Cassandra has moved. Ugo Bardi publishes now on a new site called "The Seneca Effect."

Tuesday, September 6, 2011

Cassandra and the limits to growth

Sometimes I wonder how it was that Cassandra, the Trojan prophetess, had so much trouble in convincing her fellow Trojan citizen that it was not such a good idea to demolish the city walls to let in that big, wooden horse. Maybe she spoke in riddles and using obscure language, as fitting for a prophetess. But in our case, facing global warming and resource depletion, I believe that it is fundamental today to arrange our knowledge in ways that can be understood by citizens and decision makers. Otherwise, all the work we have done will be lost and we'll remain just Cassandras.

In 1992, William Nordhaus wrote an article (1) where he strongly criticized "The Limits to Growth" (LTG) study. Referring to the 1972 version of LTG, he said that,

" seems apparent that the dynamic behavior of the enormously complicated Limits I model was not fully understood (or even understandable) by anyone, either authors or critics."

Which we may take as correct at least in one respect; that is, if Nordhaus meant to include himself among these "critics". Indeed, with this sentence, Nordhaus may have been admitting that his 1973 paper (2), where he had even more strongly criticized world modelling, was completely wrong. Simply, in 1973 he hadn't understood how the model worked, and not even in 1992. (I discuss in detail these papers by Nordhaus in my book "LTG Revisited" (3).)

It is also true that the large majority of those who criticized the first LTG study after its publication, in 1972, did so without really understanding world modelling. But is it true that the "world3" model at the basis of the study was not "understandable," as Nordhaus maintains? Possibly, Nordhaus had based his evaluation on this graph:

This is a scan of the graphical representation of the world3 model taken from my personal copy of the 1972 edition of LTG. The boxes are labelled in Italian but, either in English or in Italian, the logic of the model is very difficult to grasp. It appears just as a random collection of boxes and arrows, not unlike the plan of the subway of a major city. What you have here, indeed, is an example of a "spaghetti model", a typical bane of system dynamics (SD) models (as discussed, for instance, by Jacques Lefevre). It is possible that it is this complex and apparently haphazard scheme that confused LTG critics and supporters alike. It may have been one the reasons of the flood of criticism that accused the LTG study of being based on arbitrary assumptions, if not a hoax purposefully designed to trick the public. People just could't believe that the mass of spaghetti shown in the figure could generate to a cycle of growth and decline and that this cycle was to be the destiny of our economy.

But the world3 model was not arbitrary. As one of the first models of this kind in history, it is not surprising that its graphic representation left something to be desired. That didn't affect the performance of the model, which withstood very well the test of time. The real world parameters, so far, have behaved close to the results of the "base case" scenario of the 1972 LTG study, as Turner shows. Critics had to work hard to find weak points in the study that went beyond simple statements of disbelief, as I discussed in a post of mine. In the end, they had to settle on very minor points that had no relevance to the significance of the study.

The LTG model was not impossible to understand, either. If you look at the text of the original 1972 LTG book, you'll see that the figure shown above came only after several pages that described in detail how the model worked. The authors made a thorough job in showing diagrams of the various subsets of the model. That made the model understandable even by economists.

Unfortunately, that was not enough. No matter how well the model was explained, understanding LTG required an effort that most people were not willing to expend. It is difficult to fight against the human tendency of disbelieving bad news - the Cassandra effect, in short.

But we can learn something from the LTG experience. A fundamental point is related to the public perception of models. For a scientist, the need for models is obvious; but it is not so for a politician or for the public. In this sense, world modelling and modern Climate Science have the same problem. Both fields are seen as based on complex models that are beyond the capability of understanding of the non-specialist. So, what is exactly the role of models in the public debate on the issues of climate change and resource depletion?

Sometimes, people seem to believe in models just because they are complex. Otherwise they see complexity as proof that the model is wrong or irrelevant. The problem of complex models is that they leave people free to chose one or the other attitude, depending on their feelings or their political ideas. So, I think we badly need to frame our models in "mind sized bites" of knowledge - as suggested by Seymour Papert - that people can grasp.

As an example, here is how Magne Myrveit has represented the five main stocks of "The Limits to Growth" model (from a paper titled "The World Model Controversy").

This figure can be criticized as an oversimplification, but it is a huge step forward in the sense that it gives an immediate visual idea of what the main elements of the models are. Yet, it has a problem. "Mind sized" doesn't just mean reducing the number of elements in the model. It means, in my opinion, providing also a clue on what makes the model tick. In other words, a representation such as this one, simple as it is, still suffers from the spaghetti syndrome. It is static; it doesn't tell you anything on where the system is going. And, yet, the results of the calculations clearly show that the system is going somewhere; it is undergoing a cycle of growth and decline. That is not clear at all from this figure.

So, I think that if we want to make useful mind sized models we must clarify that there is a tendency; a force, the result of something that in technical terms is called a "potential". Potentials generate forces, and forces move things along. I think this is the point that Jacques Lefevre was doing when he used the metaphor of chemical reactions for describing system dynamics models. But there is an even simpler metaphor: "bathub dynamics"  as discussed by John Sterman and Linda Sweeney.

Now, this is a real mind sized model, in the sense that it is clear that it is gravity (better said, the gravitational potential) that moves water in a certain direction. This representation of the model is not static, it shows what happens. It was with this example in my mind that I proposed the "three tiered fountain" image as a representation of a simple world model:

Neither a bathub nor a fountain have the characteristic that we call "feedback", which is crucial in world models as it generates non linear growth and decline. Nevertheless, these are images that clarify the fact that the system is driven by a potential. Water must go somewhere and that is because of the gravitational potential. Then, it is clear that if we start from a limited reservoir of water, then at some moment it must run out. In a world model, it is not gravity that moves things, but thermodynamic potentials, in turn related to the energy stocked in the natural resources that an economy exploits. And it should be also clear that if natural resources exist in limited amounts, they must run out at some moment. So, we can build a simple, mind sized model as:

Once these points are understood, we can use even this very simple "three stock" models to gain a surprising wealth of insight on how economic systems behave. I used this model in previous posts and I showed how it can explain the "Seneca Effect", that is why the decline of economic and social systems is so often much faster than growth.

So, I think this is a line to pursue if we want our models to be understood and, more than all, acted upon. That is true for both resource depletion and climate change, which are two sides of the same coin. But would mind sized models solve the problem of the disconnection of scientists and decision makers? Well, that won't be easy, of course. Sometimes, when playing with these models, I see myself as if I really were the ancient Cassandra, the Trojan prophetess, drawing stock and flow diagrams on the sand in front of perplexed Trojan citizens. Not easy. Yet, I think we have to try.


1. Lethal Models 2: The Limits to Growth Revisited, by William Nordhaus Brookings Papers on Economic Activity, Vol 1992, No. 2 (1992), pp 1-59. URL: 

2. World Dynamics: Measurement Without Data,William D. Nordhaus, The Economic Journal, vol. 83, No. 332 (Dec., 1973), pp. 1156-118,

3. "The Limits to Growth Revisited" Ugo Bardi, Springer 2011


  1. Hi Ugo, your mind size model is a good attempt to educate people, like Interactive Learning Environment. Do you consider to conduct experiment to test its effectiveness?

  2. I think that the three-story model can provide a good feeling about the exact situation of our resource consumption, the flow on top of the fountain representing fossil fuels. Someone would ask: "But, what would happen when we run out of fossil fuels? Where do you incorporate renewable sources?" The answer is simple: rain. Rain is going to put some additional water in your fountain, but obviously not at the same rate as the water source. This is, of course, an abuse of the metaphor, but an eloquent one when people start claiming that renewables will seamlessly substitute fossil fuels: yes, they give energy but not at the same rate.

    Nice post. Regards.

  3. Tony, it might be done. I am a professional teacher; I try to do my best, but it is very difficult. Students seem to be living in an environment where there is a lot of teaching but very little learning. Alas....

  4. Good point, Antonio. I hope that the fountain metaphor can be useful to clarify how these models work.

  5. I'm pretty convinced that LTG models provide a good description of the real resource constraints that we face. However, you will never convince mainstream economists with a model that ignores prices and incentives, and which uses fixed factor "rules of thumb" for how resources interact with capital and labour to create economic activity, and how economic activity then determines capital stock.

    The current situation is perhaps that economists have a larger share of "the ear" of policymakers. This is as a result of a couple of centuries worth of work on how economies work, largely through the mechanisms of prices and incentives. Some of this work is fantastic, some not so good. However, economists are largely ignorant of the near term resource constraints that we as a society face. This is partly due to the success of e.g. Nordhaus in critising LTG and showing that under certain circumstances, prices and incentives are sufficient to allow us to avoid collapse.

    Part of the problem is that the people who economists should be talking to to get a handle on the problem, utterly dismiss the relevance of economic theory. Restating a LTG style model that still doesn't include prices and incentives is talking cross purposes with the economics profession. We need to work together.

    My comments on your previous post on the Seneca effect described some of the work I'm doing (as part of an economcs PhD) to show that including prices and incentives in a LTG type model is not sufficient to avoid collapse - indeed even in a model without ultimate limits, prices and incentives can cause a collapse as the quality of the resources becomes poorer.

    1. Did you finish the project you described. I am interested in the mathematical modelling. Where can I see what equations and assumptions were used in the LTG model or yours for that matter?

  6. Another excellent addition ongoing attempt to refine the question of modeling. I agree that it's important to 'mind size' this aspect of the problem - primarily (at this point) so that people cannot so easily dismiss it out of hand. Kudos for continuing this effort, Ugo!

    The deeper issue remains, however: whence derives the Cassandra effect? And to what extent will making things easier to understand undercut that effect, if at all?

    I like how you put it: "the human tendency of disbelieving bad news" - and complicated, hard-to-understand models give people a 'good' (or at least a plausible) pretext to disbelieve. But even if we take away that excuse by providing easier-to-understand models, we still will face the same underlying effect, because it is a psychological one.

    Do you think it likely that it will manifest in some other way?

    It seems to me that William Rees' recent essay at the PCI is directly on point:

    wherein he notes:

    "Humans may pride themselves as being the best evidence for intelligent life on Earth, but an alien observer would record that the (un)sustainability conundrum has the global community floundering in a swamp of cognitive dissonance and collective denial."

    He goes on to say:

    'Psychologist Robert Povine argues from the available evidence that the
    starting assumption in behavioral psychology should be “that consciousness doesn’t play a role in human behaviour. This is the conservative position that makes the fewest assumptions.” '


    'Cognitive scientists have determined that cultural norms, beliefs, and values are effectively imprinted on the human brain. In the normal course of a person’s development and maturation, repeated social, cultural, and sensory experiences actually help to shape the individual’s synaptic circuitry in a neural “image” of those experiences. Once entrenched, these neural structures alter the individual’s perception of subsequent experiences and information. People seek out experiences that reinforce their preset neural circuitry and select information from their environment that matches these structures. Conversely, “when faced with information that does not agree with their internal structures, they deny, discredit, reinterpret or forget that information." '

    My personal experience in life has tended to confirm these observations, which are also in alignment with the characterization of confirmation bias made by Sir Francis Bacon centuries ago.

    It seems we are really faced here with something fundamental - or perhaps a better word would be 'primal' - to human nature, or more precisely to the nature of human psychology. We really, for the most part, tend not to be consciously acting beings, at least when it comes to matters which involve basic biological impulses (though I do not mean to imply any sort of determinism). And, I think we fail to even recognize that fact. Which makes two successive obstacles to overcome when attempting to 'reach' the public, politicians, etc.

    I have to admit being in the camp which thinks, in fact, that this will not be done. I view much of the work being done on peak oil not as an effort to change the trajectory we have already established and which seems all but certain to persist, but rather as efforts that can aid in establishing a new trajectory - the one that begins from the bottom of the cliff and goes forward.

    In that sense, I view it as crucial that we learn the proper lessons from the coming 'reset' to humanity's external conditions (so that we can let go of the cultural myths which have not, and will not serve us well). And I think the work being done here has the potential to be very useful in that regard.

    - Oz

  7. Ugo
    From this week's Science.
    Any interest?
    'Probability' is a relevant parameter?
    Simple graphical illustrations for the wider public understanding seem the 'name of the game'

    Uncertain Times Illustrated

    The uncertainty of whether or not you get rained on at your wedding or the ball game can be expressed mathematically as probability. Probabilities are notoriously hard to broadcast to a general public possessing a wide range of mathematical understanding. Knowing that pictures can say more than words, Spiegelhalter et al. (p. 1393) review the types of graphic illustrations available for explaining some of the uncertainties of the world we live in and offer a range of examples for illustrating scientific knowledge in a variety of media that can be optimized to promote understanding among different audiences.

  8. Hi,

    I've only just come across this post so a little late to the party.

    I would like to include another factor - durability. It is plain to me that modern consumerism revels in producing items that are just good enough to sell (and which fall apart / stop working quickly). This results in the tendency for declines to be sharper, for the simple reason that the stock of items in society has but a sort life.

    Noticeably shorter then in my grandfather's day; then, a suit would last a lifetime and a good pair of boots 30 years.

    These were not cheap - but then, you bought these but once or twice in a life.

  9. Amazing how the underlying principles published 40 years ago are more relevant today. I can see the limits to growth in the energy price, raw material price (food, metals, etc.) and other signs everywhere. The question is what can we do about it?

    People are very good at disbelieving bad news. Generally, the human race will only react when issues become critical.

    Politicians are in an even worse state. If they faced reality and began to prepare in public, they would definately be out of a job because they would face the people's wrath at the elections.

    I am a manufacturing optimization consultant. In our marketing, I touch lightly on the resource constraints, but purposely do not cover the limits of growth and how the global economy is now a zero sum game (forget win-win, if somebody wins, somebody else has to loose, and we all will be loosing in a short time). If I covered this, it would be so depressing to our prospects that I predict 0 sales and no ability to help delay the current predicament.

    I believe I am in a good position to influence some key decision makers. I go to plants that are spending 1-2 Million US$ per month on energy consumption alone, but have no measurement system in place to help them optimize their use. I would appreciate any comments on how to practically get people to begin to prepare to for this paradigm shift to this new world economic model?

    Barry Martin
    Consulting Engineer, Malaysia

  10. Barry, I wish I had an answer to your question. As you say, "people are very good at disbelieving bad news". I was discussing a few days ago with someone working in advertising who is active in the transition town movement. His suggestion is an attitude in which you should not scare people and not make them feel guilty. If you do that, they will accept the need for preparing for what is going to happen. That's his opinion; I think there is some merit in it, but I am not sure about its success rate!

  11. Ugo, I don't think the problem is understanding the models, once valid models are simple enough. You still need to lead people out of their own trusted culture of misconceptions, toward seeing what choices are causing what's happening.

    Raping the earth is far from our intent, but we are devoting our entire cultural effort to it, altering how nature works by ever larger steps, toward losing our grip in an irreversibly collapsing environment. A way out would mean finding a way to get people to question what they put their entire faith and trust in, that has become deceiving.

    Nature avoids boom and bust by celebrating her booms of seed growth by using the profits to put down lasting roots. That she doesn't live in a world made of mental fixations like people do, seems to explain why she does that switch of roles so very smoothly.

    Humans create knowledge and their perceived "reality" as a social construct. For men more than women (it seems) the world continues to look like it is fertile for using seed to multiply seed forever, even as the losses mount uncontrollably. All they have to say is "Oh, WE can handle it", taking the attitude that caring for the environment being exploiting, at ever growing rates, will never be needed... That controls the investment choices, making them act as if cutting and running with some profits, even as they see their society collapsing all around them, solves the environmental collapse problem the growing rape of their environment causes.

    So, that seems to be why men, in particular, act as if no budget for putting down roots will ever be needed, but only to fulfill their celebrated social role of planting seeds to multiply the planting of seeds. They can do so while remaining unconscious of how that takes their environments to and beyond their limits. From a man's view you could call it a “screw job” from nature, that screwing the world to get nature ever more pregnant runs out,… and you just have to do other things sometimes… I guess.

    As our perception of reality is a social fixation, and just doesn't track how our physical reality is changing, is then what I see as the root of the problem. We keep seeing nature as the pleasing information model given to us as our own construct of nature, which doesn't change, even as all hell starts breaking loose.

    How you break with truly widespread madness like that I'm not sure, but it seems quite sure that's what we need to do.

    1. Ok, I spent the last decade with this set of ideas, and watching my clients (25 years as a professional executive coach), i realized they couldn't change anymore than they could, so i looked at how we were being socialized, Pinker's book helped name it BLANK SLATE (@BS). There is one missing component in the model and that is the clue. @BS the assumptions arose out of two seemingly exclusive events, PROPAGANDA published in 1928, and Paul Mazur's ideas being adapted by CORPORATE (meme) the 1930s...shift needs to wants. Behavioral Economics is correct, we are riding elephants (Haidt) or horses (Freud), and complexity in this system reigns to drive growth, because it's intuitive. What is counter-intuitve almost always in System Dynamics gets lost and therefore in order to decelerate this paradigm of consumption, you have to go back to where it was the irrational system using the mechanism of propaganda (now called PR, advertising, promotion and marketing, it is their bible)...

      As we become more sophisticated with this 'mechanism' we get people to do insane things, as it appears in the limits to growth, it's clearly a simple model on the OTHER side of complexity that people climbing up the ladder on this side, can't comprehend, anymore than they can understand the long economic cycle where depression awaits to reboot the system.

      For me, I'm going to convene a symposium on the limits to growth next spring called Growth IS Killing You, Me and We?

      I just soft-launched my book, couldn't wait any longer to finish the three "scaffolding" chapters because i have been sitting on the book for 10 years and it took time for us to have what we need to cause change..."burning platform" that anyone and everyone can see, soon, we will have that, not just yet, but soon, as you all know.

      In the meantime, what can we do, we have to do something fairly quickly, or NOT do it, as we have 1.5 billion middle-class aspirants who are being conditioned to consume wants, instead of needs waiting on our we have 2-10 years, my best bet and we need a 50 year plan for the 50 year anniversary of LTG...and that's also by design, as it will take 50 years (3 asian generations (i work now part time in philippines to study the pacific rim and what is happening, to inform my own models) make this happen, and it won't be easy.

      But if you are going to take away, UNLESS by force and that WILL happen sooner rather than later, one of the cells of my forecast matrix this year contains violence sooner than later, military law in USA, China grabs western russia, Baikal has 1/5 of fresh water in world, etc...

      So you have to substitute memes and what is at stake always since the beginning of time is PSYCHOLOGY, and I'm going in the direction of happiness, and that remains stable at incomes above 20-70k, depending on your context, so instead of 20% of teh people on the planet with 90% of the wealth, the system that has caused that @BS, must be substituted @F-L-O-W is what i call the system i have created to shepard in the a. b. normal, which will transcend the WIRED new normal that will kill us.

      If you want to read my notes on this, how i make the case against the current value system IN USA anyway, progressivity, without us all becoming amish or acetic, go here: and you can see how i developed the why behind my approach.

      Unless we are prepared to FORCE people, consciousness will not change anyone, only 1% of the population is at the level of thinking that can do something with LTG, in the context @BS, so we are just kidding ourselves, and those 1% are NOT the same as the 1% @BS who are wealthy, an unfortunate divergence of events, referring to our philsopher shakespeare. This is a very good piece tony, i will spread it.



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)