forces were operating on Mars, long ago, and so there could be ores to mine, there. But the cost to go there and back are truly out of this world. The same considerations hold for schemes involving new forms of mining on the Earth, for instance from seawater. The very low concentration of the rare elements dissolved in seawater makes the task so expensive to be, again, unfeasible [143].

So, the ultimate destiny befalling humankind is to stop all mining, at least in the forms known today. It will be the end of the cycle of human mining that had lasted from the time when our remote ancestors started mining the flint they used for their stone tools. It is what I called the “mineral eschatology,” [123], from the Greek term “eschatos” that means “the furthest,” “the extreme end.” Alicia and Antonio Valero (daughter and father) proposed the suggestive name of Thanatia (“deadland”) [142] for planet Earth as it would become after that human mining will have extracted all the exploitable mineral ores and dispersed their contents uniformly in the crust.

So, what kind of world could Thanatia be? Would humans have to return to stone age, or would they still have access to at least some of the minerals they have used to build their industrial civilization? It depends, of course, on what minerals we are considering. Some elements turn out to be extremely rare. For instance, the average gold concentration in the earth’s crust is on the order of 3 ppb (parts per billion) by weight [122]. This means that metallic gold is least eight orders of magnitude more concentrated than in the average crust. Take copper as another example. It is not as rare as gold; a reasonable average value of its concentration could be 70 ppm (parts per million). But compare this with metallic copper we still have a concentration ratio of about five orders of magnitude. This kind of ratio between a pure metal and its concentration in the Earth’s crust is typical for most of the metals that are defined as “rare,” say, zinc, chromium, cobalt, lead, and many more. Keeping a supply of these metals after we run out of the concentrated ores we are exploiting nowadays is nearly impossible, at least if we want to keep the current production levels. Other metals, instead, are relatively common. Iron, silicon, and aluminum, all are not only common, but they are the most common components of the Earth’s crust and it would be hard to think that we would ever run out of concentrated sources of them. So, even in Thanatia, something can still be mined. But could Thanatia still support an industrial civilization?

A sustainable mining system would not be impossible but, of course, we would have to learn how to manage without extremely rare resources that can’t be easily recycled, such as precious metals (platinum, rhodium, palladium and others) for catalysis, rare metals (indium, tantalum, gallium, and rare earths) for electronics, and other sophisticated hi-tech applications, such as rare earths for magnets. That’s not impossible if we accept a reduced performance; for instance, we would have to return to use iron based magnets instead of the more powerful rare earth based ones. We would have to go back to cathode ray tube (CRT) displays for the lack of indium for the LCD screens. And we would probably need to return to the old tungsten filament light bulbs for the lack of gallium for LEDs and of mercury for fluorescent bulbs. Some applications, such as three-way catalysts for the exhaust control of gasoline based engines would be totally impossible for the lack of the precious metals needed for the task (Pt, Pd, and Rh) and that would mean the end of gasoline engines and, probably, of all internal combustion engines. That would be no disaster, since they could be replaced with electric motors.

Some rare metals could still be supplied to the system, but in very small amounts that could be defined as “homeopathic.” An estimate of these amounts can be done by considering that the mining industry today produces about 3000 tons of gold per year (www.statista.com) from ores that contain around 10 ppm of it. That’s not far from the concentration of copper in the average earth’s crust, and so it would be possible to produce similar amounts of copper, a few thousands of tons, without the need of ores as long as we manage to maintain a supply of renewable energy comparable to the present one. For these low levels of production, we could also think of extracting minerals from plants which, in turn, extract them from the undifferentiated crust [145, 146]. But a thousand of tons of copper per year is such a small amount in comparison to the current supply of more than 15 million tons that it is nearly unthinkable to use it for such commonplace applications as electrical wiring. A larger supply could be obtained by supplementing the supply from mining with recycling technologies but, to have an impact, recycling should be truly ferocious in comparison to anything we are doing today. At present, we are recycling most metals at levels of around 50% and that means that most of the metal is lost forever after just a few cycles. To preserve significant amounts of a metal resource for a long time, the recycling rate would have to be raised to well above 90%. This is a difficult technological problem: no metal has ever been recycled at this level on a large scale. Still, we may find reason for hope by thinking that this ferocious kind of recycling is typical of ecosystems. Plants have been “mining the crust” of planet Earth for hundreds of millions of years and they never ran out of anything. In a sense, they have been always living on Thanatia and they seem to be prospering nevertheless.

The main strategy for the human industry to survive depletion would be to run mainly on the “metals of hope,” as they have been defined by the Dutch researcher André Diederen [144]. These are the common metals in the crust that, in many cases, can provide the same services as the rare ones we are using today. For instance, aluminum and magnesium for structural purposes, carbon steel for tools, aluminum for electric conduction, silicon for semiconductors. With these materials, we can manufacture most of what is needed to harness solar energy by means of photovoltaic cells and distribute it in the form of electricity. We can build all sort of structures vehicles, everyday items and also data processing equipment, even though probably not with the kind of performance we are used to, nowadays. So, planet Thanatia may not be the end of the human industrial civilization if we prepare in advance for it. Unfortunately, at present, it doesn’t seem that the world leaders or the public understand the problem of mineral depletion and we are moving only very slowly in the right direction of a more parsimonious use of resources and a much more careful recycling of what we use. But, no matter what’s done or not done today, large changes are unavoidable in the world’s industrial system, changes so large that it is not impossible to think that the whole system could will cease to exist in another case of Seneca Ruin.

3.6 Overshoot

Every morning in Africa, a gazelle wakes up, it knows it must outrun the fastest lion or it will be killed. Every morning in Africa, a lion wakes up. It knows it must run faster than the slowest gazelle, or it will starve. It doesn’t matter whether you’re the lion or a gazelle-when the sun comes up, you’d better be running.”

From: Christopher McDougall, Born to Run: A Hidden Tribe, Superathletes, and the Greatest Race the World Has Never Seen

Give a Man a Fish, and He will Eat for a Day. Teach a Man How to Fish, and He will Strip the Ocean Clean. The town of Stintino, in Sardinia, has splendid beaches that face a blue and clear sea . What makes the town a truly unique place in the world is the fleet of old sailboats kept and maintained in perfect shape by the descendants of the ancient fishermen. These boats were once used for fishing, but, today, nobody in Stintino lives on fishing anymore and the boats are kept for pleasure trips only. You can rent one of these boats, or maybe a friend will give you a chance to sail in one. Taking one of these boats to some distance from the coast gives you a chance to swim in waters so clear that you can see all the way to the bottom and for hundreds of meters in all directions. Then, you may notice something strange: there are no fish anywhere to be seen, just an abundance of jellyfish swarming around you. The risk of being stung by one of these ethereal creatures will force you to take a paranoid attitude, watching your back while swimming as if you were a first world war pilot fearing the plane of the Red Baron tailing you. The lack of fish near Stintino is particularly troublesome if you notice it after having dived off an old fishing boat. What were the old fishermen fishing? Not jellyfish, obviously. Today, jellyfish are considered a delicacy in some Oriental cuisines, but they are low in nutritional value and it could hardly have supported a whole town. So, the only conclusion that you may take from this experience is that the world has changed. Once, the sea in front of Stintino must have been teeming with fish, but not anymore. You are witnessing the Seneca ruin of fish!

The depletion of the Mediterranean fishery is not an isolated case: most of the world’s fisheries are in trouble. It is a story that can be told starting with the first case for we have reliable quantitative data: that of the American whale fishery in the ninetieth century. The history of this industry can be found, for instance, in the book by Alexander Starbuck, “History of the American Whale Fishery”, written in 1878 [147]. Earlier on, in 1851, Herman Melville had described the same world in his novel, Moby Dick. Both books tell a similar story: Starbuck’s one is full of data and technical descriptions, but, by reading it, you can perceive the dismay of the author facing the disappearance of a world that he knew so well. Melville’s novel, then, is an epic saga that ends in defeat; the pervasive melancholy of the story may reflect the fact that the whaling industry, at Melville’s time, had already started a decline that was to be irreversible.

The objective of the herculean efforts described by Starbuck and Melville was a substance wholly unfamiliar to the modern reader: whale oil. In the ninetieth century, whale oil played a role similar to that of crude oil in our times. It was a fuel used for many purposes and, in particular, for oil lamps. It was cleaner and cheaper than most vegetable oils and it was by far the preferred way to light homes. That generated a brisk market for whale oil and a whole industry engaged in hunting whales all over the world’s oceans. As it is normally the case with most human endeavors, whalers didn’t care so much about the conservation of the resources that they exploited. That had bad consequences for them and for the whales, too. Figure 3.26, created from the data reported by Starbuck, shows the production of whale oil for the American whale fishery over most of the ninetieth century. Even though whales are, theoretically, a renewable resource, their production followed a “bell-shaped” production curve similar to the “Hubbert curve,” typical of non-renewable resources [148]. It was not exactly a “Seneca collapse;” the decline was approximately symmetric with respect to the growth phase. Nevertheless, it was a remarkable case of the collapse of an entire industrial sector, one of the first for which we have quantitative historical data.

The obvious explanation that comes to mind for the decline of whaling is that the whalers were running out of whales. But that was strongly denied at that time and, in his book, Starbuck declares more than once that the difficulties of the industry were not due to the lack of whales. Rather, it was because whales, he says, “had become shy.” Another explanation reported by Starbuck was the extravagance of many ship captains who fitted their ships with overly expensive fishing equipment.

As it often happens when discussing the subject of depletion, stating that people may be destroying the very resources that make them live evokes very strong emotional denial responses, then as now. The idea that the decline of the ninetieth-century whaling had nothing to do with having killed too many whales remains popular to this day. Among the several explanations, it is easy to read that the whaling industry was killed by kerosene; a new and cheaper fuel obtained by the distillation of crude oil. Seen in this light, the disappearance of the whaling industry is described as a triumph of human ingenuity: another example of how new technologies can overcome depletion and always will. But things are not so simple.

The first problem with this explanation is that kerosene smells bad when burned, and people much preferred to use whale oil in their lamps, if they could. Then, unlike kerosene, whale oil was also an excellent lubricant. There were also products made from whales that couldn’t be replaced by kerosene; one was “whale bone,” a stiffener used for ladies’ corsets (maybe the reason why ladies fainted so often in ninetieth-century novels). Then, there was whale meat; never considered a delicacy in restaurants in the Western world, but it has a good nutritional value and was consumed in Asia. Indeed, in Moby Dick, Melville presents to us an unforgettable scene in which the second mate of the Pequod, Stubb, eats whale steak in the light of whale oil lamps. But the main point, here, is that the production of whale oil peaked and started declining at least ten years before the production of kerosene reached comparable values [148]. Clearly, we can’t imagine that the whaling industry was destroyed by a fuel that didn’t exist yet.

Another way to look at this question is to examine estimates of the number of whales [149]. The data are shown in Fig. 3.27 and are, of course, affected by uncertainty since they can only be based on historical catch data. So, maybe these results can’t completely rule out Starbuck’s hypothesis that whales “had become shy.” But it is reported that right whales had gone nearly extinct by 1920, with only about 60 females reported to be still alive in the Oceans [149]. A little extra push would have killed them off and, even today, the number of right whales alive is around one-tenth of what it was when large scale industrial hunting started. Evidently, despite the competition with kerosene, there was an economic incentive to hunt whales all the way down to almost the last one and that’s compatible with the existence of products other than fuel that could be obtained from whaling. In the end, the right whales were victims of the phenomenon that we today call “overfishing,” a major problem for the world’s modern fishing industry. Indeed, the data for many modern fisheries are similar to those for the ninetieth-century whaling cycle. As an example, look at Fig. 3.28 that describes the yields of the UK fishing industry [150].

In the upper box, you see the fish production (“landings”). These data refer to the fishing technique called “Bottom Trawling,” that consists in towing a net along the sea floor, scraping everything away. It is a kind of “take no prisoners” fishing technology and, as you may imagine, it is devastating for the ecosystem [151]. In addition, bottom trawling also destroys an irreplaceable cultural heritage in the form of ancient shipwrecks [152]. The lower box of the figure shows a parameter called “fishing power” calculated in terms of “smack units,” which refers to the fishing power of a typical 1880s sail trawler, or “sailing smack” as they were called. Now, compare the upper and the lower box, and you’ll see that the fishing industry was ramping up its fishing power at high-speed in the second half of the twentieth-century. Note that it was done just when the fishing yields had started to decline. This is a phenomenon reminiscent of the “extravagance” described by Starbuck about the captains of the ninetieth-century whaling fleet. Apparently, a common reaction of the fishing industry to fish scarcity is to invest in better and more efficient fishing equipment. But no matter how powerful were the boats of the British fishing fleet, they could not catch fish that wasn’t there.

The decline of the British fishery is just a regional case that’s part of the overall trend in the world’s fisheries. It is a modern phenomenon: in the past, the sea was commonly considered as infinitely abundant and the idea that we could ever run out of fish was simply inconceivable. During the Middle Ages, fish was seen as a lowly kind of food that only the poor would eat every day; a penance for all those who could afford better food. There is an interesting note in Jared Diamond’s book Collapse [153] where he discusses how the Viking colonists of Greenland might have survived the loss of their cattle herds if they had switched their diet to fish. But they seem to have refused to do that because of the bad reputation of fish as food. In our times, people took a decidedly different attitude. As fish became rarer, during the second half of the twentieth century, prices increased and people started perceiving fish as a fancy, high-value nutrition item. Think of the parable of the Japanese “sushi,” once a cheap food of the poor, now a refined item in the menus of expensive restaurants. So, unlike the Vikings of Greenland, not only we don’t object to eating fish, but the demand for fish kept increasing. That generated a new kind of industry: aquaculture.

The term “aquaculture” refers to raising aquatic creatures in controlled conditions; it includes crustaceans, algae, and other species. Fish farming is a branch of aquaculture that deals with fish species. According to a 2012 FAO report [154], more than 50% of the world production of fish comes from fish farming. This development may be seen as another triumph of human ingenuity that overcomes overfishing; but, in reality, in fish farms, valuable fish such as salmon are fed mainly with lower value fish, just moving the problem down the food chain. You may have never heard of a fish called “sandeel” and surely you have never ordered it at a restaurant. Yet, for many years, sandeels were a major target for the world’s fishing industry to be used as feed for the more valuable farmed fish. That lasted until aggressive overfishing destroyed the sandeel fishery and catches dwindled to almost zero in the early 2000s [155]. The declining production of low-value fish has led to attempts to feed farmed fish with food that their ancestors never tasted in the wild, such as pork, chicken, and even wheat and barley. The result is the production of a kind of fish that has little to do with the version that once was fished in the wild, among other things being depleted of some nutritional characteristics. For instance, wild salmon was known for being rich in vitamin D that derived from a diet of plankton. But farmed salmon, nourished on pork or on wheat, doesn’t provide that vitamin anymore.

Not only fish farming produces a low-quality product but it didn’t stop the destruction of the marine fisheries, just like the appearance of kerosene as fuel didn’t stop whaling in the ninetieth century. The worldwide decline of the fish stocks continues and it is by now well documented [156–161], even though its actual extent is sometimes contested [162]. One consequence of this phenomenon is that, with less fish in the sea, the invertebrates prosper because they are not eaten anymore by creatures at a higher level of the trophic chain. That’s the reason why, not long ago, lobsters and crabs were an expensive delicacy, while today they have become reasonably affordable. And if you are stung by a jellyfish while you swim in the sea near Stintino, or anywhere else in the world, now you know exactly why: it is because of the Seneca collapse of fisheries.

3.6.1 What’s Good for the Bee, Is Good for the Hive

An entrenched idea in standard economics is that of the “invisible hand,” proposed long ago by Adam Smith in his The Wealth of Nations (1776). The concept is that the search for personal profit leads to the optimization of the whole system. It is a reversal of the old saying “what’s good for the hive, is good for the bee.” Maybe, according to the current economic theories , we could say that the honey yield of the beehive would be maximized if individual bees were paid in proportion to the amount of honey they produce. Obviously, real beehives don’t work in this way but the idea may make sense for humans who seem to work like bees only when they are paid to do so. This is the standard wisdom of economic liberalism: the economy works best if left to work on its own, having people seeking to optimize their personal profits the best they can.

The idea of letting complex systems optimize themselves is fascinating and it seems to have been confirmed by the ignominious demise of the old Soviet Union with its cumbersome centrally planned economy and “five-year plans.” But if we look more closely at the way ecosystems work, we see that the idea that they are optimized needs some qualifications, to say the least. We tend to think of nature as being in an idyllic state of equilibrium, and we speak of the “balance of Nature.” But, in the real world, things are never in equilibrium and they cannot be. In ecosystems, the parameters of the system tend to remain close to a state we call the “attractor,” but only on the average and with plenty of oscillations. Natural ecosystems are affected by fires, droughts, nutrient loss, invasion of foreign species, epidemics, and all kinds of factors that cause their pretended balance to be rapidly lost. A good example of this perfectly natural tendency of ecosystems to experience the equivalent of periodic Seneca collapses is given by Holling in a paper published in 1973 [163], where he describes how periodic invasions of budworms kill trees and create havoc in apparently stable forest ecosystems. A real ecosystem, just like a real economy, is not a place where interactions occur only in pairs, between sellers and buyers, as the basic concept of economics optimization would have. No, the system is networked, and what a buyer does affects all buyers and all sellers. As we saw in the previous chapters, strongly networked systems tend to show oscillations and collapses. That’s what we see in real ecosystems just like in the world’s economy.

Oscillations and collapses may be a natural phenomenon, but that doesn’t mean that they are pleasant or even unavoidable. Budworms would have a better and easier life if they could limit their reproduction rate in such a way as to avoid killing the trees that are their source of food. Of course, budworms can’t be expected to be able to engage in long-term planning but we can perfectly well imagine that human beings could be smart enough to do that. For instance, we can imagine that fishermen would see the advantages of limiting their fishing activity to avoid the collapse of the fish stocks, their source of wealth. But, in practice, it turns out that humans don’t seem to be better at managing fisheries than budworms are at managing forests. In the real world of the human economy, we continuously see wild oscillations that create disasters and great suffering for many people. So, could these oscillations be avoided or, at least, reduced in amplitude? It is not impossible, but we need to understand how the laws of complex systems affect markets.

In 1968, Garrett Hardin proposed a concept that was the first attempt to apply what was known in population biology to an economic system. Hardin’s model was called the “Tragedy of the Commons” and it has remained a milestone ever since in this field [164]. Taking inspiration from the collapse of the British common property pastures in the ninetieth century, Hardin proposed a chain of logical steps that made the tragedy unavoidable, given the human tendency to maximize individual profits. In a pasture run as a “commons,” every herdsman can bring his sheep to feed. Then, each herdsman has a choice: should he increase his herd of one more sheep? This is the core of the problem of overexploitation (or also “overshoot” as it was defined later, in 1982, by William Catton [165]). Hardin writes the following:

As a rational being, each herdsman seeks to maximize his gain. Explicitly or implicitly, more or less consciously, he asks, “What is the utility to me of adding one more animal to my herd?” This utility has one negative and one positive component.

The positive component is a function of the increment of one animal. Since the herdsman receives all the proceeds from the sale of the additional animal, the positive utility is nearly 1. The negative component is a function of the additional overgrazing created by one more animal. Since, however, the effects of overgrazing are shared by all the herdsmen, the negative utility for any particular decision-making herdsman is only a fraction of 1.

Adding together the component partial utilities, the rational herdsman concludes that the only sensible course for him to pursue is to add another animal to his herd. And another; and another... But this is the conclusion reached by each and every rational herdsman sharing a commons. Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit—in a world that is limited.

Hardin’s model isn’t just a compelling series of logical statements; it has a deep thermodynamic significance. We can say that predator and prey in an ecosystem are both dissipative systems in the sense given to the term by Prigogine [41]. Sheep can be seen as machines that dissipate the chemical energy contained in grass, and grass as a machine that dissipates solar energy. All these machines do their best to maximize the dissipation speed according to the principles of non-equilibrium thermodynamics. The same is true for all the elements of the trophic chain of ecosystems; natural selection favors those species that dissipate potentials faster. There is a side effect in this rush to dissipation: the system may be so efficient that it dissipates a potential faster than it can reform. At this point, the dissipation structure cannot sustain itself anymore and it collapses.

Of course, nobody can win against entropy, but adapting the exploitation rate to the availability of resources does not require going against the all-encompassing second principle of thermodynamics. Just common sense may be enough to do better than budworms. Indeed, Hardin’s model was criticized for being too schematic and for not describing how the commons were managed in ancient times [166]. In general, there is no evidence that resources managed at the village level, such as wood, mushrooms, and even grass were ever overexploited so badly that they led to collapse and “tragedies”. Rather, it seems that the social stigma that comes from mismanaging the resource is a sufficient deterrent to avoid overexploitation. That, in turn, requires that the agents exploiting the system continuously communicate and interact with each other, which may well be the case in a rural village. But when the commons exist on a large, or very large scale, it is another matter. At this point, the agents don’t care about what other agents think and they act according to the old maxim, “grab what you can, when you can.”

So, the deadly Hardin mechanism is not uncommon in the real world. Fisheries are just one of the many cases of the destruction that humans cause in ecosystems; from cave bears to the Dodo of the island of Mauritius. There is evidence for a strong human role during the past 50 thousand years in the extinction of several large land mammal species (the “megafauna”) [167]. Natural climate change is also cited as a cause for these extinctions [168], but it seems clear that humans were a major factor in altering the Earth’s ecosystem even long before modern agriculture and industry [169]. We will probably never know with certainty what caused the extinction of mammoths and of giant sloths, but, at least, we know that in historical times humans have caused the extinction of many species, a phenomenon that’s today called “the sixth extinction” [170]. To these cases of human destruction of animal species, we may add that of the destruction of the fertile soil caused by overexploiting the land [171]. Humans, clearly, tend to destroy whatever makes them live. And the most dangerous case of overexploitation is that of the atmosphere seen as a very large-scale common resource where everyone can dump at will the greenhouse gases produced from the combustion of fossil fuels. This is a case of overshoot at the planetary scale that may create immense damage to humankind.

At this point, we can try to make a quantitative model of these systems: which path will be followed by an industry engaged in the overexploitation of its resources? In Hardin’s model, each herdsman tends to add more sheep to his herd. Since breeding is the mechanism that produces new sheep, we may assume that the number of sheep produced in this way is proportional to the size of the herd. Of course, herdsmen may also buy sheep, but that takes money and—again—we may take the amount of money that each herdsman makes as proportional to the number of sheep they own. At the same time, a sheep produces money only if it can be fed with grass, so we may see the economic yield of the herd (production) as proportional to the amount of available grass. Then, production should be proportional to the product of the two factors: the number of sheep and the extent of grass. We could write a simple formula as this one,

$$ production= constant\times \left[ number\ of\ sheep\right]\times \left[ area\ of\ grass\right]. $$

This is a very general idea that we might apply, for instance, to the whaling industry where the production of whale oil should be proportional to the product of the number of whaling ships and the number of whales. We can also apply it to many other cases and, in this form, it is a simplified version of what economists call the “production function.”

There is a problem in writing the production function in this way: it implies constant returns to scale. That is, if you double one of the factors, production doubles, too. But that can’t be: if you double the area of land available, production won’t double unless the number of sheep increases in proportion. The same is true if you increase the number of sheep without proportionally increasing the area of the grassland. Because of this, economists have developed a form of the production function where each factor is raised at an exponent smaller than one. These exponents are called “elasticities” and they have the effect that the function doesn’t rise linearly in proportion to the size of each component but tapers down gradually as it grows. In this form, the formula is known as the “Cobb-Douglas” function [172] and it is often able to describe economic systems of various sizes. For instance, in 1956 Robert Solow used it to describe the GDP of the American economy obtaining a result that’s still widely known today, a continuous exponential growth that both politician and the public seem to have taken for granted for the economy [173].

The problem with this kind of production function is that it can’t describe collapses; which nevertheless happen. So, we need a different mathematical approach. We can find it in a well-known model in population biology developed in the 1920s, independently, by Alfred Lotka [174] and Vito Volterra [175]. The model is known today as the “Lotka-Volterra” (LV) model. Sometimes it is also known as the “predator- prey” model or the “foxes and rabbits” model. The relation between the LV model and Hardin’s tragedy is known [176]. Basically, the LV model is a quantitative description of the overexploitation mechanism proposed by Hardin.

You’ll find details on the LV model in the appendix, but here I’ll describe it in a synthetic way. It is based on two coupled differential equations where the simple production function that we saw before is just one term. Further terms describe the feedback phenomena of the system: there is a growth factor for the resource (the prey population) that’s proportional to the amount of the resource, to consider the fact that it is renewable. Then, there is a second equation that describes the production of capital (the growth or decline of the predator population) as proportional to the production of the resource. Finally, a further term is the decay of the capital (of the predator population) to describe the natural entropic factor that dissipates the energy potential of the system.

We can write the Lotka-Volterra equations taking “C” as standing for capital (predator population) and “R” for resources (prey population). Then, we can write that production (R’, the variation of R with respect to time) is proportional to CR. So, we can write that R =–k ₁ CR, where k is a proportionality constant related to how efficient production is. Note the minus sign that is a convention to indicate that the resource is consumed as a function of time. Then we can write the other terms as follows (1) Resource reproduction rate as R’ = k ₂ R. (2) Capital production: C’=k ₃ RC and (3) capital dissipation: C’ =–k ₄ C. The final form of the LV model is:

R’ =–k ₁ RC + k ₂ R
C’ = k ₃ RC–k ₄ CR

stands for “resources,” such as grass, rabbits, or anything that’s predated by a species one step up in the trophic chain. C, instead, stands for capital. It can be herdsmen, foxes, or anything that predates the resources one step below in the trophic chain.

There is no analytical solution for the equations developed by Lotka and Volterra, but it is possible to use iterative methods to determine the behavior of the variables. The result is that the populations of predators and prey oscillate in phase with each other and neither population ever goes to zero or shoots to infinity. When there are too many rabbits, foxes grow to cull their number. When there are too many foxes, they die of starvation. We can see the Lotka-Volterra model as an extension of Hardin’s ideas. He had qualitatively considered a single cycle that, in his narrative, would have ended with the destruction of the pasture. But, after the herdsmen butcher all their sheep and move away, the grass has the time to recover and, in principle, there would be another cycle with new herdsmen returning. Then, the whole process would repeat, generating a large number of cycles.

Another element of the Lotka-Volterra model is that that there exists a couple of values of the resource and of the capital that stabilize the system. That is, the system can arrive at a stable number of foxes and rabbits or of sheep and grass covered area. This couple of values is called the attractor of the system and, in most cases of natural homeostasis, the stocks will change their size while circling forever around the attractor without ever reaching it. The attractor defines the sustainability level of the exploitation of the resource that may be defined as the carrying capacity of the system: the maximum population size that the system can sustain indefinitely.

Of course, the LV model is very schematic and oversimplified, but it can be used to describe some simple cases of coupled predator/prey species. For instance, it was applied with some success to such systems as bacteria in a Petri dish [177]. Figure 3.29 shows the behavior of a predator/prey couple in the form of two species of mites in an experiment carried out by Huffaker [178].

When the Lotka-Volterra model is applied to real ecosystems, it generally fails. Even some cases that are commonly reported today in biology texts, such as the Canadian lynx population, turn out to be not so well described by the model [179]. That’s not surprising: we wouldn’t expect that such a simple model could describe complex ecosystems composed of a tangle of hundreds—or maybe thousands—of interacting species. But there are real world cases where even the simple Lotka-Volterra seems to work well. That’s the case of some human industrial systems, much simpler than ecosystems. Indeed, Volterra had developed the model not for a generic ecosystem, but for an economic system: the fisheries of the Adriatic Sea in the early twentieth century, generating successive studies on the subject [180]. A fishery, indeed, can be seen as a simple two-species system where fishermen play the role of foxes and fish the role of rabbits. It is not so simple as this, obviously, but it turned out to be a good approximation when myself and my coworker Alessandro Lavacchi tried the model on the historical data for the American whale fishery in the ninetieth century [181]. In a later study performed with two more of my coworkers, Ilaria Perissi and Toufic El Asmar [182], we found several cases in which the model describes the behavior of major fishery collapses. It is surprising that the behavior of human beings can be described so well by a model that seems to describe little else than bacteria and other single-celled animals. But once you understand that they all follow the same laws of thermodynamics, then it may not be so surprising anymore.

In these studies, we often found that the crash of a fishery was irreversible. That is, the overexploited species never recovered its former numbers, just like the right whales never returned to the numbers they had at the time of Herman Melville. That doesn’t mean that the species was hunted all the way to extinction, but it shows a factor related to the complexity of ecosystems that the simple Lotka-Volterra model ignores. Once a biological population has crashed, its ecological niche is often occupied by another other species. That may leave no space for the original one to re-occupy the niche once the factor that had led to its demise (e.g. human fishing) disappears. That’s a problem we are seeing right now with overfishing: even if human fishermen cease their activity, fish don’t return as abundant as they were before because their ecological niche was occupied by the invertebrates, e.g. jellyfish. So, the simulations carried out using the LV model can often neglect the need of taking into account the reproduction of the prey [182] and the model produces a single “bell shaped” curve, just like for a non-renewable resource. In these cases, the Seneca collapse is irreversible (Fig. 3.30).

The standard LV model normally generates symmetric or nearly symmetric curves as long as it involves just two species. But, in a real trophic chain, each species is normally subjected to predation on one side, while it predates some other species on the other side. So, for each trophic step, a species that overexploits its resources is facing the additional trouble of being itself subjected to predation. The combination of overexploitation and predation leads to the “Seneca Shape”; with decline being much faster than growth. This three-species model can be legitimately called the “Seneca Model.” A historical case of a “Seneca Collapse” of a fishery is that of the sturgeon fishery in the Caspian Sea, a fishery that once produced the best form of caviar: the Beluga black caviar (Fig. 3.31).

The graph clearly shows how badly sturgeon fishing crashed in the 1980s–1990s, turning black caviar from something that was expensive but available into something so rare to be nearly impossible to find except in the form obtained from farmed fish; of lower quality and often badly polluted. This historical case, as many others, may be explained in various ways but, quite possibly, as the result of the combination of two factors: increasing pollution and increasing fishing that caused the sturgeon population to collapse. The final result was exactly what Seneca had said: ruin is rapid.

Growth Mechanisms of Complex Systems

Complex systems behave in a non-linear way and that generates a variety of behaviors that can be studied and classified. Typical complex systems are biological and economic system and we all know that both populations and the economy tend to grow, when they are not ruinously crashing down. So, here is a summary, not pretending to be exhaustive, of the “growth modes” of complex systems as it has been understood over a couple of centuries of study.

1.
Exponential model. The simplest and best-known growth mode, characteristic of bacteria in a Petri dish. It implies that one of the parameters of the system, e.g. population, increases in size doubling at regular intervals. It was qualitatively described for the first time by Malthus in the late eighteenth century [89] for the behavior of the human population, then it became widely known and applied to a variety of systems. In economics, exponential growth is often observed and it is always supposed to be a good thing, both for firms and for entire economies. But, of course, nothing can grow forever in a finite universe, so that this model describes only the initial growth phases of a complex system.
2.
Logistic model. A mechanism that takes into account the limits of the system and that applies well, for instance, for many chemical reactions or for the market penetration of some products. The mechanism produces a “sigmoidal” curve that grows rapidly but then tapers down and reaches a constant level. In its simplest form, it was developed by Pierre Francois Verhulst (1804–1849) who built it on Malthus’ ideas, taking into account the impossibility of exponential growth to last forever. Note that Malthus was qualitatively reasoning in terms of this model in his description of the future of humankind—he lacked the concept of “collapse” [90]. Today, various forms of sigmoidal curves are popular for the description of social, economic, and physical systems, but few systems keep following this nice curve for a long time . Complex systems, as mentioned several times in this book “always kick back” [3].
3.
Bell-shaped model. This mechanism takes into account not just the physical limits of the system, but the fact that the entity that grows keeps dissipating entropy at the expense of some exhaustible thermodynamic potential [41]. So, it doesn’t just reach the limit’s and then stays there. After having reached a tipping point, it will start declining, retracing its previous path. There are several mathematical functionss that can produce a bell-shaped curve, the best-known one is the “Gaussian”, but it can be obtained as the first derivative of a Verhulst function, by various other equations, and as the result of system dynamics modeling [181]. It is also known as the “Hubbert curve,” often interpreted as the derivative of the Verhulst logistic function. This kind of curve was applied for the first time to ecological system in the 1920s by Lotka [174] and Volterra [175] and by Hubbert in the field of resource depletion [130]. This is a realistic model for many economic and ecological systems and, within limits, it can describe the trajectory of oil production in a region or the spread of a viral epidemics. As with all models, it takes a lot of caution to use it to make predictions regarding real world systems.
4.
Seneca model. This is the name I gave to the kind of growth kinetics where the decline is much faster than the growth, resulting in a true collapse [319]. It describes complex systems where more than a factor “gang up” together in order to accelerate the decline of one of the parameters or of the whole system. It was described for the first time in qualitative terms by the Roman philosopher Lucius Annaeus Seneca (4 BCE–65 CE). There doesn’t seem to exist a “Seneca equation” that describes this model, but the curve can be simulated by means of system dynamics [319]. This is behavior is commonly observed in systems of a certain complexity, where several subsystems are linked to each other by feedback effects. It describes, for instance, the fall of Empires or that of major economic enterprises.

3.6.2 The Fall of the Galactic Empire

In the 1950s , Isaac Asimov (1920–1992) published the three novels of his “Foundation” series that, over the years, became a classic of science fiction. The story is set in a remote future in which humankind has colonized the whole galaxy, creating a galactic empire. The empire is described as powerful and glorious but also starting to show ominous hints of a dark future. At that time, a bright scientist named Hari Seldon develops his “psychohistory” theory and understands that the Empire is doomed. He tries at first to alert the Galactic Emperor of the need for reforms, but he doesn’t listen to him. So, he sets up a colony on a remote planet that takes the name of the “Foundation.” During the dark ages that will follow the fall of the Galactic Empire, the people of the Foundation will maintain the knowledge and the technologies of old that will be used to start a new civilization.

For these novels, Asimov was clearly influenced by Gibbon’s work, “Decline and Fall of the Roman Empire.” But another source of inspiration for him might have been his co-citizen of Boston, Jay Wright Forrester (1918–2016). While Asimov was developing his science fiction cycle, Forrester was developing mathematical models of social systems that echoed the fictional psychohistorical models of the Foundation series. Was the character of Hari Seldon patterned on that of Jay Forrester? We cannot say; neither Asimov nor Forrester ever wrote that they knew each other or each other’s work and it may well be that Forrester hadn’t yet developed his models when Asimov was writing his stories. Still, it is fascinating to think that some archetypal ideas seem to pervade humankind’s intellectual history. Hari Seldon and Jay Forrester are both heirs (one fictional, the other real) of a long line of thinkers, Socrates, Seneca, Merlin, Laozi, Kong Fuzi, and many others who provided words of wisdom for humankind (and that humankind usually ignored). Forrester’s story, in particular, is the story of a successful major scientific development; that of “world modeling,” that led to the well-known 1972 study, The Limits to Growth. But the imperial rulers of the twentieth century couldn’t accept the results of world modeling that showed that the world was running toward a catastrophe. Just as Hari Seldon failed to reform the Galactic Empire, Forrester’s ideas failed to change the way the Global Empire was run. The prediction of a future collapse was ignored and nothing was done to avoid it. Today, it may be already too late and nobody, so far, seems to be building a “Foundation” to keep alive the old knowledge.

To understand the origins of world modeling , we need to go back to the age of optimism of the 1950s and the 1960s . It was the time of abundant fossil fuels, two-digit economic growth, and promises of energy “too cheap to meter.” But some people remained stubbornly unimpressed, believing that the age of abundance could not last forever. One reason was, probably, the ghost of Thomas Malthus that had been lingering for more than a century in Western thought with a vision of a future of famines and poverty. Then, not everybody had forgotten that the great wars of the first half of the twentieth century had been waged in large part to gain and maintain the control of the precious and limited resources of fossil fuels. So, the unthinkable could be thought and perhaps the first to make these thoughts public in the twentieth century was the American geologist Marion King Hubbert. In 1956, Hubbert proposed that the world’s oil production would have had to peak and then decline at some moment in the future, perhaps as early as around the year 2000 [130]. It was a prediction that was, as usual, widely disbelieved at the time, even though today we can see that it was approximately correct.

At around the same time, a new problem started to be recognized: pollution. It was a concept that had been almost unknown before the twentieth century but, with the growth of population and of the industrial activities, it started to gain prominence in the debate. A strong push in this direction came with the book by Rachel Carson, Silent Spring (1962) [183]; a powerful indictment of the chemical industry for the damage it had created on human health and on the ecosystem by the excessive use of pesticides. Then, fears of a "population explosion" became widespread in the 1950s and 1960s. In 1968, Anne and Paul Erlich published a book titled “The Population Bomb” [324] that became very popular, even though the catastrophes it described as imminent would not occur as predicted. So, at that time not everybody agreed on the idea that the future was to be always bright.

Against this background, in 1968 , an Italian intellectual, Aurelio Peccei (1908–1984) created an organization that took the name of the “Club of Rome” to study the future of humankind and what could be done to make it better. From what Peccei wrote, it seems that, at the beginning, neither he nor the other members of the Club understood the problem of overshoot, nor that the world’s economy could be heading toward collapse. What they understood was that there were limits to the available resources on a finite planet and they were thinking that the world economy would simply slow down as it reached the limits and stay there. At that point, the human population would be kept in check by famines and epidemics; much like Thomas Malthus had reasoned in earlier times. In this view, the aim of the Club was mainly to ensure a fair distribution of the world’s wealth and avoid widespread suffering for the poor. With this idea in mind, Peccei met Jay Wright Forrester in Italy, in 1968, in an encounter that was to change forever the intellectual history of humankind. Peccei understood the potential of the modeling methods developed by Forrester and managed to provide a research grant for his research group. The task of Forrester and of his coworkers was to create a world model that would tell the Club of Rome where exactly the limits to growth were situated and what the consequences of reaching them would be. The results of this work were probably unexpected for both Forrester and Peccei.

A first set of results from world modeling came out in a book authored by Forrester alone, “World Dynamics” in 1971 [184]. A second study, based on a more extensive and detailed set of data appeared in 1972 with the title of The Limits to Growth. It was authored by Dennis Meadows, Donella Meadows, Jorgen Randers, William W. Behrens III, and others [185]. The innovative character of these studies was impressive. It was the first time that someone had attempted a quantitative assessment of the effect of the limits of natural resources on the behavior of the economy. Another innovation of the model was that it explicitly considered the negative effects of pollution on the economy: a parameter that, up to then, had been much discussed but whose effects had never been incorporated into quantitative models. The model could also simulate the growth of the human population and could take into account the effects of technological progress in terms of providing more resources and the capability of abating pollution.

The results of the model’s calculations were presented as a set of possible “scenarios,” depending on different initial assumptions on the abundance of the world’s resources and on the human strategy in exploiting them. Therefore, the results were variable but always showed one robust trend: the world’s economy tended to collapse at some moment during the twenty-first century . The “base case” scenario was obtained using as input the set of data that appeared as the most reliable and that no changes in the world’s policies and in human behavior would take place. It saw the collapse of the industrial and the agricultural systems at some moment between the second and the third decade of the twenty-first century. The human population would stop growing and start declining a couple of decades afterward. More optimistic assumptions on the availability of resources and on technological progress could generate scenarios where the collapse was postponed, but the end result was always the same: collapse couldn’t be avoided. It was also possible to modify the parameters of the model in such a way as to have the simulated economy reach a steady state, avoiding collapse. But transferring these assumptions to the real world would have required policies completely opposite to the conventional wisdom in economics; that is, government should have acted to stop or slow down economic growth.

The results of world modeling were nothing less than the perspective of a Seneca-style collapse that would occur in less than half century in the future. In terms of impacting on the generally accepted worldviews, it was the equivalent of a flying saucer landing on the lawn in front of the White House in Washington D.C. and discharging troops of little green men armed with ray guns. There is a lingering legend that says that the study was laughed off as an obvious quackery immediately after it was published, but that’s not true [131]. The Limits to Growth study was debated and criticized, as is normal for a new theory, but it raised enormous interest and a large number of copies were sold in many languages. Evidently, despite the general optimism of the time, the study had given voice to a feeling that wasn’t often expressed but that was in everybody’s minds. Can we really grow forever? And if we can’t, for how long can growth last? The study provided an answer to these questions, although not a pleasant one. But the study failed to generate further research and, a couple of decades after the publication, the general opinion about it had completely changed.

It would be a long story to go into the details of the rabid negative reaction that the Limits to Growth received from several sectors, in particular from economists. Let’s just say that there has been some debate on whether this reaction was spontaneous or it had the character of a sponsored political campaign. We have plenty of evidence of spin campaigns waged against science [186]. We also know that the chemical industry sponsored a spin campaign against Rachel Carson [187, 188] and, of course, the political nature of the present-day attacks against climate science is well-known [189, 190]. In the case of The Limits to Growth, we have no proof of such a concerted attack carried out on behalf of some industrial or political lobby. What we can say is that the demolition of the study was another case of “Seneca ruin,” in the sense that it involved a rapid collapse of the reputation of the study and of its authors. Up to a certain point, the debate on The Limits to Growth remained relatively balanced but, eventually, an avalanche of negative comments submerged the study and consigned it to the dustbin of the “wrong” scientific theories, together with phlogiston, the cosmic ether, and Lamarck’s ideas on how the neck of the giraffes became so long. The tipping point for the fall of the Limits study may have been an article by Ronald Bailey published in 1989 in Forbes [191] that took up and reproposed an early criticism that had appeared in the New York Times [192]. It was nothing but the misinterpretation of some data presented in the study, but it was very effective. The attack rapidly took a viral character: even though the Internet didn’t exist at that time, the media were sufficient to create a classic case of enhancing feedback. The legend of the “wrong predictions” spread over and, in a few years, it was common knowledge that the whole study was nothing but a set of wrong ideas and silly predictions of a group of eccentric professors who had really thought that the end of the world was near.

Today, the trend is changing and the Limits to Growth study is experiencing a renaissance. So, it is worth examining how the model worked and what were the assumptions used. To start, we could describe the first attempts to use computers to describe feedback-dominated systems (that we may also call “complex systems.”). One of the first researchers to engage in this task was Norbert Wiener (1894–1964) who influenced Forrester’s work. Forrester introduced many innovative elements in these studies, including the use of digital computers that he himself had developed, creating the field called today “system dynamics”. Today, system dynamics is used for a variety of fields, but it is most often seen as a method to understand the behavior of social, economic, business, and biological system that share the characteristic of being feedback-dominated and that are impossible to describe by means of analytically solvable equations.

The core of the model used in the 1972 study , Limits to Growth, was called “World3” and it is still being used today in various modified forms. It assumes five main elements, or “stocks,” in the world system. These are: (1) natural resources, (2) agriculture, (3) population, (4) capital, (5) pollution. In qualitative terms, the inner mechanisms of the model are not fundamentally different from those of a simple predator/prey model. The extraction of resources from a stock, mineral resources grows rapidly as the result of the enhancing feedback relation it has with the industrial sector. The more resources are extracted, the larger the industrial sector becomes. The larger the industrial sector, the faster the resource extraction rate becomes. This rapid growth continues until the energy necessary for the extraction of the resources remains relatively small. But, as the resource stock is depleted, more energy must be drawn from the capital stock to continue extraction. This is a damping feedback effect and, as the process continues, the industrial capital stock peaks and starts falling. This process is enhanced by the interactions with the “pollution” stock, that draws resources from the capital stock. Eventually, both the resource stock and the capital stock start declining and tend to dwindle to zero. The mechanism is the same for non-renewable and renewable resources, the latter mainly related to agriculture. The fact that renewable resources have a nonzero carrying capacity doesn’t change much in the model since they are exploited so fast that there is no time for the stocks to be replaced by natural processes.

A typical result of world modeling of The Limits to Growth study of 1972 is shown in Fig. 3.32 for what the authors called the “base case” model, that is the run of the model that incorporated the data that were considered the most reliable and realistic at that time. The model generates “bell-shaped” curves for all the stocks of the model. Note how the industrial and agricultural production stocks start declining well before the system “runs out” of natural resources. In the model, resources never actually run out, but they are reduced to an amount too small and too expensive to sustain civilization as we know it. Note the asymmetric shape (the “Seneca collapse”) of the production curves. In the simplest case, it is the result of the fact that, in a multi-stock model, each element is sandwiched between a prey and a predator in a three-element chain. When the prey stock starts diminishing, the intermediate element is under pressure from both sides. This is the main factor that generates rapid collapse of the stocks in the form of a typical “Seneca ruin”. Note also how the pollution curve is nearly symmetric; it is because the pollution stock has no predator, no other element of the system that draws from it in an enhanced feedback relationship. Finally, note also how the population stock also grows and then peaks and declines.

The asymmetry of the production or of the stocks as a function of time is graphically shown in Fig. 3.33 from the 1972 edition of The Limits to Growth. This is the essence of the depletion-generated Seneca effect. The system lacks the energy resources necessary to maintain its network structure and must eliminate a certain number of nodes and links; it just can’t afford them. The result is a rapid reduction in complexity that we call “collapse,” another manifestation of the Seneca effect.

The model tells us that a large system , such as an entire civilization , can collapse because of the combination of the depletion of its main resources, both renewable and non-renewable, and of the pollution that their exploitation creates. Different scenarios provide different pathways to the collapse. For the base case scenario of the “Limits to Growth” study, depletion is the main forcing that leads the system to crash. In other scenarios, where the availability of natural resources was assumed to be larger, the crash is mainly driven by pollution. Note that the stock called “pollution” can also be seen as the overblown bureaucratic and military systems that tend to plague all declining empires. In this case, the collapse is generated mainly by the “diminishing returns of complexity” that Tainter had described in his study on the collapse of civilizations [14]. We see how complex systems are driven by a tangle of feedbacks where, depending on the relative size of the stocks, one or another factor can take the lead in causing the collapse. Complex systems tend to fall in a complex manner but that the ultimate cause is always the depletion of some physical factor, either natural resources or the capability of the system to absorb pollution.

A peculiar element of the base case scenario of the 1972 version of the Limits to Growth is how the human population keeps growing for about three decades after the collapse of the agricultural and industrial systems. That looks strange; how can population keep growing while the food resources diminish? The problem, here, is that modeling population turned out to be the most uncertain and most difficult element of world modeling. Whereas the exploitation of natural resources could be analyzed simply assuming that all the agents work to maximize their short-term profit, this is not an assumption that can be used to determine birth rates: what’s the short-term economic profit of having a baby? Clearly, it is a human decision that depends on a host of factors; social, economic, political, and religious. The authors of The Limits to Growth did the best they could by basing their model on the historical data on human fertility as a function of wealth. They took into account the well-known phenomenon called the “demographic transition” that sees a correlation of increasing wealth with the reduction of birthrates, “running the tape in reverse,” assuming that the inverse proportionality would still hold after the tipping point, during the collapse of the industrial and of the agricultural systems. Impoverished families, then, would go through the demographic transition in reverse and restart having many children. This would lead to an increase of the population during the decline of the economic system.

Obviously, these assumptions are debatable, as we saw in the section on famines. It is known that people react to local disasters with increasing fertility [196], but we don’t know how they would react to a global a societal collapse due to economic distress. In such case, they may decide to have a smaller number of children and concentrate their scant resources on them, maximizing their chances of survival. This happened in modern times, for instance, with the collapse of the Soviet Union, in 1991, that led to widespread economic distress but not to increasing birthrates [197]. The authors of the Limits to Growth themselves recognized that it was unlikely that people would react to hardship by having more children. So, later versions of the model included corrective factors that considered the cost of raising a child. You can see the result of the 2004 version [198] of the base case model in Fig. 3.34. The correction on the demographic assumptions generates a much more plausible result, with the decline of the population starting just a few years after the start of the decline of the economic system.

All this doesn’t change the overall behavior of the world system, but there is a subtle effect related to the delay of the population peak. Note how, for an earlier population peak, the curves for the agricultural and industrial production are not anymore so asymmetric (“Seneca shaped”) in the 2004 version as they were in the 1972 version. There is a reason for this: the near-immediate start of the decline of the population generates a lower strain on the resources and creates less pollution. Therefore, the collapse is less abrupt, less “Seneca-like,” although it is a Seneca collapse nevertheless.

Where do we stand in terms of the validity of the Limits to Growth study, almost a half century after its publication? The authors of the study have always been careful in noting that their results were scenarios, not predictions (and, surely, not prophecies). But all scenarios showed the same trends in the assumption that the world’s economy would keep striving for growth, generating the collapse of the world’s economy and of the population at some moment during the twenty first century. Of these, the “base case” scenario indicates that the global collapse should occur in the 2015–2025 range. We are already in a period in which we could expect this collapse to be starting and, if it were to take place, the “base case” calculation would turn from a scenario to a successful prophecy. Indeed, some ominous signs of a global economic slowdown indicate that a collapse may be starting. But, it is also true that the world’s economy is still growing, the production of most mineral resources is increasing, while the human population is also increasing. In short, we can’t say yet whether we are on the edge of a collapse or not, but we may well be.

Maybe the most telling indication that something is rotten in the globalized state is the piecemeal collapse of several formerly wealthy countries. The Limits to Growth results are relative to an average of the whole world, but it would be surprising if the global collapse were to occur at the same time everywhere and not rather, starting in some economically weak regions. This is exactly what we are seeing. One indication is the disaster that’s befalling several North-African and Middle Eastern countries and that appears to be the result of a mix of depletion and of pollution, the latter also in the form of climate change. The paradigmatic example is Syria, where oil production peaked in 1996, then starting a gradual decline. When the domestic production matched consumption, around 2010, the Syrian economy lost the income deriving from oil export, and we may see the start of the civil war as a consequence. The Syrian economy was also badly damaged by a persistent drought that has nearly destroyed the local agriculture, an effect in large part attributable to climate change. The case of Syria tells us that the Seneca cliff that comes after the peak is not a smooth decline as the models tell us, but rather a bumpy descent generated by wars and social turmoil. We find some less dramatic cases in the Southern Mediterranean countries; Greece, Italy, Spain, and Portugal, to which Ireland is sometimes added to create the “PIIGS” group. In all these countries, we see plenty of economic problems; even very serious ones such as in the case of Greece which suffered a brutal economic collapse starting around 2009. Can we see these countries as the “canary in the mine” that alerts us of an impending global collapse? It cannot be proven, but the similarity of the behavior of these economies with the results of the models of The Limits to Growth suggests that it may be the case. If so, a global collapse may be around the corner.

These data should be interpreted as indicating serious risks for humankind in the near future, but the possibility that we are on the verge of a global collapse is not recognized by the public nor discussed in the media. The old legends survive despite the evidence that the world models correctly described the behavior of the world system up to the year 2000 [131, 194]. For instance, the most recent report of the Club of Rome, “Reinventing Prosperity,” by Maxton and Randers [193], was criticized in 2016 on the basis of arguments that go back to the story the “wrong predictions” that the first report produced by the Club made in 1972 [194]. Even in the most difficult moments, politicians and government advisors loudly claim the need of “restarting growth” that will cure all the economic problems. They don’t realize that growth is exactly the reason for the predicament we face: it is growth that creates overshoot and overshoot that generates collapse.

I stated more than once in this book that collapse is a feature rather than a bug, but it is also true that a global collapse that affects the whole human population could be a major disaster for humankind. Unfortunately, it seems that little can be done to avoid it: politicians have little chance to take a different position than always claiming for more growth: there is some method in their madness. At present, the main problem faced by all governments, just as by institutions, companies, and people, is how to manage debt. In a condition where compound interest generates growing debt for everyone, the only policy that offers a hope to solve the problem, or at least to postpone it, is economic growth. So, we seem to be running at full speed toward that rapid ruin that Seneca warned us about.

3.7 Gaia’s Death: The Collapse of the Earth’s Ecosystem

Back in the seventeenth century, when the modern study of geology first got under way, the Book of Genesis was considered to be an accurate account of the Earth’s early history, and so geologists looked for evidence of the flood that plopped Noah’s ark on Mount Ararat. They found it, too, or that’s what people believed at the time. John Greer, “The Archdruid Report,” 2016 [199]

3.7.1 What Killed the Dinosaurs ?

In 1914, one of the first animated films in the history of the movie industry showed “Gertie the Dinosaur” in action, an indication of how deep is the fascination of modern humans for dinosaurs. In 1940, the movie “Fantasia,” produced by Walt Disney, was one of the first full-length animated features and it showed dinosaurs in full color, walking, running, and battling each other. Then, the creatures were shown clumsily marching onward in a hot and desert planet, collapsing one after the other because of thirst and exhaustion. That reflected the theories of the time that were converging on the idea that the dinosaurs had been killed by a planetary heat wave that had destroyed their habitat and their sources of food. But the story of the slow process of understanding the causes of the extinction of the dinosaurs is long and complicated.

For many years after that the dinosaurs were discovered, in the mid-nineteenth century, their disappearance remained a mystery. At the beginning, the only thing that was clear was they weren’t around anymore but, as the studies progressed, it became increasingly evident that, some 66 million years ago, at the end of the Mesozoic era, the dinosaurs had rapidly disappeared, at least on a geological timescale. Paleontologists later understood that some groups of dinosaurs had survived in the form that today we call “birds”, but that didn’t change the fact that the end of the Mesozoic coincided with a major reduction of the number of species in the whole biosphere, a true Seneca-style catastrophe.

Understanding what had caused the Mesozoic catastrophe turned out to be quite a challenge and the number of theories proposed was large and involved some creativity. In 1990, Michael Benton listed some 66 theories purporting to explain the demise of dinosaurs [200], chosen among those that could be described as scientific ones. So far, it seems that nobody has engaged in the task of listing the probably much larger number of cranky theories involving, for instance, extermination carried out by aliens using nuclear weapons, the beasts being just too stupid to survive, assorted improbable catastrophes and the ever-present wrath of God. Obviously, this overabundance of theories indicates that, up to relatively recent times, nobody really had any idea of what had happened to the dinosaurs. It is a situation not unlike the plethora of theories proposed for the demise of the Roman Empire, once more illustrating the difficulties we have in understanding the behavior of complex systems.

Sometimes, science progresses slowly , but it does progress and it contains some built-in mechanisms for removing bad ideas and unsupported theories. With time, scientists were able to rule out most of the fancy theories that had been initially accepted and to concentrate on the clues that the extinction of the dinosaurs had been accompanied, and perhaps caused, by a period of warming. The concept that heat killed the dinosaurs gained ground in the 1970s, when it was realized that the greenhouse effect caused by volcanic CO₂ emissions could have caused a sufficient warming to strongly perturb the Earth’s ecosystem [201]. So, a giant volcanic eruption started being seen as the probable cause of the catastrophe. But, in 1980, the situation changed abruptly when Luis Alvarez and his son, Walter, proposed for the first time the “impact theory” of the extinction [202]. The clue came with the discovery of an iridium-enriched layer in the sedimentary record at the “K-T boundary,” the name commonly given to the layer that separates the Cretaceous period from the Tertiary one (it is now correct to refer to it as the Cretaceous–Paleogene (K–Pg) boundary).

Iridium is a very rare element in the earth’s crust, and its relative abundance in the boundary layer could be explained considering that it is sometimes present in significant amounts in asteroids. So, it could be supposed that the layer could be the remnant of a major asteroidal impact. The event would have surely been catastrophic if the debris had spread worldwide and the Alvarez’s proposed that it was the actual cause of the demise of the dinosaurs and of many other species. The extinctions were not to be attributed to the direct impact, even though, surely, it would have done a tremendous amount of local damage. Rather, the main effect of the impact would have been planetary cooling. It would have been an effect similar to the “nuclear winter” phenomenon proposed by Turco and other authors in 1983 as the effect of a modern, large scale, nuclear war [203]. The large amount of debris generated by the detonation of several nuclear warheads or, equivalently, by a major asteroidal impact, would shield the planetary surface from solar light for some time. Plants would be killed by the combined effect of cold and lack of solar light and, obviously, animals wouldn’t survive for long without plants. A similar phenomenon, although on a much smaller scale, took place with the eruption of the Tambora volcano in 1815. The ashes emitted by the volcano obscured the sky so much that the following year was called “The Year without a Summer” because of the widespread cooling of the atmosphere. The Tambora volcano didn’t cause extinctions, but it gives us an idea of the effect of a large amount of dust in the atmosphere .

As usual in these cases, the new theory was not immediately accepted. It was pointed out, for instance, that the iridium layer was not necessarily of extraterrestrial origin, but could have been the effect of volcanism [204]. In some cases, the debate degenerated into bitter fights; one pitted Luis Alvarez against the geologist Dewey McLean, a supporter of the volcanic extinction theory [205]. In 1988, Alvarez declared that geologists are “not very good scientists… more like stamp collectors” as it was reported in a New York Times article [206]. Clearly, some geologists remained unconvinced about the impact theory, but the debate took a decisive turn in 1991, when it was noticed that a giant crater in the region with the unpronounceable name of Chicxulub, near the Yucatan Peninsula, in Mexico, had an age approximately corresponding to that of the great extinction of the end of the Mesozoic [207]. That seemed to be the true “smoking gun” of the impact that had killed the dinosaurs. From then on, the impact theory rapidly made inroads in the scientific world .

The impact theory had everything needed to stimulate the fantasy of the public: a cosmic collision followed by all sorts of dramatic events: earthquakes, tsunamis, a shroud of darkness that covered the Earth, the withering of the plants and the death by starvation of the animals. It was the occasion for Hollywood movie producers to create and to market a few blockbusters about the valiant efforts of humans to save the Earth from a new deadly impact. But it was not just a spectacular story; it looked like a triumph of science. Finally, we had the explanation that superseded all the past crankiness and made the demise of the dinosaurs crystal clear. If there ever had been a “black swan” in the sense that Nassim Taleb had given to the term [55], the asteroid that had killed the dinosaurs was one: unpredictable, unexpected, deadly. A true embodiment of Seneca’s words that “ruin is rapid”.

Yet, something in this explanation just didn’t click together . One problem was that the data indicated that the end-Mesozoic extinction event was already well in progress when the asteroid struck [208]. Another, more important problem was how to fit the asteroid theory with the other known mass extinctions. There had been many during the past half billion years, the Eon that we call “Phanerozoic.” You can see the record in the figure. These data are often described in terms of the “five large extinctions” or “the big five” [209], something that led to the idea that we are today living the “sixth extinction” [210]. But, no matter how we classify extinctions, the record shows that there have been many of them (Fig. 3.35)

Even a cursory glance at the data shows that the extinction of the dinosaurs, 66 million years ago, is no outlier. Other extinctions have been as large, or even larger, in terms of the percentage of species going extinct. That’s not just an impression: the whole extinction record seems to be part of a structured pattern. In 1996, Per Bak showed that the record could be analyzed in terms of a simple power-law; the same kind that had been derived from studies of models of sandpiles [50]. In later papers, Bak and his coauthors found more evidence of a correlation between the events in the extinction record [211]. These results show that extinctions are not uncorrelated random events; that is, they are not “white noise.” They are correlated to each other and part of an overall trend. So, they are not “black swans” intended as completely unexpected events. They are unpredictable, but not unexpected.

It is likely that most paleontologists are no experts of scale-free patterns and power-laws; so the result that Bak and others had presented didn’t have the impact on the debate that it should have had. But the problem was there and the lack of evidence for other impacts besides the one at Chicxulub led to gradually emerging doubts about the impact hypothesis. In science, theories are judged for their general validity and it was hard to accept a theory that only explained one event among many that were clearly similar. That left only two possibilities: either all extinctions are caused by asteroidal impacts (or, at least, all the large ones), or none of them is, including the one that corresponds to the disappearance of the dinosaurs.

There is some evidence that the size of asteroidal bodies follows a power-law [212], so those falling on the Earth should follow the distribution as well. That might be consistent with the distribution analysis of the extinction record assuming that the size of the extinction is proportional to the size of the impacting body. So, it may be possible that impacts could have caused several, if not all, of the major extinctions on record. But this hypothesis needed to be proven and that led to an effort to find traces of impacts corresponding to the dates of the major extinctions. The results were disappointing. An especially intensive search was performed for the largest extinction on record, the one at the Permian-Triassic boundary, 250 million years ago. There were claims that evidence of an impact was found in the form of fullerene molecules in the sedimentary record; a form of carbon that can be created only at high temperatures and pressures. A supposedly corresponding impact crater was also reported to exist at Bedout, in Western Australia [214]. But these claims could not be replicated nor confirmed in later work [215]. In general, no correspondence with asteroidal impacts could be found for the end-Permian extinction, nor for any of the other extinctions. The only case of impact found to have had a major effect on the ecosystem (in addition to the Chicxulub event) was a cometary impact that appears to be correlated with the temperature spike at the Paleocene-Eocene Thermal Maximum (PETM) of 55.5 million years ago [213]. But, as far as it is known at present, this event didn’t generate a mass extinction.

The lack of evidence of correlation between extinctions and asteroidal impacts led to a re-examination of the impact theory and to a new surge of interest in the idea that the largest extinctions are caused by global warming. It was already known that episodes of strong warming could be generated by the greenhouse gases emitted by the giant volcanic events called “large igneous provinces,” (LIPs). These events are just what the name says: “large” means areas that may be as large as a small continent; “igneous” means burning; that is, they are composed of red hot molten lava, “province” means that these events affect a large but limited region of the crust. Most LIPs are predominantly basaltic lavas and so are referred to as “large basaltic provinces,” even though not all LIPs are basaltic. So, a large igneous province is an event as spectacular and as destructive as an asteroidal impact, possibly more spectacular and even more destructive. Imagine, if you can, a few million square km of continental surface, say, the entire Indian sub-continent, becoming a red-hot expanse of molten lava. That’s what a LIP looks like.

LIPs are rare events, but the history of Earth is long and over hundreds of millions of years, plenty of LIPs appear in the geological record. They are the result of giant plumes of hot molten rock that form inside the Earth’s mantle, perhaps generated by the “blanket effect” of a large continent floating over the magma, below. Being hotter, and hence less dense than the surrounding magma, these plumes tend to move up, toward the surface. If you look at a “lava lamp” toy, you can see the mechanism in action, although on an immensely more rapid timescale and an enormously smaller size. A very large magma plume can remain active for tens of millions of years and, in several cases, plumes appear to have generated the breakup of the continents that created the “dance” that the earth’s landmass has performed over the past few billion years. Lava plumes need not be large igneous provinces; they may be smaller hot spots that generate local volcanoes. The Hawaiian Islands have been created by one such plume that surfaces in the middle of the Pacific Ocean, perhaps a residual of an older, much larger plume.

The volcanoes of Hawaii are an impressive reminder of the power of geological forces, but their effect is negligible on the Earth’s ecosystem. The case of a giant lava plume is different: it seems clear today that there is a good correlation between the major extinctions and the presence of LIPs [216–219]. We cannot say with certainty whether all extinctions are correlated to large volcanic phenomena; many could be the result of internal dynamic mechanisms operating within the biosphere only. Indeed, some data indicate that the geological extinction record is best fitted with two different distributions related to different mechanisms, although little is known on this point [220]. In any case, LIPs are geological phenomena correlated to the collective behavior of the interface between the crust and the mantle. Just as earthquakes are “scale-free” phenomena that follow power-laws, it is not surprising that LIPs have the same property; another link they have with the mass extinction record. When we go into the details, we see that the end-Permian extinction correlates well with a LIP that appeared in the region known today as Siberia, while the extinction of the dinosaurs at the Cretaceous-Tertiary boundary correlates with a LIP that appeared in the region known today as the Deccan Plateau, in India [217]. The remnants of these gigantic eruptions are called “traps,” a name that comes from the term trapp in Scandinavian languages that indicates what in English we call “stairs” or “steps.” In both Siberia and in the Deccan region, successive expansions of basaltic lava flows generated giant steps of rock that are still visible today.

But, if LIPs are the culprit, what is the mechanism that causes mass extinctions? Clearly, no dinosaur could have survived for long with its feet immersed in molten lava, but no LIP ever covered more than a fraction of the Earth’s continental surface. The extinctions, instead, appear to be the effect of gaseous emissions into the atmosphere. All volcanic eruptions release gases, including the greenhouse gas CO₂, and the result is a tendency to warm the atmosphere. The volcanoes we see erupting today are enormously smaller than any LIP, so their greenhouse warming effect is minimal and it is more than balanced by the light reflecting effects of the of ash and aerosols they emit. But, with LIPs, it is another kettle of boiled fish; so to say. The cumulative amount of greenhouse gases emitted by a giant molten lava region is enormous; so much that the normal mechanisms of absorption of the ecosphere can’t manage to remove it fast enough. The direct emissions from LIPs may also have triggered indirect emissions of more greenhouse gases in a classic case of enhancing feedback, burning large amounts of fossil fuels stored in the crust. In particular, LIPs may destabilize frozen methane clathrates, methane stored in the permafrost at high pressures and low temperature. The release of this methane would have created more warming in a classic enhancing feedback process. The final result would have been a gigantic “spike” of global warming that may be the signature of most of the disastrous extinction events in the history of the earth. So, even though the matter is still controversial, it seems more likely that it was heat, not cold, that killed the dinosaurs. Note also that there exists an intermediate hypothesis that says that the extraterrestrial impact at the K-Pg boundary triggered a LIP or, at least, reinforced an already ongoing LIP [221].

Once more, we see how collapses tend to occur in networked systems . The Earth’s ecosystem is a gigantic complex system that includes a series of interacting sub-systems, the biosphere, the hydrosphere, the geosphere, the atmosphere, and others. Mass extinctions, such as the demise of the dinosaurs, are mainly correlated to interactions between the geosphere and the atmosphere, but all the subsystems play their role in the cascade of feedbacks that generates the collapse of the ecosystem. Fascinating and impressive as they are, mass extinctions are no more so mysterious as they used to be. And it is not surprising that the ecosphere moves onward in time in a bumpy trajectory that includes all sorts of collapses which are, after all, not a bug but a feature of the universe .

3.7.1.1 Gaia: the Earth Goddess

In very ancient times in human history, female deities seemed to be more popular than male ones. In those times, the world may have been more peaceful than it is today, at least according to the interpretation of Marija Gimbutas who examined several early human civilizations, describing them in her book “The Living Goddess” (1999) [222]. But, in time, humans became more violent and war-prone, perhaps as a result of the appearance of warlike male Gods who became the standard kind of worshipped deity, at least from the time of the “axial age” that started with the first millennium BCE. But, surprisingly, the ancient Goddess of the Earth, Gaia, reappeared in a prominent role in the twentieth century with the work of a modern scientist, James Lovelock, who proposed the “Gaia hypothesis” for the behavior of the Earth’s ecosystem for the first time in 1972 [223] and, later on, together with his coworker Lynn Margulis [224]. The Gaia hypothesis states that the Earth’s ecosystem has a certain capability of maintaining parameters suitable for life to exist and that it behaves, at least in part, as a living being. That is, Gaia is supposed to maintain the homeostasis of our planet; making the ecosystem able to avoid major catastrophes and to recover from those that can’t be avoided.

As you may imagine, the Gaia hypothesis turned out to be more than a little controversial. Scientists don’t like teleological explanations for natural phenomena, and they like theological ones even less. Consider that the Gaia hypothesis can be seen as both teleological and theological and you can understand the reasons for a debate that, in some ways, reminds us of the ancient Mesopotamian myths that tell of how the Goddess Tiamat battled the God Marduk. For instance, Toby Tyrrell in his book “On Gaia” states that the Earth has maintained conditions favorable to life for some four billion years mainly because of "hazard and happenstance" (p. 206) [225]. Peter Ward dedicated an entire book “The Medea Hypothesis” (2009) to the concept that the Earth’s ecosystem behaves in exactly the opposite way from that of the (supposedly) benevolent Gaia. Rather, according to Ward, it behaves as the evil Medea who, in Greek mythology, is said to have killed her children [226]. Still, the Gaia hypothesis has made considerable inroads in the way of thinking of many scientists, mainly because of its systemic character. The Earth system is a complex system and it makes sense to examine it as a whole. Then, it is possible to give it a name. So, why not “Gaia”?

The Gaia hypothesis is neither teleological nor theological. It is, rather, the embodiment of some well-known principles that govern complex systems. We already saw that “complex systems always kick back” [3] (which is a somewhat teleological version of the concept of homeostasis) and that’s surely a characteristic of the Earth’s ecosystem. In practice, Gaia shouldn’t be seen as a Goddess but, rather, as a planetary version of a principle that you may have encountered in high school: “Le Chatelier’s principle,” proposed by Henry Louis Le Chatelier in 1885. The principle says that if a system is perturbed, then the parameters of the system will shift in such a way to counteract the effect of the perturbation. So, imagine heating a vessel with some water inside: the heat tends to raise the temperature of the system, but the system will react by evaporating of some water, which reduces the temperature increase. The principle smacks more than a little of teleology; it seems to imply a certain degree of conscious will on the part of the system. It is like if the vessel were saying, “you want to raise my temperature? Oh, yeah? Then I’ll evaporate some water in order to lower it, and that will fix you!” But, teleological or not, there is no doubt that the Le Chatelier principle works well in most cases, although not always [227]. When you perturb a system a little, it tends to return close to the local minimum of energy potential, the “attractor”. The trick is in the meaning of “a little,” because if you perturb the system a lot—or just enough—it will do as it damn well pleases, generating sudden phase transitions that may take the shape of the Seneca collapse.

Apart from the great confusion created by the choice of the deity “Gaia” as a name, what Lovelock and Margulis proposed was not so much different from what Le Chatelier had proposed earlier with his principle, although without giving to it a theologically relevant name. The idea of the Gaia hypothesis is that the Earth system tends to oppose changes and that, when perturbed, it modifies its internal parameters in such a way as to reduce the effects of the perturbation. So, when dealing with the global ecosystem, we have several similarities with the organic systems that we normally term “living beings.” In particular, the Gaia hypothesis assumes that the Earth is a feedback-dominated complex system that has been able to maintain an approximately constant temperature during the most of its history and, in particular, to maintain it at levels that made it possible for organic life to survive. There are different ways to express this concept and some people speak of the “weak” and the “strong” Gaia hypothesis. In the first case, the weak hypothesis, Gaia just maintains the temperature in the right range. In the second, the strong hypothesis, Gaia regulates the temperature and other parameters of the system in such a way to optimize it for organic life. But let’s not get into this; the question is, rather: how does Gaia manage to regulate the Earth temperatures?

Here, we face a problem that was noted perhaps for the first time by Unsøld in 1967 [228]. How can the Earth’s narrow range of temperature variations during its history be reconciled with the fact that the Sun’s luminosity grows gradually over the geological time scale? Our Sun is a star of the so-called “main sequence.” Because of its internal structure, the Sun’s luminosity increases approximately of 10% every billion years. That creates “the faint young Sun paradox,” as termed by Sagan and Mullen in 1972 [229]. The young Sun that irradiated the Earth during the Hadean eon was of more than 30% dimmer than it is today. If the Earth of those times were the same as it is today, we can calculate that, with such a weak Sun, it should have been a frozen ball of ice. Nevertheless, we have evidence of liquid water even in those remote times [230]. Organic life appears to have existed continuously on the Earth for at least 3.7 billion years [231, 232] and that means that at least some regions of the planet must have remained always within the range in which organic life can survive, from about 0°C to 40°C. Surely, there were periods in which, on the average, the Earth may have been considerably hotter than it is today [233] and periods in which it was much colder. But, if life survived, there must always have been regions where the temperature limits were not exceeded.

More evidence of this phenomenon comes from the data for the past 542 million years that correspond to the Phanerozoic eon, the time of complex life forms living on the surface of the continents. During this period, we see no obvious long-term trend, even though we observe wide temperature oscillations (Fig. 3.36). But, if we take into account the increasing luminosity of the Sun over that period, we would expect a detectable trend of warming. Something affected the Earth’s temperatures during this period, compensating for the increasing intensity of the solar irradiation; a manifestation of Gaia.

To explain how Gaia manages to control temperatures, Lovelock and his coworker Watson proposed a model that they termed “Daisyworld” [234]. In its simplest form, the model consists of a planet where the only form of life is daisies of which there are two varieties: black and white. Both varieties are supposed to reproduce and compete for space on the surface of the planet, and both thrive when their temperature is at an optimal level. At the beginning of the simulation, the sun’s irradiation is weak and it is too cold for any kind of daisy to survive. As the luminosity increases, the planet’s temperature increases enough to allow black daisies to appear; this variety is more suitable than white daisies for low temperature because it absorbs more sunlight, heating itself. These daisies not only survive but cause an increase of the planetary temperature by reducing the planetary reflectivity (called “albedo”). As the planet warms up, white daisies appear, now able to survive. The two species compete and, as the solar irradiation keeps growing, the white daises gain an evolutionary advantage because they can better maintain an optimal temperature by reflecting sunlight. The number of white daisies grows and this increases the albedo so that the planet doesn’t warm up as it would have done if there were no daisies. Eventually, the black daisies disappear, completely replaced by white daisies. At this point, there is no longer a mechanism to vary the albedo and keep the temperature in check. The temperature rises with rising irradiation, pushing it away from the optimal level for daisies to survive. White daisies start dying off and this generates an enhancing feedback that reduces the albedo, increases the temperature even faster, and rapidly kills off all the daisies. It is a Seneca collapse for the daisies! (Fig. 3.37).

The model can be made more complex by considering several species of daisies of different colors, or even of a continuous series of different shades of gray. Other life forms can be added, such as animals that graze on the daisies. All this doesn’t change the behavior of the system: the daisies stabilize the temperature of the planet despite the gradual increase of the solar irradiation.

Obviously, the Daisyworld model remains extremely simple when compared to the Earth’s ecosystem and it should not be considered as a realistic model of anything. Its only point is to show how a biological system can maintain nearly constant a parameter of the system, temperature, without any need of consciously planning for that. The daisies of Daisyworld are not intelligent, they do not plan anything. They simply compete and the fittest ones survive. The model explains and undercuts the “teleological/theological” content of the Gaia model: there does not need of a benevolent deity controlling the system. Just like many other complex systems in homeostasis, Gaia tends to maintain the conditions in which she finds herself, as long as the perturbation is not too large. And, indeed, the Daisyworld model shows that when the perturbation becomes too large,—in this case a large level of solar irradiation—the system becomes unable to regulate itself any longer and it “dies.”

But what mechanisms could be operating in controlling the temperature of the real Earth system, surely not populated just with white and black daisies? Lovelock based the Gaia hypothesis on the temperature control generated by different concentrations of CO₂ in the atmosphere. As we know, CO₂ is a greenhouse gas that controls the radiative balance of the Earth system by absorbing part of the outgoing radiation. The more CO₂, the hotter the Earth becomes and if CO₂ were the “planetary thermostat” of the Gaian model, we would expect its concentration to show a gradual decline over geological times to compensate for the gradually increasing solar irradiation. This is what we see in the geological record, although only approximately and with many oscillations. Two-three billion years ago, the concentration of CO₂ was more than two orders of magnitude larger than it is today [233, 235], and that may account for the faint young sun paradox, even though other factors, including a smaller albedo, may have been at play. At the beginning of the Phanerozoic, some 500 million years ago, the CO₂ concentration may have been at about 5000 ppm [236], or, according to some recent results, ca. 1000 ppm [237]. The present concentration is about 400 parts per million, but it never went above ca. 300 ppm during the past million years or so, before humans started burning fossil fuels. Clearly, the trend has not been smooth but, overall, there has been a reduction of CO₂ concentrations in the atmosphere over the past Eons. That’s what we should expect if CO₂ was, indeed, the main planetary thermostat all over the long history of planet Earth.

If CO₂ is the planetary thermostat, we need to understand what makes it work. Any thermostat needs a two-way feedback effect: it must generate warming when temperatures go down and do the reverse when temperatures go up. In other words, it must act like the black/white daisies of Daisyworld. In the case of the real Earth, the mechanism of the thermostat could be the biological control of CO₂ concentrations, as Lovelock had initially proposed. Plants need CO₂ to survive and, if we assume that more CO₂ leads to more plant growth, that would remove CO₂ from the atmosphere, cooling it. The reverse holds true as well, with less CO₂ leading to less plant growth and with a lower rate of removal of CO₂ from the atmosphere. These phenomena would lead to a stabilizing feedback that would affect temperatures. The problem with the idea of a biological control of the CO₂ concentration is that the amount stored in the biosphere, about 2000 Gt (gigatons), is not much larger than the amount stored in the atmosphere (about 750 Gt) [239]. That implies that the thermostat could operate only by means of rather large variations in the size of the biosphere, something that seems improbable and for which we have little or no proof. The problem is even more important if we consider remote ages when there was much more CO₂ in the atmosphere than today and the biosphere would surely have been too small a sink to operate the kind of control required by the Gaia model.

So, we need a different mechanism to explain the planetary temperature control and it exists: it is the “long” (also “ultra-long” or “geological”) carbon cycle . It still based on the greenhouse effect of CO₂, but on different mechanisms that control its concentration. It works in this way: CO₂ is a reactive molecule that slowly corrodes the silicates of the Earth’s crust. The result of the reaction are solid carbonates that remove CO₂ from the atmosphere. The process is slow, but it is possible to calculate that it could remove all the CO₂ present in today’s atmosphere in times on the order of a million years or less [240]. Of course, photosynthesis would cease to function much before reaching zero CO₂ concentration and the biosphere would die as a consequence. Fortunately, CO₂ is continuously replenished in the atmosphere by another inorganic process. It starts with the erosion of carbonates by rain and their transport to the ocean where they settle at the bottom, also in the form of the shells of marine organisms. The carbonates are transported at the edge of the continents by tectonic movements and pushed inside the Earth’s mantle. There, high temperatures decompose the carbonates and the carbon is re-emitted into the atmosphere as CO₂ by volcanoes.

This long-term carbon cycle can be seen as a closed cycle chemical reaction controlled by temperature. This is the key point that makes the cycle a thermostat. The reaction of CO₂ with the silicates of the crust speeds up with increased temperature: the higher the temperature, the faster CO₂ is removed from the atmosphere. In addition, the presence of plant life accelerates the reaction rate since it generates a porous soil where the reaction can occur in a wet environment. In these conditions, the removal of CO₂ from the atmosphere overcomes the amount released by volcanoes and the lower concentrations generate lower atmospheric temperatures. The opposite effect occurs when low atmospheric temperatures slow down the reaction, giving the time to volcanoes to replenish the atmosphere with CO₂. So, we have a thermostat that appears to have been the main cause of the relative stability of the Earth’s temperatures over the past four billion years. Note also that the thermostat has a time constant of several hundred thousand years. It means that the system tends to react to perturbations, but does so very slowly. This explains the strong temperature oscillations observed in the geological record.

An especially catastrophic case of temperature oscillation took place during the period called “Cryogenian,” from 720 to 635 million years ago, when the Earth cooled down so much that it became completely covered with ice (it is commonly called the “snowball Earth” episode). In these conditions, the reaction of silicate erosion couldn’t take place any longer simply because there was no more land in contact with the atmosphere. But that didn’t prevent volcanoes from pumping CO₂ into the atmosphere and that led to a gradual increase in CO₂ concentrations. Eventually, the system arrived at a tipping point when the atmosphere became so warm that icecaps experienced a sort of Seneca collapse, melting down in a relatively short period, perhaps in less than 1000 years. It must have been spectacular to see the Earth shedding its ice cover so fast, after having been frozen for millions of years. Oscillations such as these may have been disastrous for the ecosystem, but the end of the Cryogenian may also have been the trigger that led to the appearance of multicellular creatures in the Earth’s ecosystem. Growth and collapses are part of the way the universe works. In the end, Gaia and Medea may be the same person.

3.7.1.2 Hell on Earth

In the science fiction stories of the 1940s and 1950s , the planet Venus was often portrayed as a warm and humid world, full of swamps and often populated with dinosaurs and beautiful alien princesses. Reality turned out to be very different. The first temperature measurement of Venus was carried out during a flyby of a US probe, Mariner 2, on December 14, 1962. Later on, starting with 1967 and for some two decades afterward, the Soviet Union sent a series of probes to Venus and most of them landed successfully on the surface. None survived for more than a few hours: too hot and too acidic were the conditions they encountered. Venus as a planet doesn’t live up to the reputation of the Goddess that gave it the name. Instead, it is a true hell with a surface temperature around 450°C and an atmosphere composed mainly of CO₂, also including clouds of sulfuric acid. Not exactly a place to visit in search for alien princesses.

What made Venus such a hellish world is an unavoidable effect of being much closer to the Sun than the Earth and, therefore, receiving almost twice as much energy. That would not, by itself, bring the temperature of Venus all the way to 450°C. Rather, we have here a stark example of how powerful the greenhouse effect is and how it can generate the phenomenon called “runaway greenhouse effect” [241]. In a remote past, Venus may have had oceans of water and a climate not unlike that of the early Earth [242]. It may even have had organic life [243]. But Venus couldn’t maintain Earth-like conditions for more than a few hundred million years, much less than the four billion years that life has lasted on our planet. We don’t know exactly when the transformation from paradise to hell occurred but, evidently, the Sun’s gradually increasing temperature caused Venus to pass a climate tipping point leading to a “runaway warming.” Eventually, the oceans evaporated and organic life died out, if it ever existed. Then, Venus became what it is now: truly an example of the Seneca ruin.

We may be sad for the lifeforms that may have existed on Venus long ago but their destiny was unavoidable. The question is, rather, whether a similar catastrophe could occur to our planet. Up to now, the ecosphere (Gaia) has been able to compensate for the slowly increasing solar irradiation by a feedback involving decreasing the CO₂ concentration. But, just like the daisies of the Daisyworld model, at some moment there won’t be any more room for feedback regulation because further lowering the CO₂ concentration would kill the biosphere, unable to perform photosynthesis anymore. This is the physical limit to the stabilizing feedback mechanism that, so far, has kept the Earth’s temperature under control. If that mechanism fails, the result would be a runaway warming of the planet that would eventually lead to the death of the biosphere. How far away are we from that limit? Not so far, apparently.

There is evidence that during the past million years the biosphere has been having troubles in adapting to the progressively increasing solar irradiation and the consequent lower CO₂ concentrations needed to keep temperatures within acceptable limits. That seems to be the reason for the appearance of new, more efficient photosynthesis mechanisms that need less CO₂ to operate. The oldest photosynthetic pathway is called “C3.” It is probable that it evolved more than three billion years ago in an atmosphere that contained high concentrations of CO₂ and no oxygen [245]. The C4 pathway is much more recent, no more than a few tens of million years old. It is not very different than the C3 one, but it can concentrate CO₂ in the plant cells. In this way, it can be more efficient at low CO₂ concentrations and in dry conditions. The third mechanism, CAM (Crassulacean-Acid metabolism) is a special kind of photosynthesis that operates only in extremely dryconditions for the kind of plants that we call “succulents.”

The minimum concentration of CO₂ for photosynthesis to operate in C3 plants is normally reported as around 220 ppm, but it could be lower if the atmospheric oxygen concentration were to decrease. C4 plants, instead, could perhaps still survive at concentrations as low as 10 ppm of CO₂ [246]. In these extreme conditions, it is probable that neither C3 nor C4 photosynthesis would be efficient enough to sustain complex forms of life. It is worrisome to note that the data from ice cores show that the CO₂ concentration during the ice ages of the past one million years or so could have been as low as 180 ppm at some moments. We may have edged quite close to the extinction limit for the C3 plants that form the largest fraction of the world’s plants. We cannot say with certainty if we risked a major catastrophe, but it surely was the harbinger of things to come. The ecosphere seems to be running out of the mechanisms that make it able to cope with the progressively increasing solar radiation (Fig. 3.38).

Franck et al. tried to model the future of the biosphere over the next billion years or so [247]. Their results are obviously just an approximation, but it seems that the biosphere’s productivity may have peaked around the start of the Phanerozoic Eon, some 540 million years ago, declining ever since. Multicellular creatures are expected to disappear some 800 million years from now, together with the oceans boiling off and being in part absorbed into the mantle [248]. Single celled organisms are expected to persist for about 1.5 billion years beyond that, as long as some water remains available, deep in the crust. Finally, they will be destroyed by temperatures reaching levels that will make organic life impossible [249].

These phenomena would be accompanied by profound changes in the atmospheric composition . The rising temperatures would gradually increase the concentration of water vapor in the atmosphere. This would eventually lead to a condition called “moist greenhouse” [250, 251], with the Earth blanketed by a thick layer of water vapor blocking most or all the outgoing infrared radiation coming from the surface. That would cause the Earth’s surface to warm up considerably, eventually causing the oceans to boil. The water vapor accumulated in the atmosphere would be gradually removed by a reaction with ultraviolet solar light that decomposes water into in hydrogen and oxygen, with the lighter hydrogen escaping to space. Eventually, liquid water would disappear from the Earth’s surface. In these conditions, the reaction of weathering of silicates that stabilizes the CO₂ concentration would cease to function and the concentration of CO₂ would greatly increase as volcanoes keep pumping out CO₂, resulting from the decomposition of carbonates . At the same time, without a biosphere, or with a greatly reduced extent of the biosphere, photosynthesis would no longer be able to remove CO₂ and replenish the atmosphere with oxygen. In time, the oxygen would disappear because of the oxidation of the organic compounds contained in the crust, mainly kerogen. The final result would be an atmosphere mainly composed of CO₂ and a very hot Earth that would look very much like Venus does today [251, 252, 215]. Because of that, this runaway greenhouse effect is sometimes called the “Venus effect.”

We may imagine that sentient beings of the future might be able to avoid this catastrophe by shielding the Earth from the excess radiation using, for instance, mirrors placed in space. Or they may be able to push the Earth farther away from the Sun. But that’s not something that we should be worried about right now. Rather, there is a nagging question: could human activities trigger a much faster Venus effect than the one we expect to take place in about one billion years from now? Stated in a different way, would Gaia be able to survive the human perturbation in terms of greenhouse gases emitted into the atmosphere? The climatologist James Hansen has strongly argued that the human-caused Venus effect is not only possible but something to be worried about in our times [253]. Initially, model calculations didn’t confirm Hansen’s hypothesis [252], indicating that CO₂ concentrations as high as 10,000 ppm would be needed to trigger the Venus effect, and human activities are unlikely to emit so much of it. But later studies that took more factors into consideration arrived at the opposite conclusion. In their recent study (2016), Popp and his coauthors [251] say, “we have demonstrated with a state-of-the-art climate model that a water-rich planet might lose its habitability as readily by CO₂ forcing as by increased solar forcing through a transition to a Moist Greenhouse and the implied long-term loss of hydrogen.” They calculated that some 1500 ppm of CO₂ could be enough to turn the Earth, eventually, into a hot hell [251]. Given the uncertainty in these calculations and considering that today we have increased the CO₂ concentration to 400 ppm starting from about 280 ppm before the industrial revolution, we may not be so far from the limit to feel completely safe. But how much carbon can we emit into the atmosphere?

No matter how much they love their SUVs , humans wouldn’t knowingly burn so much fossil carbon that they would choke themselves to death by consuming all the of oxygen in the atmosphere. Nevertheless, they could emit very large amounts of carbon. According to Rogner [254, 255] the total amount of fossil fuels reserves corresponds to 9.8 × 10¹¹ t (around a trillion tons). In a 2012 study, Jean Laherrere reported a total of 1.3 × 10¹² tons of carbon as the total amount burnable [256]. In a paper published in “Nature” in 2015, McGlade and Ekins report a value of 3 × 10¹² t [257]. Clearly, there is some agreement that the amount of burnable carbon is on the order of one to three trillion tons. Burning so much carbon would mean adding 500–1500 ppm of CO₂ to the present value of some 400 ppm. Part of this amount would be absorbed by natural “sinks” in the ecosystems, mainly dissolution into the oceans. But the sinks may not operate in the same way forever; they might be saturated and be turned into sources. So, these values of potential CO₂ concentrations are already too close for comfort to the possible tipping point to the runaway greenhouse. Then, there is an even more worrisome problem: the warming of the planet could cause the release of the methane present in the permafrost in the form of solid hydrates (or “clathrates”) stored at high pressure. It has been estimated that this could add a further two trillion tons of carbon to the atmosphere in the form of gaseous methane [258], which is an even more potent greenhouse gas than CO₂ (although it would be slowly oxidized to CO₂). This is called the “clathrate gun,” the true embodiment of the concept of “enhancing climate feedback,” the same feedback that’s believed to be the cause of several past extinctions and catastrophes [259]. We cannot prove that these emissions would lead to a runaway greenhouse effect that would kill the whole biosphere, but we cannot be sure that they would not, either. In any case, the damage done to the ecosphere would be gigantic [260, 261].

The accepted wisdom that derives from these considerations is that, to be reasonably safe, we need to prevent the industrial system from adding more than about 5 × 10⁺¹¹ t (half a trillion tons) of carbon to the amount already emitted in the atmosphere in the past. That corresponds to about a third of the estimated carbon reserves. The consequence is that humans should willingly refrain from burning all the carbon that they could burn but that’s problematic, to say the least. The concept of the need of curbing CO₂ emissions at all is still hotly debated at the political level and we are witnessing the development of a concerted campaign of public relations designed to convince the public that climate science is wrong, or not to be trusted [262]. The 2015 COP21 conference Paris established some targets to limiting CO₂ emissions, but it provided no binding rules that would force countries to reduce their emissions at the required levels. So, we can be reasonably skeptical about the possibility that it would be possible to agree on a cap on the worldwide use of fossil fuels.

The situation looks grim in political terms but other factors may intervene to curb the human consumption of fossil fuels. As mentioned in an earlier chapter, estimates of “resources” and “reserves” are poor predictors of the actual production trends. In order to burn fossil carbon, we need a functioning industrial system that can provide the resources necessary to find, extract, and process fossil resources. Gradual depletion and the resulting lower net energy yield could make such a system collapse much before the ecosystem goes through a climate tipping point. Collapse could also occur much before the declining EROEI of fuels makes their extraction useless in terms of generating useful energy. A financial collapse could simply make it impossible to keep extracting fuels for the lack of the necessary money. In other words, the tipping point generated by depletion or factors related to the control of the system could precede the climate tipping point. Indeed, some authors have maintained that peaking fossil fuels would make climate change a secondary problem [263], although others calculated that, even in a “peak fossils” scenario, emissions would still generate to dangerous CO₂ concentrations [264]. The issue has been reviewed in detail by Hook and Tang, who show that the peaking of fuel supply resulting from depletion is an important constraint in determining the ultimate CO₂ concentration, but not necessarily a factor that will limit it below the safe levels [265]. The question remains very complicated and difficult to assess; the only certainty is that we risk multiple collapses unless we manage to get rid of fossil fuels and move fast to a civilization based on renewable energy [266, 267]. Can we make it? Only the future will tell. If we don’t manage to do that, Gaia may still survive while we disappear, but it may also be possible that that in the fight of man vs. Gaia neither will be left standing.

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Ugo Bardi

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Bardi, U. (2017). Of Collapses Large and Small. In: The Seneca Effect. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-57207-9_3

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