Table of Contents
On the Confounding of Overshoot and Collapse
Predictions by Economic Dynamics
Corey Lofdahl
SAIC, 20 Mall Road, Suite 130
Burlington, Massachusetts USA 01803
clofdahl@ bos.saic.com
Abstract
At the 19th International Conference of the System Dynamics Society held in A tlanta,
Willard Fey and Ann Lam (2001) asked why system dynamicists by and large believe
that the world population is limited and yet don’t act on this belief on a day to day basis.
Because this is a deceptively difficult question, this study addresses it from several
different perspectives. From the literature, it examines current critiques of The Limits to
Growth, Malthus, and Simon’s bounded rationality. The study finds that theories,
predictions, and criticisms concerning complex systems cannot be answered definitively.
Instead both the initial theory and its criticisms must be considered together, a conclusion
supported by 20" century philosophy.
From this perspective, instead of offering definitive, closed-form solutions, three
heuristics are developed. The first contrasts notions of possibility and prediction from an
information theory perspective. The second examines the mechanics of standard
overshoot and collapse systems and how collapse predictions can go awry. Third, an
example of overshoot and collapse is examined with an eye towards timing the collapse
and understanding how decision makers interpret information from within the system.
Systematic errors from this smaller, economic system are then applied to Fey and Lam’s
concem regarding world population, a system that may have overshot but has not yet
collapsed.
1. Introduction
At the 19th International Conference of the System Dynamics Society held in A tlanta,
Willard Fey and Ann Lam (2001) discussed, explored, and furthered some of the key
themes of The Limits to Growth (Meadows et al 1972). Although many of the
discussion’ s details have faded over time, one portion of their question and answer period
remains vivid. It was asked of the plenary session audience how many believed that the
Earth was in the midst of an overshoot and collapse scenario. Almost all raised their
hands. Then it was asked how many people were actively accounting for this possibility
in their day-to-day behavior. Almost every hand went down. This raises a question:
Why is it that an entire room full of system dynamicists believed that something quite
catastrophic was likely to occur and yet few were doing anything about it?
This paper seeks to construct a plausible answer for this question while
understanding that the source of this question is likely to be subtle, systemic, and hidden.
First, it is recognized that this is a levels of analysis questions, which - within the
international political economy literature - reveals itself in several different forms and
contexts. Harold and Margaret Sprout (1965; 1968; 1971) posit an ecological triad of
entity, environment, and entity-environment interaction: entity and environment
constitute two separate levels of analysis, with their interaction forming a dynamic, third
subject of study. Waltz (1959) forwards a multi-level structure consisting of three images
- man, the state, and the international system. North (1990) extends this structure with a
fourth image, the world system, that captures and allows for global environmental
degradation. Hardin (1968) addresses the problem by exploring the microeconomic
decisions that lead self-interested, rational people to collectively and unintentionally
degrade their surrounding environment. Meadows et al (1972) examine the long-term
consequences of these micro dynamics from a macro, planetary perspective.
This paper begins by reviewing current critiques of Limits with an eye towards
understanding the basic argument as well as its underlying assumptions regarding reason,
evidence, and inference. In so doing, a number of underlying philosophical debates are
rediscovered, and these are quickly reviewed in Appendix A. After establishing the
terms of the debate, answers are forwarded in the paper’s second section. In the grand
systems tradition, a single definitive answer is not offered; rather, three dynamic
responses are reviewed that together would confuse a boundedly rational decision maker
living within a complex surrounding and supporting environment. These dynamics,
including economic dynamics, complicate and confound predictions based on overshoot
and collapse dynamics.
2. Establishing Questions
This section addresses three variations on the Limits theme. The first directly addresses
Limits and the work on which it is based, Forrester (1973), by examining two recent
criticisms. The second looks to interpretations of an earlier and related work by Thomas
Robert Malthus (1798). Finally, because the driving question and their ultimate answers
derive from a tension between macro-level economic dynamics and micro-level decision
making, a work relatively unrelated to Limits is examined regarding macroeconomics and
rationality by Herbert Simon (1983).
2.1 Forrester
The 20" Century saw an unprecedented increase in the world’s human population, which
has led to a literature regarding the threat this might pose -- Forrester (1973), Meadows et
al (1972), Meadows, Meadows, and Randers (1992), Fey and Lam (2001), etc. - that
predicts the global environment will ultimately prove unable to support this still growing
human population, leading to a worldwide environmental and population collapse.
Recent critics including The Economist (1997) and Lomborg and Rubin (2002) have
pointed out that early predictions made by these researchers have been proven incorrect.
The Economist (1997) focuses its criticism on predictions made by Meadows et al
(1972) regarding predicted shortages of oil, natural gas, silver, tin, uranium, aluminum,
copper, lead, and zinc. They also address Meadows, Meadows, and Randers (1992) who
predicted food shortages as well. In each case, the envisioned shortages did not occur
because of the economic dynamics of exploration, innovation, and substitution. If a
shortage was about to occur, as indicated through market pricing, new supplies or
substitutes were found through the natural workings of the market. Such faulty
predictions are grounded in misspecificifying the overshoot and collapse archetypical
dynamic (see section 4.2), and thus mispredicting the limit of human population growth.
This error was made by incorrectly counting the underlying resource base on which the
world system is based and thus mistiming when it would become exhausted. Economic
dynamics, the normal workings of the international market, enabled and extended the
global growth dynamic well beyond that initially envisioned by Limits. From this
experience it can be inferred that when the underlying resource base is a complex system,
1) it is hard to count the stocks in the system, 2) it is hard to understand the relationships
among them, and 3) it is hard to understand how the market will find substitutes for
depleted stocks. Thus the world economic system may be headed toward collapse, but it
hard to predict exactly when and how this might occur.
Lomborg and Rubin (2002) move beyond simply noting failed predictions to offer
explanations about why this might be so. These explanations tend do be economically
but not dynamically informed, so it makes sense to review them in order to understand
not only how they might be improved but also how the original systems-based
predictions might have been improved. Lomborg and Rubin (2002, 42) contend that,
“Due to an exponential increase in population growth, the world should be facing
desperate shortages of arable land and rising food prices,” but this assertion denotes a
misunderstanding of the overshoot and collapse dynamic. It is perfectly reasonable for an
unsustainable, exponential growth dynamic not to exhibit shortages, at least initially. The
question is one of relative timing (see section 4.2 for details). Growth processes can
continue until they are limited by shortages of underlying resource, in this case of land
and food, with the limit likely arriving rapidly and unexpectedly.
Lomborg and Rubin (2002, 43) continue, “Tempting though it may be to attribute
these faulty predictions to flawed methodology and bad math, their real weakness is the
underlying assumption that planet Earth has finite, essential resources (such as oil, water,
and grain) for which there are no substitutes.” This statement is partially true. The world
indeed has finite resources, but predicting which they are and when these limits might be
reached is a difficult and inherently uncertain undertaking. As has been noted, the
material expansion and temporal extension of food, minerals, and oil beyond limits
previously thought possible has been accomplished through a combination of technical
and market forces. But other necessities like clean air, fresh water, and arable land are
not as readily expanded or substituted. Lomborg and Rubin (2002, 43) conclude, “In
short there is no law dictating an exponential mounting pressure on Earth’s ecological
resources. The limit of sustainability is not a static ceiling but is formed and expanded by
human innovation and technological progress.” Once again, this statement is partially
true. Indeed, economic dynamics have expanded the growth limits to make feasible
levels of population that previously would have been thought impossible based on lower
levels of innovation, technology, and globalization. But while limits can be extended,
they cannot be extended indefinitely. Moreover, in systems that previously have
exhibited overshoot and collapse dynamics, their limiting factors were often reached
quite suddenly, dramatically, and unexpectedly.
2.2 Malthus
The predictions offered by Limits and their subsequent refutations are not unique.
Thomas Robert Malthus, concemed about the adequacy of British farmland to support its
burgeoning population, wrote Essay on the Principle of Population in 1798. His fears
also were not confirmed, but Kates, Tuer, and Clark (1990, 14) note that despite this,
“almost each generation seems to rediscover Malthus.” Each generation however slightly
varies the chief measure of concern and the feared limiting factor. Concerns change from
population growth to pollution absorption, from farmland depletion to oil and metal
shortages, and from regional perspectives to the global, but the essential formulation of
the question remains essentially constant - fear of dramatic environmental change.
The back and forth nature of limitation predictions and their criticisms over time
thus takes the form a conversation, and from this conversation three observatoins can be
made (Kates et al 1990, 14--15). First, it must be acknowledged that limit predictions
and their answering criticisms cannot be “proven” true or false through logical argument
or empirical evidence, at least not in any simplistic, conventional sense. Rather, like any
conversation it changes as old factors and concems drop off, new insights and questions
become incorporated, and the scale and scope of the discussion changes. This leads to a
second observation, that not only will old concerns fade away as new ones appear, but as
time passes and generations progress, previously vital concems will seem quaint or
mystifying. It is entirely possible that the focus of study for today’s models will meet
that fate. This leads to a third observation, that should a prediction be proven false, the
reason might not be grounded in faulty logic or math, but because the analysis was taken
seriously and policies were undertaken to prevent the problem.
2.3 Simon
Herbert Simon won the 1978 Nobel Prize in economics and created the theory of
bounded rationality, which exists almost implicitly within the discipline of system
dynamics (Morecroft 1983). However, this study makes a slightly different observation
regarding Simon’s bounded rationality - that it helps to explain persistent, spirited, and
almost irresolvable debates.
Friedrich Hayek, who won the 1974 Nobel Prize in economics, wrote The Road to
Serfdom (Hayek 1944) that critiqued the then fashionable trend towards socialist,
centrally directed economies. Hayek argued that such economies would fail due to
information processing limitations. Economies distribute decisions across a range of
owners, experts and interested others who respond to specialized technical and general
pricing information. To expect that a centralized bureaucracy would be able to
synthesize such information and determine accurate prices and planning policies would
be essentially impossible. Moreover, prices and policies would inevitably be made to
serve essentially political goals, which would cause further economic inefficiency.
From a 21" century perspective, Hayek (1944) makes good theoretical sense and
has been shown historically correct. The point made here though is one of intellectual
debate, and thus it is instructive to review Finer (1945), The Road to Reaction. The tone
is, by any measure, harsh and angry. Let us resist the temptation to review the specifics
of Finer (1945) and instead state consider the general tone. First, Hayek argued against
trend of the age, which is always bound to provoke a reaction. Second, Hayek's
argument was mathematically subtle, resting on a then ill-understood cybernetic theory
and information flow to reconcile supply and demand. Third, Hayek's thesis countered
something that Finer very much wanted to be true and in which he had much
professionally invested. A quick google search will tum up sentiments similar to Finer’s
that persist even in the present day.
Quite apart from the reaction it provoked, Hayek has benefited from analytic
advances, many of which were employed by Simon in his bounded rationality work.
Working from the synthetic perspective of social science, computer science, and
experimental psychology, Simon (1983) addresses the levels of analysis question from a
Hayekian perspective. So while Simon studied a boundedly rational decision maker in a
larger economy, Forrester and Malthus study individual resource consumers in a larger
environment. Simon (1983) confirms Hayek from his studies of decision making within
larger organizations, finding that they human mind is unable to capture the complexity
necessary to make accurate predictions and process the information necessary to set
accurate prices. It follows that the human mind is similarly unable to process the
information necessary to represent interactions between the social economy and the
global ecology, which is why Forrester (1971) advocates the cognitively prosthetic use of
computers to further the information processing capability of the human mind. However,
it is true that computers are similarly, though differently limited in their ability to
represent reality - a fact readily admitted by modelers when they say that all models are
wrong, it’s just that some are more useful than others.
This section has sought to put current criticisms directed at Forrester, Meadows et
al, and Malthus into perspective. Y es it is true that predictions were made that have not
proven completely accurate, but is also true that there are some important, beneficial, and
even true aspects of these models that should be recognized, saved, and studied. Like
Finer (1945), criticisms of this work must be examined for their underlying motivation,
all the while recognizing that taking such criticisms seriously does not imply accepting
them completely.’
3. Forwarding Answers
In forwarding answers regarding current debates regarding Limits, one is tempted to offer
“answers” because, for interesting, complex or hard problems, definitive replies of ‘true’
or ‘false’ are impossible. Instead three heuristics are offered that help reconcile the
disparity between the initial predictions of Meadows et al. and the criticisms they evoked.
3.1 Possibility and Prediction
It is generally recognized that complex chaotic systems capture important aspects of
everyday, real-world systems. Here they are reviewed to gain insights into the nature and
possibility of prediction.
Finding that there is merit to both sides of the current Limits to Growth debate - i.e., the original argument
as well as the current criticisms -- is more than just an abdication of judgment through equivocation.
Instead it is a rediscovery of many of the most interesting and hard to interpret aspects of 20" century
philosophy, a condensed discussion about which can be found in Appendix A.
1o—
1
oe
Figure 1. During (Chaotic) Oscillator (Thompson & Stewart n986, 3--5)
Figure 1 contains a representative chaotic system, a Duffing Oscillator (see
Appendix B for definition), which demonstrates standard non-repeating behavior within a
limited mathematical space. That is, the dynamic response never extends beyond 4 or -4
on the horizontal axis or 7 and -7 on the vertical axis, but within these limits the system’s
dynamic response never repeats. This observation however implies certain things about
the predictability of the system. As the response moves further toward the dynamic edge
or boundary, it becomes increasingly “predictable” that the response will “regress” or
change direction back towards the origin.
In making this observation, we rediscover a classic result. Claude Shannon
introduced the statistical thermodynamics concept entropy to the study of systems. The
equation S = k log w, where S is entropy and w is the number of possible states
(Campbell 1982, 46), is used to measure the order in a system, a concept that implies
predictability. The fewer the possible states, the lower the entropy, and the more likely it
is that the system will be in one of the states. Thinking about successful, long-term social
predictions, there are times in history when certain events “have to happen” and other
times when the future is “up for grabs.” These translate to periods of high and low
entropy respectively, which can be demonstrated experimentally.
4 0 4
Figure 2. Point of Possibility (High Entropy)
In Figure 2, we start the simulation at nine different points at the far right side of
the graph as the response heads down and back towards the left. As can be seen, at the
end of the simulation the nine different curves are in nine very different places. This
demonstrates two things: 1) standard chaos dependence on initial conditions and 2) high
systemic entropy. Small differences at the beginning of the simulation soon become big
differences at the end. High levels of systemic entropy make the simulation inherently
unpredictable, and the large changes at the end -- changes that are driven by small
changes in initial conditions -- make this starting point a “point of possibility” in the
sense that anything can happen and the future is “up for grabs.”
Figure 3. Point of Prediction (Low Entropy)
Figure 2 should be contrasted with Figure 3, which in some sense demonstrates
the opposite side of the entropy continuum. The Figure 3 trajectories begin in the center
of the graph as the trajectory pushes up and out towards the left edge. Despite different
starting points, all curves end up in essentially the same place, making this part of the
curve one of low systemic entropy. This is called a “point of prediction” because small
differences that lead to big differences on other parts of the curves at other times make no
difference here - the same dynamic response occurs regardless. Note also that although
the curves all follow the same path, they do so at different times. That is, the curve on
the inside of the response makes it only partway around the curve, while the curve on the
outside travels much farther over the same time. Differences in relative system timing
that result from different initial conditions are explored further in the next section.
3.2 Overshoot and Collapse
births Population deaths
8
birth fraction
death fraction
food per capita
consumption per day
Figure 4. Overshoot and Collapse System Structure (HPS 1990, Ch. 9)
Figure 4 depicts a different type of system, one that exhibits classic “overshoot
and collapse” response, as shown below in Figure 5 (for equations and descriptions, see
Lofdahl 2002, App. E).
1: Population 2: Food
L Be
rn ‘;
20.00 320.00 40.09
Yesrs
Figure 5. Overshoot and Collapse dynamic response
In Figure 5, we see just how the two Figure 4 stocks, Population and Resources, are
connected: Population grows until Resources run out, and then Population “collapses” by
dropping back to zero. This is the basic nature of the overshoot and collapse response.
births Co > ‘leaths
ere INS J
\stoei
Figure 6. Overshoot and Collapse feedbacks (Lofdahl 2002, 133).
The feedback relations of Figure 6 show how the overshoot and collapse response
occurs. The initial growth of Population is driven by the first, positive feedback loop.
Population grows until it is limited by lack of food, at which point dynamic dominance
shifts to the negative feedbacks, loops 2 through 5.
0.00 10.00 20.00 W.00 40.00
Figure 7. Overshoot and Collapse dynamic response with varying Food levels
The simulation is run with increasing levels of food in Figure 7, and two things
happen: first, Population grows ever higher, and second, the collapse gets postponed ever
later. Regardless of the initial food level, population collapse inevitably occurs in each
run. Thus, the overshoot and collapse system is a predictable, low entropy system.
Whatever the initial food value, the same result occurs, population collapse. However,
this simulated system is very much an artificial one because no provision is made to grow
and restore the food supply. Looking to Figure 4, food can only be withdrawn from the
stock -- it cannot be replenished. Thus it can be argued that the collapse is “dialed in”
and does not accurately represent the real world. This objection is addressed in the next
section, in which several real-world systems are reviewed.
3.3 Economic Dynamics
Economics dynamics are examined here to the extent that they confuse and conflate the
predictability of standard overshoot and collapse dynamics, which is accomplished from
two perspectives. First, the overshoot and collapse system is considered from a purely
macro perspective - the system as just a system. Second, the discussion expands the
perspective of the sentient, boundedly rational observer embedded within the system,
which entails identifying the limited information available to decision makers as well as
the decisions that are likely to be made with that information.
3.3.1 Substitution and Technology Effects
Overshoot and collapse is not a topic of limited academic interest. There is a rich history
of this widespread economic phenomena that has impacted many lives and had lasting
effects: examples include 1) the 1593 Tulip-bulb craze in Holland , 2) the 1720 South Sea
bubble in Britain, 3) the 1926 Florida real estate craze in the US, and 4) the 1929 US
stock market centered on Wall Street (Malkiel 1999, Ch. 2). This study instead focuses
on a more recent example, the late 1990s overshoot and collapse of the NASDAQ index,
as shown in Figure 8 below.
5,500
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
NASDAQ
Composite
Index
1994 1996 1998 2000 2002
Figure 8. NASDAQ Overshoot and Collapse (www.bigcharts.com)
World Population Growth,
1750-2150 3
Popuation in billions
°
1750 1800 1850 1900 1950 20C0 2050 2100 2150
1960 1970 1980 1990 2000
Figure 9a & b. World Population, long and short-term
(www.worldpopulation.org; World Bank 2001)
Comparing Figure 7 with Figure 8, it can be seen that the NASDAQ index
demonstrates a classic overshoot and collapse response. This inquiry into the NASDAQ
example is motivated by a desire to gain insights into the possible overshoot and collapse
of the global environment. This includes not just the underlying systemic forces behind
the phenomena but also the ways people think about overshoot and collapse and the kind
of conclusions they draw at different points in the process. The NASDAQ example is
chosen because much has been written on its buildup between 1996 and 2000 and its
collapse from 2000 to 2002. This provides an easily accessible record of the mental
errors people made with regard to the NASDAQ economic system.
Beginning with the mechanics, let us look to what caused the bubble in the first
place and what eventually limited it. The story begins with the August 1995 Netscape
initial public offering (IPO) that demonstrated an unexpected demand for tech stocks.
Tech entrepreneurs, venture capitalists (VCs), and investment banks combined to provide
dot.com companies and shares to meet that demand (Smith 2002). The problem was that
the public markets valued dot.com shares at a premium but the companies themselves did
not make money. The dot.com bubble was based almost solely on investment capital
from the VCs and public markets. With investment capital being spent to cover operating
costs, the companies had only a short time to live unless sales could be generated. This
led to two questions: 1) When would sales increase to justify the share prices and allow
the companies to live? and 2) When would share prices drop to the levels warranted by
lackluster dot.com sales, and when would the companies die? Given the high prices tech
stocks reached, the first question was eventually rendered unanswerable - share prices
had to come down at some point. This left only the second question: When would the
dot.com bubble end?
As early as 1996, experienced investors were predicting an unhappy end to the
dot.com run-up. Barton Biggs and Byron Wien, both of Morgan Stanley, advised their
investors to lighten up on U.S. stocks because they felt the system and the companies that
comprised it were unsustainable (Cassidy 2002, 118— 9). Unfortunately for Biggs and
Wein, they were bears at the beginning of a four-year bull market that ended only in
April 2000. While their analysis was sound - indeed, the business fundamentals like
sales, markets, and profits were not there for long-term, successful businesses - the
timing proved much harder get right due to the economic dynamics at play. The ability
to predict when a system will “collapse” is only possible if it is understood when the
underlying, foundational resources will exhaust themselves. In the case of the simple
system depicted in Figures 4 and 5, Population decreases at precisely the time when
Resources completely run out. Calculating the exhaustion point for the complex investor
behavior and attendant economic dynamics that supported the late 1990s NASDAQ could
have been done as an educated guess, but it would have been just a guess. The best that
can be said, as depicted in Figure 3, is that entropy decreases as the system moves
towards its natural limit. The system becomes more likely to collapse, but it is
impossible to say exactly when. Thus the actual situation is more like that depicted in
Figure 7 with varying Food levels: the larger the resource base, the larger the overshoot
and the more postponed the collapse. However, since the underlying resource is a
complex economic system rather than a simple homogeneous stock, its exhaustion point
is harder to predict. Biggs understood this dynamic when he wrote in 1996, “I believe
that U.S. stocks are overheated, overvalued and vulnerable to a bear market... The longer
the craziness in the United States goes on, the higher the price we will have to pay.”
(Cassidy 2002, 119) Who then would or could have predicted it bull market would
continue for four years?
3.3.2 Market-driven cognitive effects
Biggs maintained his views far longer than most bears, especially considering that
bulls like Mary Meeker, Henry Blodgett, and Jack Grubman were so lavishly rewarded
for their ultimately unfounded optimism. In the summer of 1999, Biggs debated James
Glassman, coauthor of Dow 36,000, in Sun Valley:
During the debate with Biggs, [Glassman] argued that the Internet was the
transcending invention of the twentieth century, more important than the
jet aircraft, the contraceptive pill, and nuclear fission. Biggs considered
Glassman’s argument to be ridiculous. Even the humble air conditioner
had altered history more than the Internet, he said. Without air
conditioning, Atlanta would be a small town and modern Singapore
wouldn’t exist. After the speeches were over the issue was decided by a
show of hands. Glassman won by 180 votes to 2. One of the people who
voted for Biggs was his wife. (Cassidy 2002, 251)
The notable thing is not only is it hard to withstand the social pressure of being in the
minority, but the financial pressure for fund managers is even more intense. Imagine
predicting collapse in 1996, and then waiting while your clients watch their peers make
money by listening to your more optimistic competition, year after year. It is still
difficult to fathom both the duration and magnitude of investment funds that were made
available by venture capitalists and public markets to fund the dot.com bubble, one
consequence of which were the lopsided and ultimately incorrect popular views like those
demonstrated in Sun Valley. Biggs was right in the long-term, but the majority,
responding rationally to short-term economic incentives, reached the opposite, short-term
conclusion and were ultimately proven wrong.
4. Conclusion
This paper began with a question: Why do so many system dynamicists believe that the
global environment is engaged in an overshoot and collapse scenario and yet do so little
about it? (Fey and Lam 2001) This paper began by reviewing three different economic
thinkers - Forrester, Malthus, and Simon - as well as their critics. Then it reviewed two
system dynamics models. First, a chaotic oscillator was examined noting that its
dynamic response moves through “periods of possibility” and “periods of prediction.”
Prediction is most likely when the response moves toward the edge or limit of its range -
that is, an area where no previous response has been noted. Second, an overshoot and
collapse model demonstrated the relationship between growth and underlying resource
responses. It was noted that the greater the level of underlying resources, the greater the
level of growth that is achievable before systemic collapse. Therefore, if the quantity of
the underlying resource is unknown, then so too is the amount of growth it will support.
Next a real-word example of the overshoot and collapse dynamic - the NASDAQ
index or dot.com bubble - was reviewed. In this example, growth of the NASDAQ was
made possible so long as capital could be obtained from venture capitalists and the public
markets to fund tech companies because their low profits made them unsustainable. This
was noted by stock analysts as early as 1996, but the NASDAQ did not collapse until
April 2000, four years later. Two lessons can be drawn. First, growth can continue for
far longer than seems possible to somebody who recognizes the systems’ eventual
unsustainability and foresees limitation and collapse. Economic dynamics work to
expand and extend the underlying resource in ways that prolong growth and confound
prediction. The strongest statement that can be made is that as growth continues, the
likelihood of system limitation and collapse increases. For the individual, the growth
dynamic can prove so overwhelming that the possibility of collapse begins to seem
unlikely and remote as naysayers are continually proven wrong. As was the case with the
NASDAQ, the actual likelihood of collapse grows ever larger, while for those under its
thrall, the possibility of collapse grows ever more distant. When the system eventually
collapses, it does so suddenly, dramatically, and unexpectedly.
Systems lessons from the dot.com bubble can be considered with respect to the
critics of The Limits to Growth. Early predictions of population limitation due to
shortages of oil, metals, and food have not come true. In retrospect, economic dynamics
grounded in technical innovation have greatly expanded these resource bases and created
substitutes when technical innovation proved impossible. This in turn has allowed the
human population to reach historically unprecedented levels. Note however that there are
natural resources for which substitutes do not exist including clean air, fresh water, and
arable land. Moreover, the global ecology on which the world population is based is far
more complex and unpredictable than the economic system that supported the dot.com
bubble. Given that the strongest statement that can be made regarding a complex
resource base in an overshoot scenario is that it is increasingly likely that it will collapse,
itis probably premature to state that technology and innovation will obviate any natural
limits to world population.
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Appendix A. Underlying Philosophical Debates
In finding that both sides of the Limits to Growth debate are partially correct, potential
criticism that this is a simplistic equivocation in the face of a contentious and difficult
question is defended against in three ways. First, the weaknesses of logic to describe
completely the realm of mathematics and by implication reality and the natural world are
reviewed. This means that, for complicated questions, sharp distinctions of ‘true’ and
‘false’ become grayer, less focused, and nuanced. Second, the notion of falsifiability in
science is reviewed. Third, the concept of rationality is contrasted with more empirically
verifiable notions of cognition.
A.1 Logic
The weaknesses of strong logic establish the working context for 20th century
philosophy. In many ways, philosophy from the last century is unsatisfying because its
most significant advances are not readily understandable, even by those who made them.
First, consider the philosophical triple of Russell, Godel, and Turing. Whitehead and
Russell (1927) tried to provide a complete, axiomatic, and positivistic descriptive
framework in Principia Mathematica. Gédel's incompleteness theorem of 1930
demonstrated that one can say something complete or provable only about uncomplicated
systems, which is to say uninteresting problems (Hofstadter 1979). Complex and
interesting problems can, in contrast, only be described incompletely. Interpretations of
this result vary, but if one recalls that language reduces to logic, Gédel says that a logical
or linguistic description of a hard and complex problem will always fail to capture the
total nature of the problem or system.
Turing extends the notion of uncertainty with his theory of computation, which
corresponds roughly to a deterministic or “digital” universe (cf. Wolfram 2002). While it
is still a source of lively debate just how Turing applies to the real world -- some say "not
at all" while others say "quite a bit" -- this theory does bear on the argument at hand.
First, a Turing machine is wholly deterministic, unlike a neuron or a human mind (i.e.,
many neurons) that is comparatively probabilistic. Second, the whole notion of
parallelism (which is present for neurons) disappears for a Turing machine because a
parallel Turing machine reduces to a single, really fast Turing machine. The interesting
part is this: Given a strongly deterministic Turing machine and a digitally defined input
tape, it cannot be determined before hand whether or not the Turing machine will halt.
Whether it halts or not must be determined empirically, by actually running the machine.
And if it cannot be determined whether or not the machine will halt, neither can it be
determined if it will assume any other state of interest.
So how does this pertain to determinism, probabilism, and prediction? If one
cannot predict the behavior of a wholly deterministic machine with complete information,
then how can one hope to predict the behavior of the semi-deterministic complex
interaction between social and environmental systems with incomplete information? The
answer is that the prediction of complex and interesting systems is impossible, and so the
best that policy makers can do is employ heuristics that make some logical sense and
have an empirically supported history of utility. (Chaos theory provides another, more
physically based path to the same result. See section 3.1)
A.2 Falsifiability
Philosophers and social scientists effectively responded to this logic debate with, "So
what?" That is, they initially argued that computational theory has no bearing on human
philosophy. This is hard to defend because Turing's results derive from basic logic, and
so it is tough to see how philosophers can employ some logical tools (i.e., the easy ones)
and toss aside others (i.e., the hard ones). The more likely answer is that such results are
simply beyond the analytic capability of most philosophers and social scientists, so they
ignore them. After all, the popularity of Marxism can partially be explained by its being
simple enough for the average revolutionary, undergraduate, or revolutionary
undergraduate to grasp and use rather than its claims to Truth, so a competing theory that
is both hard to understand and even harder to apply is going to have trouble, regardless of
its utility or veracity.
The social science triple of Popper, Lakatos, and Kuhn illustrates that the
aforementioned analytical results have made their way slowly into mainstream
philosophy and social science. Popper's post-war, anti-historical positivism held that
statements and theories could not be proven true but could be demonstrated as false. This
view resulted in an unstable and ultimately unworkable scientific climate. Lakatos
loosened the analytic rules on falsifiability and held that theories could prove useful even
if they had led to a few false results. Kuhn’s (1962) paradigms and scientific revolutions
extended the views of Lakatos.
A.3 Rationality
So where does this leave us -- in an uncertain world of relativism? Certainly not. We're
left with the knowledge that the world is a more complicated and subtle place than some,
especially logicians, positivists, and philosophers, would have us believe. Lakatos states
that criticisms of the form, "Y ou put forward a complicated theory and one aspect of it
proved false so the whole theory is false," are unhelpful. Of course debating such
questions helps train the mind, but words and logic cannot capture the essence of
existence. In a sense we have known this since Gédel told us so 70 years ago, but
operationalizations and interpretations inevitably trail their motivating revelations.
Currently we see the brightest philosophy students voting with their feet and
moving into cognitive science, an amalgam of philosophy, computer science, and
experimental psychology. The reason why is simple: because these fields can provide
testable insights into longstanding philosophical problems, primarily rationality, which
lies at the root of so many intractable disagreements. Traditional philosophical notions of
rationality are most clearly defined in the most analytic of the social sciences,
economics. However, microeconomic definitions of rationality are axiomatic and do not
pretend to portray how people really think, which is problematic. Moreover, maximizing
one’s expected utility is possible in a heuristic, localized, temporally constrained sense,
but to do so in an absolute, global sense is impossible because rationality is bounded
(Simon 1983; Morecroft 1983). The analysis of rationality will advance to the extent that
the way people actually think and interact with their environment is accurately portrayed.
This brings us to the conclusion, which I base on the work of Lakoff and Johnson
(1999) who argue that traditional Western thought is methodologically characterized by
three assumptions: that 1) we can know our own minds by introspection, 2) most of our
thinking is literal, and 3) reason is disembodied and universal. Lakoff and Johnson, in
contrast, maintain that 1) most thought is unconscious, 2) abstract concepts are mostly
metaphorical, and 3) the mind is embodied (i.e., physical). This helps to explain the
debate between proponents and opponents of Limits to Growth in that they are both
espousing worldviews that are partially true. The ultimate question is this: Recognizing
the source and motivation for the disagreement - that is, sharply differing worldviews
based on very different assumptions - is there a way to move the debate forward? The
purpose of this study is to show that system dynamics can do precisely that.
Appendix B. Duffing Oscillator Equations
X(t) =X(t- dt) + (dX) * dt
INIT X =3
INFLOWS:
dX =Y
Y(t) =¥ (t- dt) + (dY) * dt
INIT Y =4
INFLOWS:
dy =forcing function - (.05*Y) - X3
forcing_function = 7.5*COS(time)
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