Sunday, October 28, 2018

The Seneca Rebound: why Growth is Faster after Collapse. Explaining the European World Dominance

Lisbon: the monument to the European sailors of the age of explorations, starting with the 15th century. What made Europeans so successful in the task of conquering the world? My interpretation is that it was the result of periodic "Seneca Collapses" of the European population which made it possible to accumulate resources that would then be available to propel the European expansion. It is an effect that may be called the "Seneca Rebound" that makes growth faster after a collapse.

The Middle Ages are sometimes referred to as the "Dark Ages" -- this is mostly untrue, but it is not wrong to apply this term to the early Middle Ages, called also the "Late Antiquity"(1). According to some estimates, in 650 AD the European population had shrunk to a historical minimum of some 18 million people, about half of what it had been during the high times of the Roman Empire. If you think that today the European population is estimated to be as more than 700 million people, it is almost impossible for us to imagine the Europe of the early Middle Ages: it was a minor appendage of the Eurasian continent, a poverty-stricken place, nearly empty of people, where nothing happened except for the squabbles of local warlords fighting each other.

Yet, a few centuries later, the descendants of the inhabitants of this backward peninsula of Eurasia embarked in the attempt of conquering the world and were successful at that. By the 19th century, practically all the world was under the direct or indirect control of European countries or of their American offspring, the United States. How could it happen?

The conventional explanation for the European ruling of the world has to do with factors related to the "white man's burden", a term invented by Rudyard Kipling in 1899. According to this interpretation, the European domination was a sort of manifest destiny generated by the superior qualities -- genetic or cultural -- of the European people in terms of being smarter, more laborious, better organized, driven by their Christian faith, and the like. In comparison, the populations of the rest of world were lazy, disorganized, uncultured, and in the grip of superstitions.

Maybe, but the idea that the Europeans conquered the world because they are smarter than the others is not supported by any data. Europeans may find it flattering, but it is an ad hoc interpretation that doesn't help us understand much of what led to the European world dominance. I have been scratching my head on this question for quite a while, until I stumbled into the graph below, showing two drastic "Seneca Collapses" of the European population. The term "Seneca Collapse" indicates a situation where the decline of a complex system is faster than its growth.

Graph from William E Langer, "The Black Death" Scientific American, February 1964, p. 117 -- note how growth is faster after the collapse than it was before. This is what I call the Seneca Rebound.

Note first of all that the data are uncertain and not all authors see the population drop in the European population to have been as drastic as Langer does. But there is a general agreement that a drastic collapse of the European population took place starting in mid 14th century AD. The collapse is often attributed to the spread of the "black death," a continent-wide epidemics of plague. In reality, there were several factors that led the European population to crash down so badly, including famines and a widespread economic crisis. In a complex system it always is difficult to establish a clear-cut chain of causes and effects: when the system crashes, many factors collapse together. The population crash plague that hit Europe in mid 17th century was less drastic, but also associated with a new outburst of the plague. These two Seneca Collapses followed the one I already mentioned, when the Roman Empire collapsed during the 6th-10th centuries AD.

There is a common element of these three collapse: the remarkably rapid recovery that followed. Let's describe that in more detail.

The first collapse (from the 5th to the 8th century). After the fall of the Western Roman Empire, Europe started recovering and soon it was able to mount military attacks against neighboring regions. The first crusade started in 1095 and for some three centuries successive waves of European armies attacked the region we call today the Middle East, succeeding in creating a number of European kingdoms in the area. The result was, ultimately, a failure and the European crusades and the European Middle Eastern kingdoms withered with the mid-14th century.

The Second collapse (mid-14th century). The population crash was brutal, but as soon as Europe started recovering, a new phase of expansion started: it was the age of exploration that we may consider to have started with the discovery of the island of Madeira in 1430 and then proceeding with a remarkable burst of explorations that lasted for about a century from mid 15th century to mid 6th. This burst included Columbus' travel of 1492 and the start of the gradual expansion of Europeans in Africa and in the Americas.

The Third Collapse (mid-17th century). In this case, the collapse was not so drastic as the first two and it didn't really stop Europeans from expanding. But, with the restart of population growth, Europe saw a new phase of economic growth which ushered the age of coal and, with it, the "age of divergence" when Europe truly conquered the rest of the world and started thinking of themselves as carrying the "white man's burden."

So, there is clearly a pattern here: the expansion of the European social system didn't go on smoothly, but in bursts. Over some two millennia, the European population grew from a few tens of millions up to the current 700 million people. In the process, it underwent at least three major crashes but, every time, it restarted growing. This bumpy expansion trajectory is typical of complex systems which tend to show what I call the "Seneca Effect," cycles of slow growth and fast collapse.

Europe, intended as a social system, is a complex system and it does tend to show the Seneca behavior. It is the result of the combination of resource depletion and pollution. Before the fossil fuel age, society had two main natural resources to exploit: fertile soil and forests. Both tend to be overexploited, that is destroyed faster than they can regrow. Forests are cut faster than trees can regrow and the fertile soil is eroded and washed to the sea faster than it can reform. The decline of agriculture not only puts an end to population growth, it causes it to collapse ruinously as an effect of famines and epidemics. The loss of the revenues from forests typically weakens the state and the result is internecine wars which, of course, hasten the collapse. Both wars and epidemics can be seen as forms of pollution and the final result is what I call the Seneca Effect: a decline which is much faster than growth.

But there is life after the Seneca Collapse. The disappearance of a large fraction of the population frees some previously cultivated land for forests to regrow. Then, when the population starts re-growing, people find the new forests as a near-pristine source of wood and -- once cut -- of fertile soil, and the cycle restarts. The new cycle may grow faster than the earlier one because society still remembers the social structures and the technologies of the previous cycle. This is the "Seneca Rebound" -- growth may be faster after collapse. You can see the Seneca Rebound in the curves made by Langer for Europe. Note how growth is faster after the collapses than it was before. This is because, I think, the Europeans had kept the social and technological structures they had developed before the crash -- there was no need, for instance, to re-develop their ship-making technology (3). So, they could exploit more effectively the resources that the collapse had freed.

Then, Forests are the basic resource needed to conquer the world and the Europeans exploited them effectively. Trees provide the wood for ships and the charcoal made from wood provides the material needed to make steel for weapons. Not for nothing, it was said that England had conquered an empire with ships of wood and men of iron.

But how was it that the Europeans were so much better than others at exploiting their forests? As always, success is a question of timing, opportunities, and luck. On the opposite side of the Mediterranean, the Arab civilization was socially and technologically as sophisticated as the European one - perhaps more - but their climate didn't allow forests to grow fast enough to avoid rapid overexploitation (2). The American civilizations we call "pre-Columbian" had forests, but they hadn't yet developed the technologies of steel and of oceanic ships -- they also lacked horses for transportation and as a military weapon. The Chinese, instead, had the technologies and also the forests and, indeed, they embarked in a parallel phase of explorations.

During the 12th-13th centuries an outbreak of the same plague that had affected Europe caused a decline in the Chinese population, that was followed - possibly as a consequence - by the Mongol invasion which led to the fall of the Song dynasty. When the Chinese economy experienced its own Seneca Rebound, the age treasure voyages started in the early 1400s, during the Ming dynasty, in a period when the population had restarted growing. (4)

China population trends according to a reconstruction published by Columbia University.

But the Chinese stopped their exploration phase and retreated within their borders. So, the Europeans found no competition in their worldwide expansion and that was the origin of the history we know.

These considerations are qualitative, but I think there is something in the idea of the "Seneca Rebound" as an engine that propels civilizations forward in bursts. If this is the case, if the world's civilization goes through a new Seneca Collapse, as it is likely to happen, will it restart expanding afterward?  If we manage to avoid that the coming crash is so bad that we lose the knowledge we accumulated over several centuries and that climate change doesn't erase humankind as a species, we may well restart expanding using renewable energy -- this time into space. Why not?


(1) If you are interested in the late antiquity period, and you can read Italian, you should read "L'Impero Globale" a recent book by Alessia Roberta Scopece who finds many parallels that age and our modern Globalization.

(2) The destruction of the Middle Eastern and North African forests may have been irreversible, as I note in this post of mine. (h/t Steve Kurtz)
(3) Nor there was any need to reinvent luxury and, with the rebound, Middle Ages ladies started dressing like high fashion models, as I describe in this post.

(4) Another reconstruction of the Chinese population is shown below, from an article dealing with the same question as this one -- they arrive to completely different conclusions, but it is normal. 

Thursday, October 25, 2018

Why is Overpopulation Ignored by the Media? The Reasons of a Historical Failure

Some people think there exists a conspiracy that prevents the media from ever mentioning the charged word, "overpopulation." Conspiracies do exist but, in this case, my impression is that population is such a charged issue simply because it has to do with the fact that we are all humans and discussing about reducing population touches some inner mechanisms of our psyche that we feel uncomfortable about.

But there is more to that: the real problem with overpopulation is that most decision makers lack the concept of "overshoot,"  a view that didn't exist in the study of social systems until Jay Forrester introduced it in the 1960s.If you don't understand overshoot, at best you can understand that there are limits to population, but you can't understand that population could exceed the limits and crash down ruinously with the deterioration of the agricultural system that feeds it.

The lack of a the concept of overshoot may well be what leads the concerned and the unconcerned to minimize the problem. Many people seem to think that the "demographic transition," the reduction in fertility observed in most rich nations of the world, will spread over all humankind and stabilize the world's population at a sustainable level without any need for governments to intervene to force lower birth rates.

Almost certainly, it is too late for that: we should have started decades ago. But only China implemented a serious policy birth control -- for the rest of the world it was a historical failure.

In the discussion, below, Bernard Gilland discusses the problems we will face in the attempt of stabilizing the human population mainly in terms of the degradation of the agricultural system in its dependence on non-sustainable resources. It is not the only problem, with climate change potentially able to do even more damage to agriculture. At the same time, the many young people in poor countries will push population onto a still growing trajectory. If these two tendencies, population growth and agricultural decline, crash against each other, the result might well be a Seneca Cliff for the world's human population.

A sustainable global population -and why we cannot achieve it

Guest Post by Bernard Gilland

In the period 1975 – 2018, world population increased at an average of 83 million per year, and reached 7.6 billion in 2018. The increase in 2017 was the difference between approximately 145 million births and 62 million deaths. Despite population growth, the global average daily food supply per person rose from 2440 kilocalories in 1975 to 2940 kilocalories in 2015 (1). However, over 800 million people are undernourished and 300 million adults are obese.

Cereals are the most important crops for food and feed; globally, 45 percent of the cereal production is consumed by humans, and 35 percent by livestock. The remainder is used for industrial purposes, including ethanol, beer, whisky and vodka. The rise in world cereal production since the 1960s is mainly due to two technological advances. The first was Haber-Bosch ammonia synthesis, in which atmospheric nitrogen is fixed as ammonia (containing 82 percent nitrogen) which plants utilize for protein formation. Production of Haber-Bosch ammonia began in 1913, but did not begin to rise rapidly until the 1960s. The second advance was the Green Revolution that began in the mid-1960s, after agronomist Norman Borlaug had bred varieties of dwarf wheat that give higher yields in response to heavier applications of nitrogen, phosphorus and potassium fertilizer, pesticides and irrigation. The breeding and use of semi-dwarf rice and hybrid maize paralleled that of wheat.

The most striking achievement of chemical agriculture is the maize yield in the U.S., which rose from 2.5 tonnes per hectare (40 bushels per acre) in 1950 to 11.0 tonnes per hectare (175 bushels per acre) in 2016. The global cereal yield rose from 2.81 tonnes per hectare in 1992-96 to 3.91 tonnes in 2012-16 (2). Linear extrapolation of the 1992 - 2016 yield trend (52.3 kg per hectare per year) gives a yield of 5.73 tonnes per hectare in 2050. If the population in 2050 is taken as 9.85 billion (3), and the harvested cereal area remains 718 million hectares (as in 2016), production per person in 2050 would be 420 kg, 10 percent above the 2016 level of 382 kg; the uncertainty is about 10 percent either way. Assuming that the global average cereal yield without using nitrogen fertilizer is 1.6 tonnes per hectare, and that fertilizer increases grain yield by 30 kg per kg nitrogen applied, the global average nitrogen application on cereal crops, 80 kg per hectare in 2015, would be approximately 140 kg per hectare. If the incremental yield-nitrogen ratio rises to 35 by 2050, the nitrogen application would be 120 kg per hectare.

The success of the Green Revolution created three major ecological problems:

1. Globally, about half the applied nitrogen is taken up by the crop plants; the remainder volatilizes in the form of ammonia and nitrous oxide (a powerful greenhouse gas) or leaches to groundwater, resulting in eutrophication (the formation of algae) in rivers, lakes and coastal waters; this creates “dead zones” in which fish cannot live.

2. Applying nitrogen, phosphorus and potassium fertilizer to crops changes the balance between these nutrients and those needed in small or trace amounts; the latter include calcium, sulphur, magnesium, iron, manganese, copper, zinc, cobalt, boron and selenium.

3. Approximately 40 percent of global irrigation water is obtained by pumping groundwater from tube wells; this has resulted in the depletion of aquifers and the lowering of groundwater levels, thereby contributing 0.4 mm to the global sea level rise of 3.4 mm per year (4).

As population growth increases the need for fertilizer, it follows that population reduction would ultimately solve the ecological problems. Unfortunately, human nature is such that global population reduction is not feasible. The reasons for this are given in the following.

In 1950, France had a population of 42 million and 20 million hectares of arable land, i.e. 2 persons per arable hectare. The nitrogen fertilizer application on cereals was negligible, and cereal production per person was about 400 kg per year, slightly higher than the present world average. If the ratio of population to arable land were 2 persons per hectare on the world’s 1.6 billion arable hectares, world population would be 3.2 billion. Reducing world population to this size would mean reducing the global average fertility rate (currently 2.5 children per woman) to 1.5 by 2050 and holding it at that level until 2200. The proportion of the population in the 65+ age-group would rise to 35 percent. Such a drastic change in the age distribution would mean raising the pensionable age to 70 years or more.

Adopting and enforcing a population limit for each country would be an insurmountable obstacle, as Charles Galton Darwin pointed out in 1952 (5). To lower the global average to 2 inhabitants per arable hectare, countries such as Canada, Russia, Australia and Argentina would not be required to reduce their populations, but would not be permitted to reach 2 inhabitants per arable hectare; they would be obliged to have a grain surplus for export to countries that need grain imports. China and India would each have to reduce its population to roughly 300 million; the combined population of the two countries would then be 20 percent of the world population instead of the present 35 percent (6). The relative population reductions in Japan and Egypt, which have 30 and 33 inhabitants per arable hectare respectively, would be much greater (6).

The population of China is projected to peak at 1.45 billion around 2030 and decline to one billion by 2100. This is partly a result of the so-called one-child policy launched in 1979 (in reality a 1.5-child policy). It was replaced by a two-child limit in 2016, but the fertility rate remains 1.6. Japan has a population of 126 million and a fertility rate of 1.4; the population is projected to decline to 102 million in 2050 and 60 million in 2100. These projected long-term declines are likely to be halted by pro-natalist policies based on the advice of growth-obsessed economists who believe that population decline results in a shortage of labour. A world population peak of at least 10 billion is almost inevitable, and this would make 70 percent of the world’s population dependent on Haber-Bosch ammonia. This is not sustainable, but there is no solution in sight. As a sustainable population cannot be attained by fertility decline alone, a mortality rise is highly probable. We can only guess when.

Bernard Gillan is an independent researcher with a degree in Engineering, based in Copenhagen, Denmark. He is the author of several papers on demography and population


1. FAOSTAT data.

2. World Bank data.

3. Population Reference Bureau. World population data sheet 2018.

4. Konikov, L.F. 2011. Contribution of global groundwater depletion since 1900 to sea-level rise. Geophysical Research Letters, 38; L17401.

5. Darwin, C.G. 1952. The next million years. Hart-Davis, London.

6. Lionos, T.P., A. Pseiridis. 2016. Sustainable welfare and optimum population size. Environment, Development and Sustainability, 18(6), 1679 - 1699. According to the authors, the optimum population of the world is 3.1 billion, and the populations (in millions) of the ten most populous countries are:

China 253, India 341, United States 326, Indonesia 88, Brazil 156, Pakistan 43, Nigeria 79, Bangladesh 17, Russia 249, Japan 9.2. The figure for Egypt is 7.4.

Sunday, October 21, 2018

The Fall of Empires Explained in 10 Minutes

This is the presentation I gave to the meeting for the 50th anniversary of the Club of Rome on Oct 18th in Rome. The gist of the idea is that the fall of ancient civilizations, such as the Roman Empire, can be described with the same models developed in the 1970 to describe the future of our civilization. States, empires, and entire civilizations tend to fall under the combined effect of resource depletion and growing pollution. In the end, they are destroyed by what I call the Seneca Effect.

You can find the paper I mention in the talk, coauthored by Ilaria Perissi and Sara Falsini, at this link.

Sunday, October 14, 2018

Why Economists Can't Understand Complex Systems: Not Even the Nobel Prize, William Nordhaus

The "base case" scenario of "The Limits to Growth" 1972 report to the Club of Rome. The strong non-linearity of the behavior of complex systems -- including the global economy -- is nearly impossible to understand for people trained in economics. William Nordhaus, the recent Nobel prize winner in economics, is no exception to the rule. In this post, I'll report how, at the beginning of his career, Nordhaus criticized "The Limits to Growth", showing in the process that he had understood nothing of the way complex systems work.

After having been awarded the Nobel prize in economics of this year, William Nordhaus has been often presented as some sort of an ecologist (see, e.g. this article on Forbes). Surely, Nordhaus' work on climate has merit and he is one of the leading world economists who recognize the importance of the problem and who propose remedies for it. On the other hand, Nordhaus' approach on climate can be criticized: he tends to see the problem in terms of costs and solvable just by means of modest changes.

Nordhaus' approach to climate change mitigation highlights a general problem with how economists tend to tackle complex systems: their training makes them tend to see changes as smooth and gradual. But real-world systems, normally, do what they damn please, including crashing down in what we call the Seneca Effect.

On this point, let me tell you a little story of how Nordhaus started his career at Yale by an all-out attack against system dynamics, the method used to prepare the 1972 study "The Limits to Growth," showing in the process that he had understood nothing on the way complex systems work.

In 1973, Nordhaus published a paper titled "Measurements without Data." It was directed specifically against Jay Forrester, the founder of system dynamics, accusing him of having developed a model able only to describe a world existing only in his (Forrester's) imagination. If you know something about how scientists think, you may understand that this is not just an accusation: it is an insult. And Nordhaus' paper didn't mince words, even getting into direct and personal accusations against Forrester, for instance that he was favorable to the extinction of the human race, that he lacked humility, that he wasn't testing his assumptions, that he ignored the previous literature, that his model was the equivalent of a "widow cruse", and a few more quips.

Nordhaus's attack was one of the first broadsides against world dynamics, possibly the pebble that originated the avalanche of political criticism that gave a bad name to "The Limits to Growth" in the 1980s and 1990s. To get some idea of the adversarial atmosphere of the time, note that, contrarily to all normal procedures in science, the editor of the journal that published Nordhaus' paper refused to publish Forrester's rebuttal - he was forced to publish it in a much less known journal, where it remained basically unknown while the "Limits-bashing" went on.

But what was the substance of Nordhaus's criticism? Nearly half a century after the publication of his paper, it would make little sense to go into the details of its 29 pages, dense with formulas and reasoning. Basically, the paper demonstrates how Nordhaus just didn't understand Forrester's ideas and methods, claiming over and over that standard economics was a better tool to describe the world system. He couldn't understand -- just as most modern economists can't -- that standard economics doesn't account for the kind of oscillations -- including crashes - which are observed in history and that system dynamics describes very well.

This is an especially serious limitation when dealing with the earth's climate, which is a complex system subjected to abrupt changes and tipping points: here the approach of economists is not only wrong but outright dangerous because it leads decision makers to a false sensation of safety and control which, in reality, we don't have.

The whole story is told in some detail in my book "The Limits to Growth Revisited" (Springer 2011. Below, an excerpt dedicated to Nordhaus's criticism


From "The Limits to Growth Revisited"
by Ugo Bardi, 2011

We can now examine the work of William Nordhaus, who emerged out of the debate as one of the major critics of the LTG study and, in general, of system dynamics as a method for modeling economic systems. In 1973, Nordhaus published a paper titled “World dynamics: measurements without data” [Nordhaus 1973] taking as a target Forrester’s book [Forrester 1971]. However, it is clear that Nordhaus’s attack broadly included also the LTG work.

Nordhaus's paper spans 27 pages and contains much material worth discussing, but it would be out of scope to go into all the details here. Forrester himself used 21 full pages in his response that was published in “Policy Sciences” [Forrester et al 1974]. For what we are concerned here, we may summarize Nordhaus's criticism as pertaining to basically three categories: 1) accusations ad personam, 2) unsubstantiated statements of disbelief and 3) quantifiable criticism.

As for the first category, we can take as an example the accusation of “lack of humility,” made against Forrester. The gist of this accusation is that carrying world simulations all the way to the end of the 21st century is much too ambitious to make sense. This is a legitimate opinion, but not something that can be evaluated on the basis of objective criteria. On this point, however, it is worth noting that Nordhaus himself, later on, committed the same intellectual fault – according to his own definition - with his DICE (Dynamic Integrated Climate Economy) model [Nordhaus 1992, (b)].

The second category of criticism from Nordhaus, “statements of disbelief,” collects alleged shortcomings of world modeling which, however, are not substantiated by actual proof. One such statement, taken as an example, is the following: (p. 1166)

“..we discover dramatic returns to scale of the economy: if we double both the number of blast furnaces and the number of ore fields the output of pig iron quadruples”

But nowhere in his paper does Nordhaus demonstrate that Forrester's model produces such obviously unrealistic results. In fact, Nordhaus is simply looking at one of the several equations of the model without realizing that the output of each equation will be modified by the interaction with all the other equations and that will insure correct returns to scale. This is the essence of systems thinking: that parts interact.

Let’s now consider the accusation of “measurements without data” which is the most important part of the paper and gives it its title. This is a quantifiable criticism: if it can be shown that Forrester (or the LTG group) were making models which are totally unable to describe the real world, then it is correct to dismiss their work as useless and irrelevant.

In “World Dynamics” (1971) and in “The Limits to Growth” (1972) one thing that can be immediately noticed is that historical world data do not appear in the calculated scenarios. For a reader accustomed to the common approach of “fitting” the data, that gives a bad impression. Is it possible that the authors of these studies were really so cavalier that they did not care to compare their results to real world's data?

But a more careful examination of the text of both studies shows that the authors do state that their calculations were calibrated on actual historical data. Not showing these data in the figures was a choice made in order to improve clarity. As a choice, it may be criticized, but not ignored.

On this point, note also that, in the “Models of Doom” book [Cole et al 1973] examined before, none of the several authors engaged in the study felt that Forrester’s work (or the LTG book) could be criticized in the terms used by Nordhaus. In the chapter by Cole “The Structure of the World Models” [p. 31 of Cole et al 1973] the data used in the models are examined in detail. Some of the approximations utilized are criticized and in some cases it is said that the data are insufficient for the purposes of the model. But it is never stated that the models were “without data”.

So, it is clear that the world2 (Forrester's) and world3 (LTG) were calibrated to the historical data – at least within some limits. On this point, although both Forrester and the LTG team made an effort of choosing the parameters of the model on the basis of historical data, they also felt that their models had a heuristic rather than explicitly predictive objective. Therefore, there was no need for their scenarios to use a rigorous data fitting procedure of the type used in physical studies. Again, this is an attitude that can be criticized, but that cannot be ignored.

Forrester himself describes this attitude in his book “World Dynamics”” [Forrester 1971]. On page 14 (2nd edition) he says:

There is nothing new in the use of models to represent social systems. Everyone uses models all the time. Every person in his private life and in his community life uses models for decision making. The mental image of the world around one, carried in each individual’s head, is a model. One does not have a family, a business, a city, a government, or a country in his head. He has only selected concepts and relationships that he uses to represent the real system. <..> While none of the computer models of social systems existing today can be considered as more than preliminary, many are now beginning to show the behavioral characteristics of actual systems.

System scientists have a structured approach on this point, as described, for instance, by Sterman [Sterman 2002, p. 523].

… it is important to use proper statistical methods to estimate parameters and assess the ability of the model to replicate historical data when numerical data are available <..> Rigorous defining constructs, attempting to measure them, and using the most appropriate methods to estimate their magnitudes are important antidotes to causal empiricism, muddled formulations and the erroneous conclusions we often draw from our mental models. Ignoring numerical data or failing to use statistical tools when appropriate is sloppy and lazy”

Of course, the very fact that Sterman feels that it is necessary to criticize those modelers who “fail to use statistical tools” indicates that the problem exists. Modeling socio-economic systems using system dynamics tools is not immune to the biases that are easy to see in the ordinary political debate.

So, taking into account all this, how should we understand Nordhaus's criticism? If it is intended as meaning that system dynamics models provide only approximations of the historical behavior of the world, then it is a weak criticism that hardly justifies the statement “measurements without data.” This point must have been clear to Nordhaus himself, who tried to substantiate his criticism by the following statement, referred to Forrester's world2 model (emphasis in the original) :

…..contains 43 variables connected to 22 non-linear (and several linear) relationships. Not a single relationship or variable is drawn from actual data or empirical studies. 

Let’s analyze this sentence. First of all, Forrester's model, as all models, contains three elements: the mathematical relationships, or equations, the variables (populations, resources, etc.) and the constants which appear in the equations and which determine the quantitative behavior of the model. Nordhaus speaks here only of two of these elements: variables and relationships, but not of the third; the constants. Clearly, he was aware that Forrester was using constants derived from real world's data. But, then, what does it mean that “Not a single relationship or variable is drawn from actual data or empirical studies”?

Evidently, Nordhaus thinks that the equations and the variables of the model should have been determined by fitting the experimental data. This is an approach that often goes under the name of “econometrics.” This term does not describe a specific type of model, but it refers to a series of methods and techniques used to fit a set of data, typically a time series, to a model [Franses 2002]. Econometrics can be used to test a model but, in some cases, it is the “best fit” of several models that determines which one is to be chosen. This is a legitimate technique, but one that may easily lead the modeler astray if the physical elements of the system are not sufficiently understood.

In any case, the “best fit procedure” tells you little about the physics of the system being studied. Think of Newton's law of universal gravitation. The scientists who worked before Newton on planetary motions, from Ptolemy to Johannes Kepler, had basically used a “data fitting” procedure to describe their observations but never could derive the law of universal gravitation using that approach. Instead, Newton devised a law that he thought plausible. Maybe he got the idea watching an apple falling from a tree, but that hardly qualifies as data fitting. Then, he calculated the motion of the planets according to his law. He found that simulated bodies orbiting around the Sun would describe elliptical orbits, just as it was observed for the planets. At this point, he could vary the “g” constant in his law in such a way that it was possible to use the equation to describe the movement of real planets.

So, if Nordhaus’ criticism to Forrester were to be applied to Newton’s gravitation law, then one should criticize it because it is not “drawn from actual data or empirical studies” One could actually criticize Newton for performing “measurements without data.”

Of course, Forrester’s model is much more approximate and tentative than Newton's law of universal gravitation. Nevertheless, the considerations about the validation of the model remain valid. So, in order to prove his point, “Measurements without data”, Nordhaus needs to do more. He needs to demonstrate that Forrester's model is totally unable to describe reality.

So, Nordhaus sets up in his paper to “evaluate the specific assumption in the subsectors of World Dynamics.” (p. 1160). The examination of the population subsystem is crucial in this analysis. In fig 3 of his article, Nordhaus plots data on the birth rate as a function of the Gross National Product for several countries, together with what he claims to be the results produced by Forrester's model.

Figure 15. Nordhaus model of the population subsector in Forrester's “World Dynamics.” From Nordhaus 1973

From this figure, it would seem that Forrester’s assumptions are completely wrong and this is, indeed, Nordhaus's conclusion. But what is the curve that Nordhaus calls “Forrester’s assumption”? In the article, we read that this curve is “Forrester’s assumed response of population to rising per capita non-food consumption when population density, pollution and per capita food consumption is held constant” (emphasis added).

But this is not Forrester’s assumption. Nordhaus had simply taken one of the equations from Forrester's model and had plotted it keeping constant all parameters except one (the “non-food consumption” that he equates to GNP). But Forrester’s model was never meant to work in this way. [..] In the “world3” model all the equations need to be solved together to make the model work as it is supposed to. Nordhaus’s obvious mistake was noted and described by Forrester himself [Forrester 1974]:

“The case made by Nordhaus against the population sector of World Dynamics rests on the use of real-world data that he attempts to relate to model assumptions. However, Nordhaus incorrectly compares a single dimensional relationship in world dynamics (between net birth rate and material standard of living) with time series data. He fails to account for the presence of other variables influencing the time series. As a result, he erroneously asserts that the model is inconsistent with the data. In fact, the data Nordhaus present support the validity of the World Dynamics model assumptions.”

Subsequently, Forrester runs his complete model and produces the following figure:

Figure 16 – Forrester’s response to Nordhaus

In this figure, we see that the behavior of birth rates as a function of GNP produced by Forrester's model is qualitatively consistent with the historical data. Later on, Myrtveit [2005] re-examined the question and arrived at the same conclusion.

It appears clear from this discussion that Nordhaus, in his criticism of Forrester's book, had missed some basic points of the methods and the aims of world modeling by system dynamics. Unfortunately, however, Nordhaus’s 1973 paper left a strong imprint in the successive debate, owing in part to Nordhaus’ reputation and in part to the fact that Forrester’s response [Forrester 1974] wasn’t so widely known, mainly because it was published in a scarcely known journal (Policy Sciences) which wasn't even dedicated to economics.

On this issue, it is surprising that the editors of the “Economic Journal,” who published Nordhaus’s paper, did not ask Forrester to reply; as it is a common policy, and even courtesy, in cases such as this one. We have no record that Forrester asked to the “Economics Journal” to publish his rebuttal, but that was the obvious first choice for him if he wanted to reply to Nordhaus; as he did. Consequently, it seems probable that the editors of the “Economic Journal” refused to publish Forrester's reply and that for this reason he was forced to publish it in another journal. Another indication that the debate about world modeling was especially harsh and that it did not follow the accepted rules for this kind of exchange.


The debate about world modeling by system dynamics flared again, briefly, in 1992, when three of the authors of the first LTG book (the two Meadows and Jorgen Randers) published a sequel with the title “Beyond the Limits” [Meadows et al. 1992]. In this second book, the authors updated the calculations of the first LTG study, obtaining similar results. The publication of “Beyond the limits” generated a new response from William Nordhaus; this time with the title of “Lethal Models” [Nordhaus 1992]. This new paper took up again some of the earlier arguments put forward by Nordhaus in his 1973 paper, but with considerable differences. 

Facing the 43 pages of Nordhaus' 1992 paper, we immediately see that it does not contain anymore the ad personam attacks of his first paper on this subject [Nordhaus 1973]. On the contrary, Nordhaus explicitly thanks the authors of LTG for their comments and their assistance. We also see that this paper does not contain anymore the accusation of “measurements without data” that was the main theme of Nordhaus's 1973 paper. All that Nordhaus has to say in this respect is (p. 14):

In Limits I, no attempt was made to estimate the behavioral equations econometrically, although some attempt seems to have been made to calibrate some of the equations, such as the population equation, to available data.

It appears that this is not the only point where Nordhaus is backtracking. On  page 15, for instance, we read that,

“the dynamic behavior of the enormously complicated LTG was not fully understood (or even understandable) by anyone, either authors or critics”

And we may wonder whether with these “critics” Nordhaus intended also himself.


You can find Nordhaus paper here:

And Jay Forrester's rebuttal here.

Sunday, October 7, 2018

Could Donald Trump be the Last World Emperor? States and Empires After the End of the Fossil Age

Empires are short-lived structures created and kept together by the availability of mineral resources, fossil fuels in our times. They tend to decline and fall with the decline of the resources that created them, and that's the destiny of the current World Empire: the American one. Will new empires be possible with the gradual disappearance of the abundant mineral resources of the past? Maybe not, and Donald Trump could be the last world emperor in history.

A warlord named Sargon of Akkad was perhaps the first man in history to rule a true empire, around mid 2nd millennium BC in Mesopotamia. Before him, humans had been warring against each other for millennia, but the largest social structures they had developed were no larger than city-states. Gradually, new forms of social aggregation emerged: kingdoms and empires, structures kept together by a central government that, normally, involves a larger than life male figure, emperor or king, who runs the state machine using a combination of force, prestige, and gifts.

Sargon's Empire went through the normal destiny of the empires that came after it: glory and plunder at the beginning, then struggle, destruction and, finally, collapse. Nothing unusual for a cycle that would span millennia of human history. Taagenpera shows how empires come and go (image source)

The rise and fall of empires looks like a chemical reaction, flaring and then subsidizing, as a reaction running out of reactants -- then restarting when new reactants have accumulated. For empires, the reactants might have been mineral resources -- it may well be that Sargon's empire was the result of silver having become a standard medium of exchange in Mesopotamia. With silver, Sargon could pay his soldiers. With his soldiers, he could rob more silver. And, with more silver, he could pay even more soldiers -- and there you go: the road for glory and murder is open.

The Romans built up their stupendous empire using the gold and the silver of their mines in Spain. When the mines were exhausted, so was the Roman Empire, but it left such a deep impression that for more than a millennium people tried to rebuild it. Charlemagne built his Holy Roman Empire during the 9th century AD by means of newly discovered silver mines in Eastern Europe. Later on, during the 16th century, Charles V rekindled Charlemagne's idea with his empire on which the sun never sets, built on the gold coming from the Americas. But these empires, too, went through a cycle of growth and decline, in parallel with that of the resources which had created them.

The 20th century was the age of fossil empires. The British used coal to create the biggest and the most powerful empire ever built -- it faded away with the gradual decline of its coal production. Another ancient empire, Austria-Hungary, the last remnant of the concept of a European Empire, went to pieces during WWI, the only European state which didn't survive it. The attempt of Italy to re-create the Roman Empire in 1936 with the conquest of Ethiopia had the only effect of generating the shortest-lived empire in the history of the world, just five years. At least, the short saga of the Italian Empire could demonstrate that no empire can exist for long without abundant mineral resources available. With the end of WWII, only two large empires remained: the Soviet and the American one. Both were based on fossil fuels and, in particular, on the abundant crude oil they could produce. For a while, the Soviet Empire challenged the worldwide supremacy of the American Empire - but it had to give up and fold over when its oil resources became too expensive to extract and it was impossible to use them to fuel its military apparatus.

Today, the sole heir of some four and a half millennia of empire building is the American Empire, a stupendous structure that dominates the world's oceans and a large part of the world's land. But, as for older empires, the American one will last only as long as will be able to produce the resources that created it: fossil fuels. And the end can't be too far away: conventional oil production has been declining for decades in the US territory, while the production from shales can only postpone the unavoidable. It may well be that the mighty American Empire will soon follow the path of its predecessors. If this is the case, the collapse will be fast and brutal, the kind of collapse that we call sometimes "Seneca Cliff."

The whole political debate in the US reflects this situation. The Dems (or the Left) have come to embrace the Imperialist viewpoint, pursuing an aggressive foreign policy. The Reps (or the Right) are no enemies of the Empire, but many of them favor retrenching within the US national borders. There is a certain logic in these positions: the political base of the Dems is in the impoverished remnants of the middle class and, for them, the only hope of survival is the economic expansion that could come from plundering foreign countries. The Reps, instead, represent the elites and, for them, the easiest way of maintaining their dominance is to plunder the American middle class.

Donald Trump represents well the view of the elites. He seems to understand (or, at least, to sense) in which direction the wind is blowing and what he is doing, apart from the exaggerated boasting, is to try to turn the parasitic imperial economy of the United States into a self-standing national economy. Not an easy task and Trump may well fail in what he is trying to do. But history never fails: empires have always gone through a cycle of growth and collapse, it is just a question of time.

So, the American Empire is destined to go, but what will come after the fall? Most likely, we'll see a situation resembling that of the fall of the Roman Empire, when there were no resources to build another large empire and Europe moved back into an age of independent cities and statelets. Nowadays, many people seem to think that the disappearance of fossil fuels would bring a return of the Middle Ages. It might happen: large organizations need a lot of energy to run and, in addition, our civilization will be badly hit by global warming. The result may be the fragmentation of the current political entities, returning to nation-states or even back to city-states. There will not be another World Empire and Donald Trump could be, if not the last emperor, the last who ruled an empire as large as the current American one.

The return to Middle Ages could be avoided, at least in part, if humankind were to invest some of the remaining resources into building an energy infrastructure based on renewable energy, but, right now, it seems that these resources will be squandered in a new series of resource wars. And so it goes, it is the great cycle of history that moves onward. Humans struggle, fight, and quarrel, but the best efforts of mice and men come to naught when they try to keep things as they are and they have been. The only unchanging thing in history is that things always change.


Ugo Bardi is a member of the Club of Rome, faculty member of the University of Florence, and the author of "Extracted" (Chelsea Green 2014), "The Seneca Effect" (Springer 2017), and Before the Collapse (Springer 2019)