Balanced on a Pencil Point

COMPUTING SCIENCE

Brian Hayes

n 1972 a small paperbound book called T h e ment; there is one on every desk. Readers with Limits to Gro w t h was published with much fan- hands-on experience of these machines could If a re. Reporting on “Phase One of the Project on have brought to the book a more sophisticated the Predicament of Mankind,” the book warned understanding of the strengths and weaknesses that the world was steering a course for disaster. of computer modeling. More important, some Without a drastic change in direction, the human enterprising readers would have experimented population would run out of food and natural re- with the models themselves, or created new mod- s o u rces, or else would choke on its own pollution, els of their own. This kind of direct exploration is within 50 or 100 years. This gloomy message was clearly the best way to get a sense of how the g reeted with curious enthusiasm, at least in the models work and what their predictions mean. U.S. The book sold millions of copies; govern- As it happens, The Limits to Gro w t h has indeed ments took it seriously; conferences were con- just been published—in a sense. Members of the vened; the authors were awarded the German same group of workers have issued a new book, Peace Prize in 1974. There were many critics and Beyond the Limits, which makes essentially the skeptics, but the public was largely sympathetic. same arguments as the original one. More o v e r, America was in the mood for a jeremiad. And a the computer models themselves are available in year later when the gas pumps went dry, it a form that allows convenient experimentation, seemed the prophecies were being fulfilled. using readily available computer hard w a re. Now One factor that made The Limits to Gro w t h s o everyone can have doomsday on the desktop. persuasive was the book’s reliance on computer- aided mathematical modeling. The conclusions World Dynamics w e re not just opinions or personal interpre t a- The Project on the Predicament of Mankind was tions; they flowed ineluctably from the computer. s p o n s o red by the Club of Rome, a small org a n i z a- An introductory chapter noted two ways in tion whose members might best be described as which computer models are superior to mere concerned citizens of the world. In 1970 the club mental models: “First, every assumption we was looking for a quantitative model of what it make is written in a precise form so that it is had begun calling “the world p ro b l e m a t i q u e.” At a open to inspection and criticism by all. Second, meeting in Berne in 1970 Jay W. Forrester of the after the assumptions have been scrutinized, dis- Massachusetts Institute of Technology suggested a cussed, and revised to agree with our best cur- c o m p u t e r-based methodology for such a model. rent knowledge, their implications for the future F o r rester was already a formidable figure in the behavior of the world system can be traced with- history of computing—the inventor of magnetic- out error by a computer, no matter how compli- c o re memory and the architect of Project Whirl- cated they become.” The phrase “without erro r ” wind, perhaps the most ambitious machine in the was surely meant only to rule out mistakes in first generation of digital computers. Forrester had arithmetic, but for many readers the model must developed a technique of computer simulation have seemed infallible and irrefutable. In 1972 called system dynamics, which he had applied to the computer was still a marvelous oracular factory planning (in his book Industrial Dynamics) machine, kept behind glass walls and tended by and then to city planning (in Urban Dynamics) ; white-coated officiants. It predicted the weather; now he proposed a “world dynamics.” it predicted the outcome of presidential elections; F o r rester sketched out a preliminary version of why not have it predict the end of civilization? the model, called World1, on the flight home fro m If The Limits to Gro w t h had been published 20 Switzerland. A few weeks later members of the years later, the reception would have been diff e r- club visited MIT to see early runs of an expanded ent in certain details. The computer is no longer a model, World2. Forrester was invited to direct a mysterious, expensive and inaccessible instru- re s e a rch team that would further refine and extend the model, but he declined. Leadership of Brian Hayes, a former editor of American Scientist, has been the project went instead to Dennis L. Meadows, writing about computing for 10 years. Addre s s : 2 11 Dacian one of Forre s t e r ’s colleagues at MIT. (Although Avenue, Durham, NC 27701. Internet: [email protected]. F o r rester withdrew from the Club of Rome’s pro-

2 American Scientist, Volume 81 ject, he continued to work on his own global ple, one sector of the World3 model describes the model, and his book World Dynamics a p p e a red a global stock of arable land in terms of a re s e r v o i r year before The Limits to Gro w t h. It presents an with pipes flowing both in and out. The level of even grimmer vision of the future . ) the reservoir rises when raw land is developed For the club’s undertaking Dennis Meadows for agriculture; it falls when arable land erodes or re c ruited an international team of 17 young spe- is converted to urban and industrial uses. Each of cialists. The model they constructed was a dire c t these flows is regulated by a valve, whose setting o u t g row th of Forre s t e r ’s World2, and so they is determined by a complex web of other factors, called it World3. Four members of the gro u p including the world population, the amount of w e re listed as authors of The Limits to Gro w t h : food consumed per person and the level of Donella H. Meadows, Dennis Meadows, Jørg e n industrial output. Randers and William W. Behrens III. Later, vari- The dynamics of a system begin to get intere s t- ous members of the team published two more - ing when the connections between re s e r v o i r s , technical volumes, Toward Global Equilibrium a n d valves and other components include “loops” Dynamics of Growth in a Finite Wo r l d. The latter and thus introduce the possibility of feedback. A work constitutes the project’s final report and well-known instance is the growth of population. includes a complete program listing of the Because the number of births depends in part on World3 computer model. the number of people of child-bearing age, there Beyond the Limits, the most recent product of the is a positive feedback loop that can lead to expo- long collaboration, is by Donella and Dennis nential growth. More people have more childre n , Meadows and Jørgen Randers. They explain in who, after a delay of 20 years or so, have still their preface that they set out merely to update m o r e children. This process is re p resented in The Limits to Gro w t h for reissue on its 20th anniver- World3 by a feedback connection between a s a r y, but in the end they wrote a new book. In reservoir re p resenting the number of people many ways it is a better book than the original— aged 15 to 44 and the valve regulating flow into m o re carefully argued, less strident and, if not the human population. A similar mechanism quite optimistic, at least informed by a kinder and operates in the industrial sector: The total quanti- gentler Malthusianism. But the underlying mes- ty of industrial capital—factories, machinery, sage is the same: If we don’t stop burning the can- etc.—determines industrial output, but that out- dle at both ends, we shall soon be left in the dark. put in turn affects investment in new capital G row th in population and in consumption of equipment. The greater the industrial capacity of re s o u rces must be sharply curtailed. Again they a society, the faster that capacity can expand. rely on the World3 system dynamics model, Both of these feedback loops are positive, or slightly modified, to support these conclusions. s e l f - re i n f o rci ng; unless checked by some other f a c t o r, they give rise to unrestrained growth. The Plumbing and Wi r i n g World3 model also includes negative feedback System dynamics is all about plumbing and loops, in which the output of a process re d u c e s wiring. Stuff flows through pipes from sources to rather than re i n f o rces its own input. Perhaps the sinks. Along the way some of the stuff accumu- most fundamental example is the effect of over- lates in reservoirs. The flow into and out of the c rowding. If the World3 population gets too larg e , reservoirs is regulated by valves, which open and various factors connected with crowding incre a s e close in response to signals carried by wire s . the death rate, thereby bringing the population Depending on the nature of the model, the down again. In general, negative feedback tends “ s t u ff” in the pipes and reservoirs might be food to stabilize a system, although the mere pre s e n c e or consumer goods or land or people. For exam- of a negative loop is no guarantee of stability.

Figure 1. Five main sectors of the World3 model are linked by a web of feedback loops, only a few of which are shown.

1993 November–December 3 Figure 2. “Plumbing and wiring” diagram defines the architecture of the World3 model.

Finding out whether or not the system is stable is with an explanatory booklet and diagrams, fro m a major reason for running the simulation. the University of New Hampshire (where Dennis The World3 model has five main sectors: pop- Meadows is now director of the Institute for ulation, agriculture, industry, natural re s o u rc e s Policy and Social Science Researc h ) . and pollution. Multiple feedback loops link all of A Stella II model is created by placing small the sectors. For example, agriculture and popula- icons that re p resent reservoirs, pipes, valves, con- tion have an obvious interd e p e n d e n c e — m o re of verters and other components on the computer either one implies more of the other. Industry s c reen, and drawing the appropriate connections depends on inputs of nonrenewable re s o u rc e s , between them. Then, for each model element an such as ores and fuels, and the flow of re s o u rc e s equation or a numerical value must be supplied. depends in part on the amount of industrial capi- As a rule the equations are very simple. For exam- tal earmarked for their exploitation. Similarly, ple, in World3 the valve regulating the growth of both industry and agriculture generate pollution, industrial capital receives inputs from two vari- and severe pollution has effects on both popula- ables, total industrial output and the fraction of tion (reducing the life span) and food (re d u c i n g industrial output allocated to investment; the agricultural yield). equation controlling the setting of the valve sim- A diagram of the complete model is an impre s- ply calculates the product of the two variables. sively complicated tangle, with well over 100 re s e r- Once all the connections have been mapped voirs, valves, converters, etc., and an even gre a t e r and the equations filled in (the package supplied number of connections linking these elements. On by the University of New Hampshire takes care the other hand, comparing the model with the re a l of these tasks), the model is ready to run. The world, one is struck first by how much has been computer tracks the evolution of the system in left out. All the diverse re s o u rces that drive world d i s c rete time steps. For instance, from the initial industry—metals, energ y, feedstocks—are amalga- stock of natural re s o u rces and the initial rate of mated into a single generic re s o u rce. Likewise all depletion, the computer can calculate the stock pollutants are re p resented by one undiff e re n t i a t e d remaining after one unit of time. Next, the deple- noisome substance. And there is no geography in tion rate is re-evaluated, and then the new rate is the model: All the world’s nations and peoples are used to determine the stock after the next time one nation and one people. step. The World3 simulations extend over the interval from 1900 through 2100, and the time The Standard Scenario step is typically half a year. The results of the The World3 computer model was written in a sim- simulation are presented in graphs or tables that ulation language called Dynamo, which was track the values of selected variables over time. developed by Forre s t e r ’s group at MIT. Back then, F i g u re 3 shows the output of a simulation that running a Dynamo program re q u i red a main- Beyond the Limits calls Scenario 1. The graph frame computer, but a compiler for the language is re c o rds levels of population, life expectancy, non- now available for the IBM PC and compatible ma- renewable re s o u rces, total food pro d u c t i o n , chines. In addition, the World3 model has been industrial output and pollution. The future pro- translated into the language of Stella II, a simula- jected in Scenario 1 is not an attractive one. There tion program that runs on the Apple Macintosh. is strong growth in population, life expectancy, The simulations presented in Beyond the Limits food and industrial output until about 2025; then w e re run with the Stella II version of the model, t h e re is a dramatic collapse, and by 2100 most of which is also the version I chose for the experi- the variables are well below their 1993 levels. Life ments described here. Both versions are available, has become nasty, brutish and short again.

4 American Scientist, Volume 81 The main cause of the collapse in Scenario 1 is tion—or for that matter even a declining one— exhaustion of natural re s o u rces. Over the course must eventually dig the last troy ounce of tre a- of the two centuries the world consumes five- s u re from the earth, and dwindle away. sixths of the initial stock of re s o u rces, and the As Scenario 1 shows, one of the most stringent cost of extracting what remains is so high that it limits in the model is the finite supply of nonre- siphons capital away from other sectors of the newable re s o u rces, such as fossil fuels and min- e c o n o m y, such as industrial production and agri- erals. The initial quantity of these substances was c u l t u re. The World3 group is careful to state that chosen so that in 1970 the remaining re s e r v e s this scenario is not a p re d i c t i o n; no one expects the would last for 250 years at the 1970 rate of con- variables to follow precisely these trajectories. sumption. Where did the number 250 come Nevertheless, The Limits to Gro w t h concludes a f rom? It is already present in Forre s t e r ’s Wo r l d discussion of the scenario with this italicized admonition: “We can thus say with some confidence that, under the assumption of no major change in the p resent system, population and industrial growth will certainly stop within the next century, at the latest.”

Exponential Growth Using Scenario 1 as a baseline, the World3 gro u p undertook to demonstrate that schemes for pro- longing economic growth will not solve the world’s problems. For example, suppose the actu- al supply of natural re s o u rces is double the original estimate. The change can be entered into the Stella II model simply by clicking on the natural- re s o u rces reservoir and typing in a new initial value. The consequence of this change is shown in F i g u r e 4. Population and prosperity continue g rowing for a little longer, but when the crash Figure 3. Scenario 1 exhausts the world’s natural resources. comes, it is even steeper and deeper. Intere s t i n g l y, the cause of the collapse is diff e rent: Incre a s e d industrial output generates enough pollution to poison the land. Capital is diverted into agricul- t u re to combat this effect, but food production falls a n y w a y, and by the middle of the next century people are starving. Not a pretty pro s p e c t . Further remedies suggest themselves: technologies for pollution abatement, for the enhance- ment of agricultural yield, for the control of land e rosion, for more efficient exploitation of natural re s o u rces. Figure 5 shows the result of a simulation run in which all these measures were tried at once. The human fate is a little brighter, in that the u p w a rd trends continue longer and the down- w a rd plunge is not quite as steep, but in the end the decline is inescapable. In this case what the Figure 4. Doubling initial resources leads to a pollution crisis. f u t u re holds is decay and obsolescence. So much e ffort must be bent toward averting catastro p h e s that no investment capital is left to maintain and renew the economy. The perennial theme of the World3 model—it f i g u res prominently in all of the books and essays—is the impossibility of sustaining exponential growth in a world with finite limits. Thomas Malthus made the same point almost 200 years ago, observing that when a population doubles every 25 years, it must eventually out- run its food supply. But in World3 the Pre d i c a- ment of Mankind is even worse. Under the Malthusian law, although growth cannot continue, a nongrowing population can flourish indefi- n i t e l y, always producing enough food to meet its needs. In World3, by contrast, a static popula- Figure 5. Multiple technologies fail to stabilize the system.

1993 November–December 5 D y n a m i c s , but no rationale is off e red there to A Hard Game to Wi n explain it. In The Limits to Gro w t h the 250-year I ro n i c a l l y, in view of the controversy over re s o u rc e assumption is justified by re f e rence to a table list- estimates, it turns out that changing those esti- ing estimated reserves of various re s o u rces as of mates is not in itself an effective way of impro v i n g 1972. According to the table, a 250-year lifetime is the model’s outcome. As Figure 4 shows, dou- optimistic; but then, according to the table, by bling the world’s supply merely substitutes a pol- 1993 the world should already have run out of lution crisis for a re s o u rce crisis. If the re s o u rc e c o p p e r, gold, lead, merc u r y, silver, tin, zinc and estimate is halved rather than doubled, the out- p e t roleum. The table is omitted from Beyond the come is no better: As Figure 6 shows, the economy collapses just as it did in Scenario 1, but 20 years s o o n e r. Even with essentially unlimited re s o u rc e s (a 25,000-year supply), the model foretells a very t roubled future. Figure 7 shows the result of such a simulation: a ruinous oscillation driven by inter- actions between industry and pollution. The experiments with re s o u rce stocks illustrate a general characteristic of the World3 model. No matter how you turn the model’s knobs and dials, it is difficult to avoid the crash-and-burn ending. If you view the model as a kind of game, whose object is to achieve the best possible outcome for h u m a n i t y, you find it is a very hard game to win. The tendency to overshoot and collapse is highly persistent, and policies introduced in the 1990s generally come too late to alter the outcome. Figure 6. Reducing resources by half has little eff e c t . Several features of the model help to explain why it is so intractable. Fixed limits are one factor, and they include not only the natural-re s o u rc e limit but also a limit on arable land. The model assumes that the total area that could eventually be brought under cultivation is only about twice the area being farmed in 1970. As a matter of fact, this limit is not really fixed; it diminishes with time. Land is assumed to “wear out” after a peri- od of use. In the 1972 model the normal lifetime of farmland was 6,000 years, but in the 1992 version the lifetime was reduced to 1,000 years. The arable-land equations in World3 include another feature that hastens the downward spi- ral. To re p resent the effects of erosion, the land lifetime is made to depend on the intensity of use. Anything done to increase agricultural yield Figure 7. A very large resource base induces oscillations. also has the side-effect of exhausting the land somewhat sooner. Beyond the Limits refers to all L i m i t s , which offers a diff e r ent analysis of mechanisms of this kind—not just those in the re s o u rce limits, based on the increasing cost of agricultural sector—as “erosion loops.” “These extraction as producers resort to leaner ore s . a re positive feedback loops of the worst kind. Nevertheless, the updated model still employs Normally they are dormant, but when a situation exactly the same initial quantity of re s o u rc e s . gets bad, they make it worse.” Another ero s i o n Critics of the World3 model have been particu- loop turns up in the pollution sector, where high larly skeptical of the re s o u rce estimates. Soon levels of pollutants impair the mechanisms that after The Limits to Gro w t h a p p e a red, a group at o rdinarily absorb or detoxify contaminants. the University of Sussex published a critical Still another factor that makes the model hard appraisal under the title Models of Doom; they to control is the presence of delays in many of the questioned whether it makes sense to assign any feedback loops. When a new policy or technolo- fixed limit to re s o u rces over the time span of the gy is introduced, there is a delay of some years model. Of course there is no denying that the b e f o re the effects are felt throughout the world. earth is a sphere of finite size, whose bounty can- The delay makes the system susceptible to over- not last fore v e r. In this respect the model must shooting targets and subsequent overc o r re c t i n g . ultimately be correct: There i s a limit to gro w t h . Imagine trying to drive a car with a delay of even But it makes a diff e r ence to many people a few seconds built into the steering gear: Yo u whether the limit is just over the horizon or is would almost certainly weave from side to side still centuries in the future . and eventually go off the road. Feedback delays

6 American Scientist, Volume 81 in World3 have the same effect. Beyond the Limits pyramid-building in ancient Egypt and cathe- remarks: “Any population-economy-enviro n- dral-building in medieval Europe had such a sta- ment system that has feedback delays and slow bilizing role—but the situation is more complex. physical responses, that has thresholds and ero- The real significance of Figure 10 is not the pre- sive mechanisms, is literally u n m a n a g e a b l e. ” scription it suggests for the real world but the question it raises about World3. Finding that a Strategies for Stability model is highly sensitive to a parameter is cause In spite of these considerable challenges, for caution, and for looking closely at the value Meadows and his colleagues do offer a solution assigned to that parameter. In this case the value that appears to be sustainable, at least for a time. of 0.43 adopted by the World3 group does not They begin by adopting all the technological appear to have very solid empirical support—it i m p rove ments incorporated into the model of is an average calculated from highly disparate F i g u re 5, and they also shorten the feedback delays in the model. Then they introduce addi- tional measures to eliminate growth in population and wealth. In The Limits to Gro w t h these further measures take the form of fixed allocations, but Beyond the Limits adopts a more effective and p robably more realistic plan: The feedback princi- ple is put to work again. Desired levels of pro d u c- tion and consumption are determined, and feedback loops continually tune the economy to maintain those levels. In particular, the world’s people “decide” to buy no more than $350 worth of consumer goods per year. The result of this strategy is shown in Figure 8: The economic indicators have stabilized by the middle of the next century. Even the most exquisitely tuned control mechanism, however, cannot keep an engine going after Figure 8. Lowered material expectations bring greater stability. it runs out of gas. Meadows and his colleagues refer to the scenario of Figure 8 as a pre s c r i p t i o n for a sustainable world, and they suggest that it could be maintained indefinitely if nonre n e w a b l e re s o u rces are used only as fast as they can be replaced by renewable re s o u rces. This sustainable rate is never defined, however, and no such replacement mechanism is included in World3. As a result, all of the controls and constraints in the model can only postpone the inevitable collapse. F i g u re 9 shows that most measures of well-being have sagged badly by 2400. The key ingredient in the Meadows plan for attaining equilibrium is a reduced demand for consumer goods. Paradoxically, I have found that the opposite strategy can achieve a similar end. F i g u re 10 shows a model run in which the initial Figure 9. Even the prosperity of Figure 8 fades in a few centuries. conditions are identical to those in Figure 4, but starting in 1995 the fraction of capital allocated to consumption increases from 0.43 to 0.53. The result is an improvement in both stability and s t a n d a rd of living, at least through the 21st centu- r y. The model seems to be telling us to invest less in farms and factories and to spend more on frip- pery and fast cars. Armaments also fall into the category of nonproductive spending, so perh a p s we need a good vigorous war every few decades. These modest proposals are not, of course, to be taken seriously. In World3, consumption acts as a damper, draining energy away from the m o r e volatile sectors of the economy, whose g rowth is the cause of so much trouble. In the real world a similar mechanism may also oper- ate—John Maynard Keynes once suggested that Figure 10. World3 appears to be stabilized by dissipative spending.

1993 November–December 7 data—and the true value might well be diff e re n t . would have shattered long ago. The mere F u r t h e r m o re, the world’s spending habits are longevity of civilization speaks for its stability. s u rely subject to change. Perhaps there is another I would like to conclude with a personal obser- feedback loop in need of closing here . vation. When The Limits to Gro w t h a p p e a red in 1972, I was a young man not long out of adoles- Aggregation or Homogenization cence. I read the book with fascinated horro r, I find it troubling and disappointing that with total cre d u l i t y, and also with rising anger. Meadows and his colleagues have decided to The anger was directed against my parents’ gen- rewrite their book but not their computer model. eration, which it seemed to me had enjoyed a In 1972 they acknowledged that the model was whopper of a party and had left nothing in the “imperfect, oversimplified and unfinished,” and house for the next tenants but an empty lard e r they wrote: “We intend to alter, expand, and and a mess to clean up. Later I read the critiques i m p rove it as our knowledge and the world data and rebuttals, and I recognized some limits to base gradually improve.” Yet the model they pre- The Limits to Gro w t h. The anger faded. sent today is little changed from the original. The young adults of the present moment lodge One disturbing deficiency is the absence of all a similar complaint against my own generation. geographic and socioeconomic distinctions. In a The circumstances are slightly diff e rent. To d a y world where wealth is distributed very inequit- our children accuse us not only of using up the a b l y, averages can be misleading. The importance world’s re s o u rces but also of occupying our stools of global diversity was stressed early on by too long—keeping the best jobs and the best E d u a rd Pestel, a member of the Club of Rome houses, leaving youth too long in the anteroom of who was instrumental in gaining financial sup- life. Generation X waits its turn to lay waste the port for the World3 project. In his recent book world, and to save it. Perhaps their impatience is Beyond the Limits to Gro w t h (not to be confused no more warranted than my grumbling was two with either Beyond the Limits or The Limits to decades ago—but one of these days the re c u r re n t G ro w t h), Pestel tells of visiting MIT in the spring fear of seeing the world all used up before youth of 1971 for a pro g ress report. He urged the gro u p gets its chance may finally prove justified. to divide the model into at least two regions, re p- Computer modeling could help predict when resenting rich and poor nations. “Treating the that day is coming. I hope the next generation world as a monolithic entity was not aggre g a t i o n will at least produce a better computer model. but homogenization,” he writes. Apparently a two-segment model was tried, but then aban- A Note on Sources doned. (Pestel and Mihajlo Mesarovic later went Versions of the World3 model are available for $30 from the Laboratory for Interactive Learning, IPSSR, Hood House, on to build a regionalized model of their own, University of New Hampshire, Durham, NH 03824, tele- described in Mankind at the Turning Point. ) phone 603-862-2186, fax 603-862-1488. The version for the I don’t know why the effort to re g i o n a l i z e Macintosh computer re q u i res the Stella II simulation sys- World3 failed, but I can guess why the model has tem, published by High Performance Systems, Inc., 45 not been much expanded. The problem is certain- Lyme Road, Suite 300, Hanover, NH 03755. The version of World3 for the IBM PC re q u i res the Dynamo Plus simula- ly not a shortage of computing capacity: Wo r l d 3 tion system, available from Pugh-Roberts Associates, 41 fits easily in a small personal computer, and 200- William Linsky Wa y, Cambridge, MA 02142. year simulations run in well under a minute. The critical shortage is more likely mental capacity. B i b l i o g r a p h y Although the model suppresses a great deal of Cole, H. S. D., Christopher Freeman, Marie Jahoda and K. L. detail, it is complicated enough to make under- R. Pavitt, eds.1973. Models of Doom: A Critique of The Lim- standing difficult. When you discover some new its to Growth. New York: Universe Books. aspect of its behavior, it can be difficult to track F o r re s t e r, Jay W. 1971. World Dynamics. Cambridge, Mass.: Wright-Allen Pre s s . down the mechanism responsible. Thus adding Meadows, Dennis L., and Donella H. Meadows. 1973. To - m o re stru c t u re in the cause of realism would not ward Global Equilibrium: Collected Papers. Cambridge, necessarily teach us much. We might well reach a Mass.: Wright-Allen Pre s s . point where we could not understand the model Meadows, Dennis L., William W. Behrens III, Donella H. any better than we understand the real world. Meadows, Roger F. Naill, Jørgen Randers and Erich K. O. The questions raised by World3 are important. Zahn. 1974. Dynamics of Growth in a Finite Wo r l d. Cam- What are the true dynamics of the global econo- bridge, Mass.: Wright-Allen Pre s s . Meadows, Donella H., Dennis L. Meadows and Jørgen Ran- my and ecosystem? What is the margin of stabili- ders. 1992. Beyond the Limits: Confronting Global Collapse, ty? The model suggests that the world is balanced Envisioning a Sustainable Future. Post Mills, Vt.: Chelsea on a pencil point, and it will take every bit of our G reen Publishing Company. e n e rgy and vision and dexterity to keep it there . Meadows, Donella H., Dennis L. Meadows, Jørgen Randers A c c o rding to the model, we are at a singular and William W. Behrens III. 1972. The Limits to Growth: A moment in the history of the world—the one and Report for the Club of Rome’s Project on the Predicament of M a n k i n d. New York: Universe Books. only transition from abundance to scarc i t y, fro m M e s a rovic, Mihajlo, and Eduard Pestel. 1974. Mankind at the g rowth to stasis. It may well be so. On the other Turning Point. New York: E. P. Dutton. hand, there is the argument—facile, but hard to Pestel, Eduard. 1989. Beyond the Limits to Growth: A Report to refute—that if the earth were really so fragile, it the Club of Rome. New York: Universe Books.

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