Thinking in Systems: A Primer

by Donella H. Meadows

Growth in a constrained environment is very common, so common that systems thinkers call it the “limits-to-growth” archetype.

In physical, exponentially growing systems, there must be at least one reinforcing loop driving the growth and at least one balancing loop constraining the growth, because no physical system can grow forever in a finite environment.

A: Extraction rate B: Capital stock C: Resource stock Figure 38. Extraction (A) creates profits that allow for growth of capital (B) while depleting the nonrenewable resource (C). The greater the accumulation of capital, the faster the resource is depleted.

A quantity growing exponentially toward a constraint or limit reaches that limit in a surprisingly short time.

The higher and faster you grow, the farther and faster you fall, when you’re building up a capital stock dependent on a nonrenewable resource. In the face of exponential growth of extraction or use, a doubling or quadrupling of the nonrenewable resource give little added time to develop alternatives.

Figure 39. Extraction with two times or four times as large a resource to draw on. Each doubling of the resource makes a difference of only about fourteen years in the peak of extraction.

Figure 40. The peak of extraction comes much more quickly as the fraction of profits reinvested increases.

I’ll leave you to have this argument with yourself, or with someone of the opposite persuasion. I will just point out that, according to the dynamics of depletion, the larger the stock of initial resources, the more new discoveries, the longer the growth loops elude the control loops, and the higher the capital stock and its extraction rate grow, and the earlier, faster, and farther will be the economic fall on the back side of the production peak.

Harrowing...

Figure 42. Economic capital with its reinforcing growth loop constrained by a renewable resource.

Nonrenewable resources are stock-limited. The entire stock is available at once, and can be extracted at any rate (limited mainly by extraction capital). But since the stock is not renewed, the faster the extraction rate, the shorter the lifetime of the resource.

Renewable resources are flowlimited. They can support extraction or harvest indefinitely, but only at a finite flow rate equal to their regeneration rate. If they are extracted faster than they regenerate, they may eventually be driven below a critical threshold and become, for all practical purposes, nonrenewable.

I’ve shown three sets of possible behaviors of this renewable resource system here: • overshoot and adjustment to a sustainable equilibrium, • overshoot beyond that equilibrium followed by oscillation around it, and • overshoot followed by collapse of the resource and the industry dependent on the resource.

Neither renewable nor nonrenewable limits to growth allow a physical stock to grow forever, but the constraints they impose are dynamically quite different. The difference comes because of the difference between stocks and flows.

Why do systems work so well? Consider the properties of highly functional systems—machines or human communities or ecosystems—which are familiar to you. Chances are good that you may have observed one of three characteristics: resilience, self-organization, or hierarchy.

Resilience is a measure of a system’s ability to survive and persist within a variable environment. The opposite of resilience is brittleness or rigidity.

A set of feedback loops that can restore or rebuild feedback loops is resilience at a still higher level—meta-resilience, if you will. Even higher meta-meta- resilience comes from feedback loops that can learn, create, design, and evolve ever more complex restorative structures. Systems that can do this are self-organizing, which will be the next surprising system characteristic I come to.

Resilience is not the same thing as being static or constant over time. Resilient systems can be very dynamic. Short-term oscillations, or periodic outbreaks, or long cycles of succession, climax, and collapse may in fact be the normal condition, which resilience acts to restore! And, conversely, systems that are constant over time can be unresilient. This distinction between static stability and resilience is important. Static stability is something you can see; it’s measured by variation in the condition of a system week by week or year by year. Resilience is something that may be very hard to see, unless you exceed its limits, overwhelm and damage the balancing loops, and the system structure breaks down.

Large organizations of all kinds, from corporations to governments, lose their resilience simply because the feedback mechanisms by which they sense and respond to their environment have to travel through too many layers of delay and distortion. (More on that in a minute, when we come to hierarchies.)

Systems need to be managed not only for productivity or stability, they also need to be managed for resilience—the ability to recover from perturbation, the ability to restore or repair themselves.

The most marvelous characteristic of some complex systems is their ability to learn, diversify, complexify, evolve. It is the ability of a single fertilized ovum to generate, out of itself, the incredible complexity of a mature frog, or chicken, or person. It is the ability of nature to have diversified millions of fantastic species out of a puddle of organic chemicals. It is the ability of a society to take the ideas of burning coal, making steam, pumping water, and specializing labor, and develop them eventually into an automobile assembly plant, a city of skyscrapers, a worldwide network of communications. This capacity of a system to make its own structure more complex is called self-organization.

Like resilience, self-organization is often sacrificed for purposes of short-term productivity and stability. Productivity and stability are the usual excuses for turning creative human beings into mechanical adjuncts to production processes. Or for narrowing the genetic variability of crop plants. Or for establishing bureaucracies and theories of knowledge that treat people as if they were only numbers. Self-organization produces heterogeneity and unpredictability. It is likely come up with whole new structures, whole new ways of doing things. It requires freedom and experimentation, and a certain amount of disorder. These conditions that encourage self-organization often can be scary for individuals and threatening to power structures. As a consequence, education systems may restrict the creative powers of children instead of stimulating those powers. Economic policies may lean toward supporting established, powerful enterprises rather than upstart, new ones. And many governments prefer their people not to be too self-organizing. Fortunately, self-organization is such a basic property of living systems that even the most overbearing power structure can never fully kill it, although in the name of law and order, self-organization can be suppressed for long, barren, cruel, boring periods.

Beautiful

(It is because of fractal geometry that the average human lung has enough surface area to cover a tennis court.)

Figure 46. Even a delicate and intricate pattern, such as the Koch snowflake shown here, can evolve from a simple set of organizing principles or decision rules.

Systems often have the property of self-organization—the ability to structure themselves, to create new structure, to learn, diversify, and complexify. Even complex forms of self-organization may arise from relatively simple organizing rules—or may not.

In the process of creating new structures and increasing complexity, one thing that a self-organizing system often generates is hierarchy.

Complex systems can evolve from simple systems only if there are stable intermediate forms. The resulting complex forms will naturally be hierarchic. That may explain why hierarchies are so common in the systems nature presents to us. Among all possible complex forms, hierarchies are the only ones that have had the time to evolve.5 Paraphrased from Herbert Simon,

Hierarchies evolve from the lowest level up—from the pieces to the whole, from cell to organ to organism, from individual to team, from actual production to management of production.

The original purpose of a hierarchy is always to help its originating subsystems do their jobs better. This is something, unfortunately, that both the higher and the lower levels of a greatly articulated hierarchy easily can forget. Therefore, many systems are not meeting our goals because of malfunctioning hierarchies.

When a subsystem’s goals dominate at the expense of the total system’s goals, the resulting behavior is called suboptimization. Just as damaging as suboptimization, of course, is the problem of too much central control. If the brain controlled each cell so tightly that the cell could not perform its self-maintenance functions, the whole organism could die. If central rules and regulations prevent students or faculty from exploring fields of knowledge freely, the purpose of the university is not served. The coach of a team might interfere with the on-the-spot perceptions of a good player, to the detriment of the team. Economic examples of overcontrol from the top, from companies to nations, are the causes of some of the great catastrophes of history, all of which are by no means behind us.

Hierarchical systems evolve from the bottom up. The purpose of the upper layers of the hierarchy is to serve the purposes of the lower layers.

The trouble . . . is that we are terrifyingly ignorant. The most learned of us are ignorant. . . . The acquisition of knowledge always involves the revelation of ignorance—almost is the revelation of ignorance. Our knowledge of the world instructs us first of all that the world is greater than our knowledge of it. —Wendell Berry,1 writer and Kentucky farmer

The relationship between knowledge and ignorance.

Everything we think we know about the world is a model. Our models do have a strong congruence with the world. Our models fall far short of representing the real world fully.

You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy.

System structure is the source of system behavior. System behavior reveals itself as a series of events over time.

in trying to find statistical links that relate flows to each other, econometricians are searching for something that does not exist. There’s no reason to expect any flow to bear a stable relationship to any other flow. Flows go up and down, on and off, in all sorts of combinations, in response to stocks, not to other flows.

Nonlinearities are important not only because they confound our expectations about the relationship between action and response. They are even more important because they change the relative strengths of feedback loops.

C. S. Holling of the University of British Columbia and Gordon Baskerville of the University of New Brunswick put together a computer model to get a whole-system look at the budworm problem. They discovered that before the spraying began, the budworm had been barely detectable in most years. It was controlled by a number of predators, including birds, a spider, a parasitic wasp, and several diseases. Every few decades, however, there was a budworm outbreak, lasting from six to ten years. Then the budworm population would subside, eventually to explode again The budworm preferentially attacks balsam fir, secondarily spruce. Balsam fir is the most competitive tree in the northern forest. Left to its own devices, it would crowd out spruce and birch, and the forest would become a monoculture of nothing but fir. Each budworm outbreak cuts back the fir population, opening the forest for spruce and birch. Eventually fir moves back in. As the fir population builds up, the probability of an outbreak increases—nonlinearly. The reproductive potential of the budworm increases more than proportionately to the availability of its favorite food supply. The final trigger is two or three warm, dry springs, perfect for the survival of budworm larvae. (If you’re doing event-level analysis, you will blame the outburst on the warm, dry springs.) The budworm population grows too great for its natural enemies to hold in check—nonlinearly. Over a wide range of conditions, greater budworm populati...

Many relationships in systems are nonlinear. Their relative strengths shift in disproportionate amounts as the stocks in the system shift. Nonlinearities in feedback systems produce shifting dominance of loops and many complexities in system behavior.

Clouds stand for the beginnings and ends of flows. They are stocks—sources and sinks—that are being ignored at the moment for the purposes of simplifying the present discussion. They mark the boundary of the system diagram. They rarely mark a real boundary, because systems rarely have real boundaries. Everything, as they say, is connected to everything else, and not neatly. There is no clearly determinable boundary between the sea and the land, between sociology and anthropology, between an automobile’s exhaust and your nose. There are only boundaries of word, thought, perception, and social agreement—artificial, mental-model boundaries. The greatest complexities arise exactly at boundaries. There are Czechs on the German side of the border and Germans on the Czech side of the border. Forest species extend beyond the edge of the forest into the field; field species penetrate partway into the forest. Disorderly, mixed-up borders are sources of diversity and creativity.

Whether it is important to keep track of raw materials or consumers’ home stocks (whether it is legitimate to replace them in a diagram with clouds) depends on whether these stocks are likely to have a significant influence on the behavior of the system over the time period of interest.

The great geological cycles of the earth keep moving materials around, opening and closing seas, raising up and wearing down mountains. Eons from now, everything put in a dump will end up on the top of a mountain or deep under the sea.

There are no separate systems. The world is a continuum. Where to draw a boundary around a system depends on the purpose of the discussion—the questions we want to ask.

Systems analysts often fall into the opposite trap: making boundaries too large. They have a habit of producing diagrams that cover several pages with small print and many arrows connecting everything with everything. There is the system! they say. If you have considered anything less, you are academically illegitimate.

Ideally, we would have the mental flexibility to find the appropriate boundary for thinking about each new problem. We are rarely that flexible. We get attached to the boundaries our minds happen to be accustomed to. Think how many arguments have to do with boundaries—national boundaries, trade boundaries, ethnic boundaries, boundaries between public and private responsibility, and boundaries between the rich and the poor, polluters and pollutees, people alive now and people who will come in the future. Universities can maintain disputes for years about the boundaries between economics and government, art and art history, literature and literary criticism. Too often, universities are living monuments to boundary rigidity.

At any given time, the input that is most important to a system is the one that is most limiting.

Insight comes not only from recognizing which factor is limiting, but from seeing that growth itself depletes or enhances limits and therefore changes what is limiting.

There always will be limits to growth. They can be self-imposed. If they aren’t, they will be system-imposed.

When there are long delays in feedback loops, some sort of foresight is essential. To act only when a problem becomes obvious is to miss an important opportunity to solve the problem.

Bounded rationality means that people make quite reasonable decisions based on the information they have. But they don’t have perfect information, especially about more distant parts of the system.

Bounded rationality

We are not omniscient, rational optimizers, says Simon. Rather, we are blundering “satisficers,” attempting to meet (satisfy) our needs well enough (sufficiently) before moving on to the next decision.11 We do our best to further our own nearby interests in a rational way, but we can take into account only what we know. We don’t know what others are planning to do, until they do it.