Tainter’s Law: Where is the Physics?

This is a guest post by Ugo Bardi. This post previously appeared at his English language blog, Casandra’s Legacy.

Joseph Tainter’s interpretation of the cause of the collapse of civilisations is that social structures generate negative returns when they become too complex; as shown above (fromTainter’s 1996 paper). We could call this relationship as “Tainter’s law”. But what is it exactly that generates this behavior? In this post, I’ll try to make a simple model that explains the law.

Joseph Tainter has written a fascinating interpretation of the collapse of human civilisations in his book “The Collapse of Complex Societies” (1988) (see also his 1996 paper) Collapse is a common event: it is the stuff history books are made of. The mighty empires of the past; from Sumeria to the Soviet Union, have all collapsed at some point. Yet, we don’t seem to be able to understand the reasons why collapse is so common.

In his book, Tainter examines previous studies and lists at least eleven causes (or “concauses”) of collapse that have been proposed by historians. Resource depletion, catastrophes, intruders, social conflict, and others. But is there a single cause of collapse? Or are there several? Tainter looks for a single, common root of the problem and finds it in what he calls “the decreasing returns of complexity”.

Starting from a well-known concept in economic theory, that of diminishing returns, Tainter builds his case on historical examples. It is clear that several societies have continued to build up and maintain complex and expensive structures even in conditions where it was very difficult to find the necessary resources. An example is that of the fortifications protecting the Western Roman Empire, that must have been such a burden that we may consider them to be of the factors that brought down the Empire. And, in general, we do see that societies, including ours, build up hypertrophic and complex bureaucracies which appear totally useless; an increase of complexity that generates only a waste of resources.

The idea of decreasing returns to complexity looks consistent and reasonable. But, why do societies behave in this way? Tainter does not provide a real explanation; on this point, he seems to follow the tradition of historians to describe rather than interpret. But, if you happen to have a more physics-oriented point of view, then describing what happens is not enough. You want to know what are the inner mechanisms that make civilisations evolve towards higher complexity. What is the physics of collapse?

So, let’s see if we can build a model of civilisation growth and collapse. The simplest one that I have been able to put together is the following. It is a “toy model, if you like:

The model is based on the conventions of system dynamics. The rectangles indicate stocks of something. You could say that the box on the left contains fossil fuels, whereas the box on the right contains carbon dioxide. The central box contains all the stuff the economy is made of and that is created from the availability of energy from fossil fuels: people, machinery, building, facilities, you name it.

The fossil fuel stock is processed by the economy and eventually transformed into waste, as indicated by the double-edged arrows which show the direction of the flux of matter. The single-edged arrows indicate how the amounts stored in the stocks affect the flow; that is also influenced by two constants: how fast the economy can extract resources and how fast resources are transformed into waste.

There are a few more points about the model; the first is that the resource stock is assumed to be finite – that is “non renewable”. This is an approximation, but it is a good one and not only for our society. Ancient civilizations were based on agriculture, which is supposed to be a renewable resource. But agriculture is not necessarily renewable; it is more often a way to transform fertile land into a desert by mining a non renewable resource: fertile soil.

Finally, note also that the model assumes a feedback relation between resources and the size of the economy. That is, the more resources there are, the faster they are exploited and – also – the bigger the economy, the faster it exploits resources. These assumptions imply a “positive feedback” between resources and the economy; which is a reasonable assumption. A similar relation holds for the waste and the economy.

Now, let’s go on and “solve” the model. That is, let’s see how the size of the stocks change as time goes by. Here are the results (obtained using the Vensim software for system dynamics)

As you see, the stock of resources gets depleted while the economy grows. At some point, however, the flow from the resource stock has been so much reduced that the economy can’t keep growing and it starts declining. In the end, all the stock of resources has been transferred to the “waste” stock.

Note that the model describes a closed system in terms of mass. There is no flux of matter from or to the outside. And, indeed, mass is conserved in the results: the sum of the mass contained in the three stocks is constant. But the system does exchange energy with the surroundings. Burning fossil fuels generates heat, which is dispersed outside as we may assume that all three boxes maintain at the same average temperature.

The main force behind the transformation is energy potential, in this case the chemical potential of fossil fuels. In other words, the left box (resources) has a thermodynamic potential higher than the right box (waste). As we know from the second principle of thermodynamics, the transformation occurs with the creation of entropy. The economy is a grand machine for creating entropy – it could not be anything else.

If you like to use the term “exergy” (the fraction of energy able to do useful work) you can say that the “waste” stock contains much less exergy than the “resources” stock; while the “Economy” stock has an intermediate exergy content. There is no direct system dynamics convention to express stocks in terms of exergy. It could be taken into account in the model, but let’s not go into that – let’s keep this model as a “toy” one. The important thing is understanding what makes it move.

Now, let’s go back to Tainter’s interpretation of collapse. What could we take as “complexity” in the model? There is not an explicit parameter describing that but, as a first approximation, the size of an economy determines its complexity. That has been the rule for all known history and we see it happening even today. With the economic crisis, some structures we could once afford – say, mass instruction, public health care – must shrink and disappear. Society loses complexity in times of decline and gains it in times of growth.

So the “bell-shaped” curve that describes the cycle of the economy should also describe its complexity. Now, let’s walk one further step in quantifying Tainter’s intuition. What can be the meaning of “benefits of complexity”? Well, it is clear from what Tainter says that the benefit of complexity have to do with the ability of society to solve problems. In our toy model, the only problem for the economy is to produce as much as possible in terms of resources. So we can define benefits of complexity as proportional to production, that is to the rate of exploitation of the natural resources stock.

Now we can replot Tainter’s idea from the data of the model, that is, plot production (“benefits”) as a function of the size of the economy (“complexity”). And the result is something that looks very much like Tainter’s law! Here it is. (note that in the full plot the curve is a complete loop that goes back to zero at the end of the cycle):

To compare, here is again Tainter’s original plot: the two graphs are not identical, but the similarity is evident.

Now, of course what we have been doing here is a “toy model” of the economy. When I present this kind of model at conferences, usually there is someone in the audience who stands up and says, “It is too simple; it is not realistic!”. The idea seems to be that I am modelling societies using a “spherical cow model” – a term used to disparage the tendency of physicists to over-simplify their model.

This is a perfectly understandable criticism, but it can be answered. For instance, more detailed models of the same kind provide similar results. For instance, the “world3” model of “The Limits to Growth” study leads to curves that are very similar in shape to the ones shown here.

But I think that is not the point, you can make models simple or detailed, it depends on what is their purpose. The toy model presented here is not meant to describe how real societies behave. It is meant to be “mind sized”, that is able to help us understand how physical factors affect the historical cycle of civilizations. It stresses that civilizations must obey the laws of thermodynamics; just as they must obey the law of gravity.

Some consequences of the model are obvious. It tells us that as long as we base our existence on non-renewable resources, we must eventually run out of them. But it gives us also some non-obvious hint on the path we are going to follow in this cycle. In particular, the model tells us that we will likely keep increasing the size and complexity of our society even with a diminishing flux of resources into the economy. In this sense, it confirms Tainter’s intuition, but it tells us something more; that is it extends Tainter’s curve beyond the limit of the plot shown in his 1996 paper. It says that after the phase of increasing complexity and reduced returns, the curve will loop back and, eventually, both complexity and production will go to zero as is the economy completes its cycle based on non-renewable resources. Here is the complete plot:

But the main point is that, eventually, Tainter’s law derives from thermodynamics. As we know (or should know) thermodynamics is not only a good idea, it is the law!


Tainter’s 1996 paper “Complexity, Problem Solving and Sustainable Societies”

post of mine on Tainter’s view of collapse

paper of mine on modelling resource exploitation

About Gail Tverberg

My name is Gail Tverberg. I am an actuary interested in finite world issues - oil depletion, natural gas depletion, water shortages, and climate change. Oil limits look very different from what most expect, with high prices leading to recession, and low prices leading to financial problems for oil producers and for oil exporting countries. We are really dealing with a physics problem that affects many parts of the economy at once, including wages and the financial system. I try to look at the overall problem.
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26 Responses to Tainter’s Law: Where is the Physics?

  1. Peter T says:

    On the outsourcing, see:


    I think it’s important to look at the distribution of state spending. The US seems to be spending less on infrastructure, basic welfare and education, more on prisons, internal defence, subsidies to the elites. It’s collecting as much tax from the middle and poor, less from the rich. These are, historically, signs of devolution of control.

    On Tainter’s notion of complexity, I think it is an amalgam of span of control, degree of specialisation and ability to coordinate. Hard to operationalise mathematically – Ugo Bardi’s models are a good simple approximation, but hard to see how one could do better.

  2. Peter T says:

    I’d support step back’s note. As complexity increases, problems of coordination and control increase too, but faster. Eventually, most effort is consumed in just managing, with no reserve available to cope with the inevitable external shocks.

    But how much is too much to manage in human affairs is an empirical question (and I think Tainter points to this in saying that the interesting questions are about humans, not energy as such). In ecosystems it seems to relate to the available energy (so the tropics have more complex ecosystems than the arctic). Humans evolves techniques of management and control (the sociologist Michael Mann is very good on this). So what was too much in Roman times is quite manageable now.

    The US seems to have already outsourced a good deal of governance to local elites – maybe a first sign of devolution?

    • The outsourcing might be a sign of devolution, but it seems to me that government spending in the last couple of years has hit a new high and even with outsourcing, it is ultimately government that is doing the spending (or selling off assets, and crossing their fingers that the outsourced group will really maintain them as planned).

      High government spending is acting to cover up the problems the economy as a whole really has (QE2 is helping as well). But this high spending without taxes to support it can’t continue indefinitely. That is why the government shutdown on Friday is scarier than it otherwise would be. At some point, this gap between spending and taxes may be what destabilizes the system.

    • step back says:


      Thanks for your word of support.

      Even here in a blog having such a small number of readers, it is hard to get a message across because we each read one another on the basis of different assumptions.

      Let’s go back to my elaboration on Dr. Bardi’s black box model of “The Economy” (or “The Market Place” of ideas, fantasies, and actualities if you are willing to see it that way).

      Inside this box called “The Economy” there is one specialist known as the “politician”. In fact there are many such “politicians”. They send communications to each other and to the lay public. The “politician” type of specialist basically knows that when he or one of his kind outputs a communication in the open and public square, that it is almost always a BS communication intended not to be taken seriously.

      He also knows that when another kind of close cousin specialist, “The PR man” outputs a communication in the open and public square that it is a BS communication intended not to be taken seriously.

      Hence the “politician” assumes that all communications output by all specialists into the open and public square are BS communications intended not to be taken seriously.

      Next let us consider another kind of specialist inside that box which we labeled as “The Economy”. This other specialist is known as “the Scientist”.

      This creature has an exact opposite set of expectations about all communications output by other specialists into the open and public square. “The Scientist” assumes that these public proclamations are peer-reviewed, experimentally tested, carefully assessed outputs of truthful information that are to be taken very seriously.

      Now let’s consider what happens when a “Scientist” tries to communicate something serious to the “Politicians” by doing so through the open and public square. For example, assume it is an alarm about “Peak Oil” or “Climate Change”.

      “The Scientist” assumes that these public proclamations will be taken very seriously.

      On the other hand, the “Politician” cogs of the machinery assume that such proclamations are BS and are to be disregarded.

      Hence, Tainter-plexity with just this overly-simplistic example leads to total collapse of meaningful communications. The Scientist tries to sound the alarm and the politician interprets the message as a”this is to be ignored” one.

      Then again, the same command and control sub-system within “The Economy” box is supposed to be rationally and intelligently controlling resource depletion (i.e. peaking oil) and waste creation (i.e. climate changing CO2). It looks like we are in really good shape here (I’m speaking here as a politician of course. 😉 )

  3. step back says:

    Keith upthread argued that Ugo’s model [ i.mage.+] is merely a parallel mirror of what Tainter was going after with his notion of societal complexity (Tainter-plexity).

    IMHO, Ugo should have added more detail to the black box he calls “The Economy” (see image link above).

    Inside this box (The Economy) there are so-called “specialists” who are supposed to cross-communicate with each other and provide a robust and adaptive command and control system for regulating resource depletion, waste production and more generally, growth.

    But the specialists don’t cross-communicate. We have a proverbial Tower of Babel which gets only worse (diminishing returns) as we add more specialized niches to “The Economy”. “Growth” of the Tower of Babel model becomes counter-productive.

    Well, that’s my 2 cents on the connection between Prof Bardi’s model and Tainter’s model.

    • Interesting idea.

      All of our specialists, each with their own “silos”. We see more and more, especially when complex accidents happen, as with the Deepwater Horizon blowout, and all of the resulting problems, and now with the nuclear problems in Japan. It is hard to even think about going about solving the problems.

  4. Peter T says:

    Joseph Tainter looked at large scale collapses (Anasazi, central Maya kingdoms, Rome). My field is conflict, and if you look at societies under the stress of war, what happens is that they adapt until they cannot, but do not then “collapse” – they drop back to a lower level of organisation and go on. If still over-stressed, they drop back further. And in a sense, this happened to the Maya – they (mostly) dropped back from city-states to villages and to Rome – it dropped back from from empire to kingdoms/provinces and then to counties/bishoprics. And this drop is quite sudden, and also rather unpredictable. Sometimes the level of organisation oscillates back and forth for a short time before finally dropping.

    The biologist Geerat Vermeij noted something similar in ecosystems (see his Nature – an Economic History).

    • I suppose that the drop back of the USSR to the individual states could be described as a drop back to a lower level of organization.

      In the US, there would seem to be at a least a remote possibility of the federal government withering away or disappearing completely, leaving the individual states to govern themselves or re-aggregate into smaller groups. This would seem to be a possibility, if the federal government finds it with far more financial obligations than it can handle (guarantee banks, pension funds, social security, federal debt, medicare, roads) and no way of taxing an increasingly poor population to pay for these services.

  5. Helga Vierich says:

    Gail, I would like to comment on what you said: “I was thinking that perhaps societies that use renewable resources (in a truly renewable way) and keep complexity down would have a chance of being sustainable, but that may not be the way the human mind works. Complexity solves problems; no one wants to consider the idea of going backward.”

    I am an anthropologist, like Joseph Tainter, but I specialized in small scale economic systems based on hunting and gathering, slash and burn horticulture, and mobile pastoralism. As you are no doubt aware, hunting and gathering economies were our original ones. That is, if you want to imagine the kind of economy the human mind evolved in, image a forager system. So, just to begin with, I suspect that “way the human mind works” is not, in my estimation, likely to be the root of our problems with either sustainability or complexity. The problem is more likely to be one of culture, not human nature: in our stars, as it were, and not in our genes.

    All economies, with one recent exception, are based on renewable resources. Until the recent fossil-fuel industrial experiment, moreover, they have usually been based on resources whose RATE of renewal could and in some cases was exceeded by consumption.

    Rates of consumption can be directly related to growth in human population and/or higher levels of “prosperity” (average per capita consumption). Now until fairly recently, levels of population growth were not very high. Throughout most of our species’ history, we foragers rarely exceeded .009%/year. Partly, the reasons for this are biological. Even hunter-gatherer economies can increase population densities under conditions where extra resources become available, either through technological innovation, climate change, or new territory being discovered and colonized. However most tended to stabilize over time as the optimal level of birth spacing was achieved at the point between energy supplies and expenditures. A woman having to carry too many infants could simply not gather sufficient food to keep them all alive, even with the support of a kinship group containing hunters.

    Birth spacing among foragers tends to average out at about 48 months, although it can vary, and the period of lactation is quite long – usually over 30 months, due to the fact that a little kid simply cannot digest enough calories out of the kind of diet (roots, nuts, vegetables, occasional eggs, and meat) to mature properly until it is nearly four years old. In the absence of a lot of starch and/or cereals, and of milk from domestic animals, having that top-up of calories from mum was pretty critical.

    Economies based on food PRODUCTION, however, have only been around for the last ten thousand years, but only in a few places until fairly recently. Such systems were originally (and in some places still are) based on a long period of fallow, often in excess of twenty-five years. This permits the soil fertility to be restored by a progression through natural stages of ecosystem succession culminating in the development of a climax forest. In my own experience, in West Africa, this means that over 80% of the village territory was in various stages of succession in any given year, and only about 20% of the land was actually in “production”. There was incredible ecological diversity of wildlife and plants, as the landscape was a mosaic of grassy clearings, pioneering shrubbery and herbs, early stage forest communities and more mature seres.

    This only worked well (was sustainable) if the population numbers did not grow beyond the point that culled be fed on that 20% of cleared land plus all the wild plants and animals supported by the remaining mosaic ecology.

    In many places, and for thousands of years, economies of such hand-tool based swidden (slash and burn) horticulture, supplemented by hunting and gathering, appear to have been sustainable. Overshoot seems to have been avoided by traditions of local warfare resulting in female infanticide and preservation of large stretches of unoccupied territories between major population (“n0-man’s land”) as buffer zones. Raiding and warfare tends to be associated with cults of masculinity that castes the female in an inferior position, which can be more extreme where women marry “out” of their kin-group (exogamy) and go to live with their husband’s kin-group. Where the opposite occurs (men moving to live with their wife’s relatives and resulting children belonging to the maternal lineage) this tends to foster much less local warfare (more alliances between local villages) and higher female status, but also seems to be associated with much larger cooperative aggression against other cultural groups.

    Either pattern is however, susceptible to the perils of population growth, which shortens the cycle of long fallow to the point where soil fertility is no longer being restored.

    Depending on the soil types, rainfall, and climate, some systems of slash and burn food production economies might require at least fifteen years of fallow (as in some tropical forests) while in others, thirty or forty years might be needed to restore soil fertility. This sets the limits on sustainability. And all such economies are vulnerable to any change that effectively shortens that fallow period. An increase in population density is the most obvious source of such destabilization, but increased land clearance due to demands for extra production going outside the region (either for “cash crops” or for the extraction of “tribute or tax” by more powerful neighbours) is equally damaging to sustainability over the long run.

    The development of “civilization” could be seen as the development of village and city-based population clusters that, by definition, could not be locally self-sustaining. They therefore extracted food and other products from the smaller population enclaves in the surrounding countryside. It is likely that all civilizations have tended to destabilize local food production systems based on long fallow and ultimately forced the spread of more labour intensive systems based on intensive farming, where fallow was shortened to several years of “resting” or pasture, or to no fallow at all. In such systems, fertile soils can only be maintained by the importation of manure and other organic matter, as well as various minerals, potassium, etc.

    More labour intensive systems tended to encourage larger families since this meant a larger workforce and a more reliable accomplishments of necessary work even if some family member might be out of commission due to overstrain or illness. And this of course exacerbated the tendency for population increase to occur locally.

    “Civilization” however, is so recent a phenomenon in terms of the whole human species project on this planet that they are still essentially experimental systems. As economic systems, the civilizational project seems so far to be a failure. That was Tainter’s point. There is still a lot we, as species, have to learn to make it possible to live in huge conglomerations and not thereby set off economic and ecological chain reactions that destroy themselves and lay waste to the countryside around them. It is a pretty critical and steep learning curve at the moment, too, since this time, with the help of our temporary fossil fuel windfall, we stand a chance of taking out some pretty major parts of our planet’s ecological system.

    • phil harris says:

      This has been a very thoughtful discussion, and I have just read your valuable contribution. (Thanks also to Gail I am now also a follower of Ugo’s blog – thank you Ugo; yesterday I followed your link from ‘The Great Technological Wall’ and reread the Rudyard Kipling tale for children “On the Great Wall”.)

      I think your (Helga’s) idea of agrarian and now modern industrial ‘civilisations’ as essentially ‘experimental’ is about right. As an aside, some of the apparent pre-requisites appear to have interesting histories. I understand for example, that writing and arithmetic have been invented many times, and pretty quickly at that, to match any rising trading trajectory (following from storage and transport), whereas alphabets and wheels were perhaps rarer inventions and needed to be handed on. Some civilisations missed out!

      There are, despite the pattern of rise and fall, some agrarian civilisations that maintained, albeit erratically, high density populations on the same land for very extended periods. Some were maintained over thousands of years to this day, and they shortened fallow ‘soil restoration time’ , which is as you say a key limiting factor, mostly by re-cycling a high proportion of soil nutrients. These populations also were notably, but not always, associated with ‘renewable’ deposition from large rivers; the Yangtze, Indus, Nile etc. and became Empires, or part of Empires. (Rivers could have been a long term sources perhaps of phosphate and potassium and carbon?) In those situations the ratio of the size of the ‘superstructure’ compared with the agrarian base would be severely limited by the rate that the base could renew itself. By superstructure I mean the layers of society supported by the farming base; everything from specialised local craft industry and its trading, through to regional food storage and transport (insurance against inevitable variation in crop yields), and finally political and military elites. The limiting factor for agricultural production, and in particular its ‘export’ to the superstructures, seems to have been the rate of renewal of soil nitrogen.

      A ‘new organic’ arable farming, however, emerged during 17thC that shortened the fallow period for temperate agriculture. Soil nitrogen levels in parts of England are calculated to have been raised 3 fold by the use of clover’s N fixing power, so that after 1750, England’s ‘carrying capacity’ was raised from about 6M to closer to 18M, when by 1850 22% of the population in farming could just about feed the rest. The fast growing cities of course by that stage were outgrowing domestic food production, and the British Isles soon needed to import the majority of primary calories, which is still the case.

      Large areas of North American farming, however were not able to achieve sustainable economic sale of food to the cities without mining the centuries of pre-farming soil fertility. According to Geoff Cunfer’s expert study (2005) “On the Great Plains”
      “They applied manure as it was available, rotated legumes when it was convenient. But they had no strategy for the very long term. By the 1930s, … soil nitrogen was about half what it had been at sod-breaking and crop yields declined steadily. … Soil nitrogen and organic carbon drifted steadily downward, and with them yields and profits. Faced with this dilemma, farmers … [with industry] … appropriated abundant cheap fossil-fuel energy to import enormous amounts of synthetically manufactured nitrogen onto their fields. </i) …” page 219, preview in googlebooks

      My point is that though the 'agrarian' and latterly the 'industrial' experiments have often been and will be exceedingly problematic, and perhaps unsustainable, there are examples of sustainability which at least outline the boundary conditions for retaining 'civilisation'. There are examples also I believe of cultures remaining from our hunter gather past that indicate some of the social mechanisms that might promote or help sustainability (and even mental health). For example, child birth spacing and rearing practices appear to be culturally modulated. These cultural adaptations are not just the preserve of hunter gatherers, and I can think of at least one study of an agrarian people who appear to have maintained long term communities, admittedly at low densities, in the Himalayas (Ladakh) even though the resource base has always been meagre in the extreme. The Ladakh historical example was first pointed out to me many years ago during a talk promoted by the Scottish Association for Mental Health, but a formal academic study is reported in a book: "Himalayan Buddhist Villages: Environment, Resources, Society and Religious Life in Zangskar, Ladakh" Eds Crook, Osmaston, available Amazon, or Google books.


    • Thanks for your comments. What you say fits in pretty well with what I have heard previously, although I have not had formal courses in anthropology.

      What I perhaps should have aimed for was a much lower level than I did in this post–some combination of hunter/gathering, perhaps combined with farming on 20% or so of the arable land. This 20% of the arable land would probably not support proportionately as many people as today, because irrigation would be limited or non-existent, and because wildlife and insects would get a considerable share of the crop. It would be difficult to live in very cold areas, because generally it would be hard to find / grow enough food year around, and firewood for homes could be a problem. With such a target, I expect that the number of people the world could support would be quite low — maybe 100 to 300 million. There would be hardly any countries that could support their current populations on solar energy as provided.

      My post, as it was written, has generated a fair number of upset responses, both in the comments here and in e-mails. There are quite a few people (many perhaps new to the subject) who can’t contemplate the world being substantially different from today. The idea that building more wind turbines and electric cars won’t save us is
      almost too horrible for them to contemplate. If I wrote a post talking about working on training for hunter/gatherers, even more people would have thought I was a bit loony.

  6. Ric says:

    John Michael Greer’s theory of catabolic collapse (more readable 14-page PDF monograph by Greer here) seems to do a nice job of extending Tainter’s work using physical principles from the domain of ecology.

  7. Ugo Bardi says:

    All right; my point is that Tainter’s thought has evolved over time. The book goes back to 1988; now when I heard Tainter speak in Barcelona last years, it seemed to me that he was much more focussed on resource depletion, as you may read in this post of mine


    I had discussed this point in some length in another post on “The Oil Drum”, http://europe.theoildrum.com/node/5528 . It is a bit long, sorry, but I think it goes in some depth into the point – note that when I speak of “homeostasis” I don’t mention the thermodynamic origin of homeostasis – it is something that would deserve to be discussed. But enough (actually, too much) for now:

    “After that Tainter has spoken of complexity, and of the energy cost of complexity, it is perhaps surprising for us that he doesn’t consider resource depletion as a cause of collapse. Resource depletion, after all, is the main theme of Jared Diamond’s book “Collapse”. It is how he interprets the collapse of many societies. Tainter explicitly denies that in his book. He says that if such a thing as depletion appears, then society should react against it. After all, it is normal: society always reacts to all kinds of crisis, and why shouldn’t it react to resource depletion? This point made by Tainter may appear surprising – actually unpalatable – to people who have made resource depletion the centerpiece of their thought. Peak oilers, for instance.

    The disagreement between peak oilers (and Diamond) and Tainter may not be so strong as it appears. That we’ll see as we go deeper into the details.

    The point that Tainter makes, quite correctly, in his book is that it is hard to see the fall of such a complex thing as an empire as due to a single cause. A complex entity should fall in a complex manner, and I think it is correct. In Tainter’s view, societies always face crisis and challenges of various kinds. The answer to these crisis and challenges is to build up structures – say, bureaucratic or military – in response. Each time a crisis is faced and solved, society finds itself with an extra layer of complexity. Now, Tainter says, as complexity increases, the benefit of this extra complexity starts going down – he calls it “the marginal benefit of complexity”. That is because complexity has a cost – it costs energy to maintain complex systems. As you keep increasing complexity, this benefit become negative. The cost of complexity overtakes its benefit. At some moment, the burden of these complex structures is so great that the whole society crashes down – it is collapse.

    I think that Tainter has understood a fundamental point, here. Societies adapt to changes. Indeed, one characteristic of complex systems is of adapting to changing external conditions. It is called “homeostasis” and I tend to see it as the defining characteristic of a complex system (as opposed to simply complicated). So, in general, when you deal with complex systems, you should not think in terms of “cause and effect” but, rather, in terms of “forcing and feedback”. A forcing is something that comes from outside the system. A feedback is how the system reacts to a forcing, usually attaining some kind of homeostasis. Homeostasis, is a fundamental concept in system dynamics. Something acts on something else, but also that something else reacts. It is feedback. It may be positive (reinforcing) or negative (damping) and we speak of “feedback loops” which normally stabilize systems – within limits, of course.

    Homeostasis has to be understood for what it is. It is not at all the same thing as “equilibrium” as it is defined in thermodynamics. For example, a human being is a complex system. When you are alive, you are in homeostasis. If you are in equilibrium, it means that you are dead. Homeostasis is a dynamical equilibrium of forces.

    Also, homeostasis cannot contradict the principles of physics. It can only adapt to physical laws. Think of yourself swimming in the sea. Physics says that you should float, but you need to expend some energy to maintain a homeostatic condition in which your head stays above the water. Now, suppose that your feet get entangled with something heavy. Then, physics says that you should sink. Yet, you can expend more energy, swim harder, and still keep your head above the water – again it is homeostasis. But, if nothing changes, at some moment you’ll run out of energy, you get tired and you can’t keep homeostasis any more. At this point, physics takes over and you sink, and you drown. It is the typical behavior of complex systems. They can maintain homeostasis for a while, as long as they have resources to expend for this purpose.


    So, in Tainter’s view there is this feedback relationship between complexity and energy. At least the way I interpret it. Complexity feeds on energy and also strains the availability of energy. It is feedback. And not just energy; resources in general. So, I think that Tainter is right in refusing a simple explanation like “resource depletion is the cause of the fall of the Roman Empire”. But, clearly, resources are an important part of his model. I think Tainter had in mind the Roman Empire when he developed this model, but it is of quite general validity. If this is the way things stand, his model is not in contrast with the models we have that see resource depletion as the main factor that causes collapse. But not the only cause. We must see collapse as something dynamic, and now I’ll try to explain just that.

    • Dopamine says:

      Imagine a large cylindrical volume and fill it with oil, coal, natural gas and uranium. That was and is our potential to create order. Now open the spigot at the bottom of the energy cylinder and maximize the flow into a second cylindrical volume called “order” which includes human resources, buildings, roads, tools and so on. As the fossil fuels flow from the top cylinder the pressure becomes less just as EROEI becomes less as the fossil fuels become more scarce. The “order” cylinder, located below the energy cylinder, fills up with order as the energy cylinder empties out. There is almost an unimaginable amount of order we could create with unlimited energy, but peak energy is upon us and the pressure in the energy cylinder will be falling. The level of order in the “order” cylinder will also be falling as the rate of energy application falls below the natural rate of deterioration. Below the “order” cylinder there is an entropy cylinder or waste dump. All of the order we have created so far is slowly seeping into the waste cylinder and the continued creation of new order may actually make the deterioration of existing order occur more quickly as waste sinks fill and create a backlash against existing order. Eventually our attempts at increasing energy usage to maintain order will result in an even greater rate of disorder and increase flow into the entropy cylinder. We will drill in risky areas, pump CO2 underground, build nuclear power plants, turn forest and field into ethanol factories and go to war and we will lose order into the waste cylinder faster than we can open the dwindling flows through the taps on the energy cylinder.

      In short, we’re running out of energy, things will start to deteriorate, then things will deteriorate faster as we attempt to stop the deterioration. Eventually we will give up trying to maintain the existing and unsustainable order and get back to working within our annual solar energy budgets. Energy equals more complexity (order) equals more energy will eventually fail.

  8. Ikonoclast says:

    Resource depletion may not have been the cause of all societal collapses but it will certainly be the cause of our current global civilization’s collapse.

    Ugo Bardi is much more fundamentally correct if I can put it like that. If Tainter wants to take about complexity (increased order) and yet not talk about the fact that useful work (requiring energy) is needed to create more local complexity in human civilization (while generating more environmental entropy or disorder overall) then Tainter is making the common mistake of all economists and social theorists who ignore physics in general and thermodynamics in particular. They ignore the fact that the economy is entirely dependent on the physical world. Indeed the economy is a physical sub-system of the world.

    Biophysical economics (including thermoeconomics) is or ought to be the true fundamental economics discipline.

  9. Keith Akers says:


    My thought is that you have produced a model which mirrors Tainter’s hypothesis but does not refute it or confirm it, so this post leaves me vaguely dissatisfied even though I agree that resource depletion seems to be preceding our own civilization’s collapse.

    I, too, read Tainter’s book looking for confirmation of my idea that resource depletion leads to social collapse, sort of echoing Jared Diamond’s book “Collapse,” but didn’t find it. In fact, Tainter rejects this hypothesis in pages 44-51 0f the book. On p. 50 he states: “If a society cannot deal with resource depletion (which all societies are to some degree designed to do) then the truly interesting questions revolve around the society, not the resource.”

    If what Tainter says here is not correct, and we think that resource depletion IS the critical factor in collapse, then it would be more helpful just to say that Tainter is wrong and explain why.

    Tainter’s view that resource depletion is not “the” cause of collapsing societies could be defended as follows. Consider some conventional ideas of how the United States will likely soon collapse. It goes something like this: as oil becomes less available, economic growth will stop and then reverse, the banking system will fail, leading to widespread unemployment, agricultural decline, and the inability to invest in renewable energy. This will lead to wars, famine, starvation, etc., and finally the U. S. government will just cease to exist, a la Kunstler. Not everyone agrees that this will happen, but you get the idea.

    Now suppose that this does indeed happen. Suppose that a future historian from another galaxy 1000 years from now comes along and tries to explain this collapse. They would likely say that the causes were not resource depletion per se but the banking system, the expectation of perpetual growth, and the failure of leadership. If only some sort of energy dictator had taken over, rationed out energy supplies, etc. etc., everything would have been fine and the U. S. might have lasted another 1000 years. In fact to this future historian it may be perfectly obvious in retrospect what should have been done so that society could have continued in the face of energy declines, just as to us, in retrospect, it is obvious to us what the Roman Empire could have done to stave off or prevent collapse in the face of the physical inability of the Empire to expand its military conquests.

    It is quite arguable that that resource depletion, in and of itself, is the driver of social collapse, or at least the driver of our current social collapse (NOT just a decline in standard of living, which is different). But in this case, for me at least, it would be more useful just to say that we do not agree with Tainter and explain why, rather than try to stress the points on which we do agree with Tainter.


    • Those are interesting thoughts. I wonder what Ugo has to say.

      I think one of the things about resource depletion is there is no clear end point. Instead, we keep getting lower quality resources. The cause of our banking problems can really be declining EROI, and too little energy to power society, but it is hard to explain it to people that way. So it is easier to explain it in other terms.

      I kind of asked a similar question to yours, earlier with respect to this post, asking whether if a society used resources in only a renewable way, couldn’t they build a sustainable society, and Wotfigo pointed out that Tainter had said all societies collapse, not just ones that run out of resources.

      I am wondering if the issues don’t almost get mixed. When I look at my graph of population growth (in my Obama speech post), it is clear that world population has been growing pretty steadily since 10,000 BC. This would seem to imply that societies are gradually adding complexity, to solve problems (many of which are related to resource depletion. Another thought that comes to mind is an Oil Drum post by a microbiologist called Long Term Agricultural Overshoot. This post points out that farming is inherently hard on soil and leads to erosion, so the world has been mining soils since farming began, about 8000 BCE. I don’t think farmers were the first to cause resource depletion. Jared Diamond in “Guns, Germs, and Steel” says that some hunter gatherers moved on to farming, because they had over-hunted and over-fished their areas.

      So the causality may be hard to determine very clearly, if essentially every society has run into resource depletion. Societies used more and more complex ways to get around this resource depletion. At some point, things broke down, and this is the collapse that Tainter talked about. So from his point of view, it was not being able to maintain the complexity, but the underlying need for the complexity was resource depletion, in most cases.

  10. Mandy Meikle says:

    Bicycle Dave raised shale ‘rock’ (I’m assuming shale gas rather than shale oil?). While shale gas EROEI at the wellhead can be quite high, the EROEI of all gas production plummets once we factor in the energy costs of compressing and distributing gas to end users (http://baobab2050.org/2010/10/28/shale-gas-miracle-or-mirage/). Does anyone have a reliable estimate? I’d be surprised if it was more then 5:1 all in (indigenous, not imported). Plus there are the rapid decline rates (the 100 year supply in the Marcellus shales could be 25 years or less – http://seekingalpha.com/article/245788-natural-gas-not-necessarily-the-next-big-thing).

    Shale gas is just one of the many alternatives beign considered (e.g. the idea of switching the military to biofuels!) and all have serious EROEI issues which simply aren’t being addressed. Why? We understand the laws of physics, we understand ecology, we understand the meaning of the word ‘finite’… yet we seem hell-bent on trying to replace the oil from fossil fuels with lower yeilding alternatives (from shale gas to wind turbines). Are we really this dumb?

    I don’t believe we are but too many people truly believe that because we’ve dealt with technological challenges before, we can do so again regardless of the underlying realities of what energy is. Psychology will be a big part of whether we will change our ways such that the future of all life on Earth is guaranteed. Many commentators seem to suggest that all we have to worry about is western civilisation surviving as is and that’s not going to happen!

    Quickly regarding scale of civilisation, as far as I’m aware, any species which has evolved to live in balance with its environment can life ‘for ever’ so long as that environment doesn’t change too rapidly to allow adaptation. Another problem humans’ have created apart from complexity is speed of change. I’m afraid I’m one of those who just can’t see us changing quickly enough in the right direction. As ever, I hope I’m wrong!

  11. Ugo Bardi says:

    About Tainter’s response, i have a mail from him. He says, basically, that my model is interesting but – well – from what he writes I gather that maybe he doesn’t see it as exactly fitting with the way he sees his model…. 🙂 Different minds, different ways of seeing things!

    About the question relative to a smaller economy based on renewable resources, well, of course it would have a very different behavior. And it doesn’t even have to be small. It only has to be based on renewable resources.

    Just for fun, one may tweak the model adding renewable resources, but leaving a large fraction of non renewable ones. Then, the model still shows overshoot, but the size of the economy doesn’t go to zero. It reaches a stable state after a few oscillations. Which is what I think the future will be. After a few up and down oscillation, we’ll reach a stable state. The problem is that this stable state may be at a very low level if we don’t manage the transition well

    • wotfigo says:

      Ugo. Thanks for your reply. I love your posts. Your recent one on “Old Buicks” was fabulous. I am a big fan of your science based approach to problems in complex systems. Keep them coming Cheers.

      • Ugo Bardi says:

        Well, that’s very encouraging, Wotfigo; thanks a lot. It is a big committment to start a blog; intended as something serious that takes up a lot of one’s time. “Cassandra’s legacy” seems to have had a good start. Let’s see how it develops


  12. wotfigo says:

    Ugo. This is an excellent science based description of Tainters’ thesis.

    I read it when it was posted on The Energy Bulletin and wondered then if you had any comment or approval from Prof Tainter on your description.

    I still refer back to Tainters’ book as the world shows increasing signs of chaos in unsustainable systems. There is no doubt in my mind that he is correct and the future of our civilisation is mapped out for us.

    And Gail, wrt your comment

    If a smaller economy based on renewable resources can be built up, can it last indefinitely, or does entropy take over here too? It would seem like such an economy could theoretically last forever

    Tainter basically showed that no economy or civilisation (the two words are interchangeable wrt complexity) can last forever. There are inescapable cycles of growth & decline. Remember, the collapse of ALL the civilisations prior to the late 19th century were collapses of economies primarily based on renewable resources

    Great post.

    • That is a good point. I was thinking that perhaps societies that use renewable resources (in a truly renewable way) and keep complexity down would have a chance of being sustainable, but that may not be the way the human mind works. Complexity solves problems; no one wants to consider the idea of going backward.

  13. Thanks, Ugo. That is a very interesting observation. It seems to me too that your last graph implies that not only do non-renewable resources go to zero, so does the economy based on non-renewable resource.

    If a smaller economy based on renewable resources can be built up, can it last indefinitely, or does entropy take over here too? It would seem like such an economy could theoretically last forever, because if, say, some object made our of wood or clay or fur wears out, a new one could be made to replace it. The economy based on non-renewables would tend to stay quite non-complex, because of the limited types of goods that can be made. Of course, the soil would need to be continuously renewed also.

    • Bicycle Dave says:

      Hi Gail,

      If a smaller economy based on renewable resources can be built up, can it last indefinitely? …… The economy based on non-renewables would tend to stay quite non-complex

      I think your comment really highlights two critical points: “smaller economy” – the easiest way to achieve this is with fewer people. Lower consumption based upon a less complex local economy is a model that can only support a limited number of people. It seems to me that most people in the USA believe that some god has given them an inalienable right to create as many offspring as they choose – in fact, some believe it is a duty to produce lots of offspring. And, Jevons Paradox says something about voluntary reduction of consumption.

      Non-complex: brings into question the currently fashionable belief that ever greater degrees of technological complexity will save mankind from any real unpleasantries. Most USA people hold a fundamental belief that we “deserve” our energy intensive lifestyle – in the words of Dick Cheney “it is non-negotiable” – we believe that things like private automobile ownership or air conditioning in the south is somehow “normal”.

      I hold to the notion that some kind of “powerdown” could lead to an easier trek through the “bottleneck” and a brighter future for future generations on the other side. There are many “solutions” to our current predicament that could lead to this outcome.

      Unfortunately, good solutions are normally preceded by some reasonable recognition and understanding of the problem. Setting realistic goals is also a very good idea.

      I see zero evidence that the problem has been recognized by a sufficient number of humans to avoid collapse of a fairly unpleasant nature. On MSM today, the editor of Time Mag suggested that shale rock could supply our energy needs for a hundred years. I’m sure there are caveats inside the cover, but the subtle message is that we have the energy resources if we just apply our creativity and ingenuity.

      So, be happy – don’t worry. Just get busy producing the energy we must have.

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