Limits to Growth

Limits to Growth

Limits to Growth @F-L-O-W

Frederick Jackson Turner studied the effect of the frontier on
the US and the effect of the closing of the frontier.  He
may have been the first to look at limits to growth, which may have
clues about how to remain happy while not increasing in size.

Closed Frontier
Turner saw the land frontier was ending, since the U.S. Census
of 1890 had officially stated that the American frontier had
broken up.  He sounded an alarming note, speculating as
to what this meant for the continued dynamism of American
society as the source of America’s innovation, and democratic
ideals were




Figure 1. Base scenario from 1972 "Limits to Growth", printed
using today’s graphics by Charles Hall and John Day in
"Revisiting Limits to Growth After Peak Oil"






Cassandra and
the limits to growth

Listen!  For no more the presage of my soul,
Bride-like, shall peer from its secluding veil;
But as the morning wind blows clear the east,
More bright shall blow the wind of prophecy.

(Words of Cassandra
in Aeschilus’ Agamennon)

Sometimes I wonder how it was that Cassandra, the
Trojan prophetess, had so much trouble in convincing
her fellow Trojan citizens 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,

"….it 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 modeling, 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 modeling.  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 labeled 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 couldn’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
  In the end, they had to settle on very minor
points that had no relevance to the significance of the

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 modeling 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
" as discussed by John Sterman and Linda

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

I proposed
the "three tiered fountain" image as a
representation of a simple world model:

Neither a bathtub 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
", 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
, vol. 83, No. 332 (Dec., 1973), pp.

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


Another excellent
additional 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

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

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

– Oz

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