We live in a world orderly enough that it pays to measure.
Paul Johnson, Fire in the Mind
Linearity (which has been linked for the last 200 years with the great Isaac Newton, and dubbed Newtonianism) has always rubbed up against the nonlinear world. This is inevitable, since nonlinearity has always been present, has always been representative of most of our world, and is growing. This has not always been recognized. A survey of physics textbooks showed that only 2 of the 19 published between 1910 and 1949 "treated nonlinear oscillations; one of these stated that nonlinear behavior occurs `only occasionally,' and the other called it an `important' topic but said `we shall not go into it in any detail.'" (1)
When linearity meets nonlinearity, it has established its domain by either imposing linear surrogates or excuses. In the former case, the linear has invented the calculus, statistical techniques, and elements of operations research and systems theory. These methods work in mildly nonlinear environments. While differential equations are essentially linear and reductionist (small changes produce small effects and large effects are obtained by summing up many small changes), this approach has, nevertheless, served well. "Phenomena as diverse as the flight of a cannonball, the growth of a plant, the burning of coal and the performance of a machine can be described by such equations." (2)
But linearity's real power has been its ability to produce technology, from the wheel and steam engine to the silicon chip and the unraveling of the DNA string. Remember Alan Beyerchen's point that "Linearity is excellent for the systems we design to behave predictably." Technological improvements are primarily linear, or mildly nonlinear. In the latter case, linear techniques developed to deal with mild forms of nonlinearity, such as differential equations, work well. It should be noted, however, that software development, which is often an intrinsic part of today's technology, is potentially subject to the full range of nonlinear behaviors. But, technological success often leaves behind a conundrum of migraine proportions. As this is being written, Congress is holding hearings on cloning, a sheep having recently been duplicated in Great Britain using thoroughly linear reductionist techniques.
On every other front, however, linearity alone, has not come close to meeting with the success it has enjoyed in technological innovation. The fact is that sheep don't fight back, and the silicon chip does not have its own agenda. In technology, one is faced by formidable challenges. But it is not a test of wills or opposing forces, which is precisely the environment which gives rise to nonlinear behaviors. Linear reductionism, faced with a significant degree of nonlinearity in the environment, gives way to "rounding," Peter's Principle, "good enough for government work," Murphy's Law, or looking good, if meaning nothing.
The result of unintended results, which is the manifestation of applying linear approaches to nonlinear problems, lie all about us in painful and embarrassing profusion. The 1960s with all its other calamities can be viewed as the height of arrogant confidence in the power of the linear paradigm, which was undoubtedly a contributing cause of its travails. Linearity was expected to win both the Vietnam War and the War on Poverty, simultaneously, and failed in both.
The major inadequacy of linear reductionism is its inability to deal with interactions. It inherently focuses on agents or objects, in the process of taking a complicated and large problem and breaking it up into manageable pieces. It does not account for the fact that in any system, the number of ways for pairs of agents to interact is almost, but not quite, equal to half the square of the total number of agents in the system. As a result, as the number of agents grows, the number of possible interactions increases even faster, as follows: 10 agents can generate up to 45 interactions; 100 up to 4,950; 1000 up to 499,500; 10,000 up to 49,995,000; and 100,000 agents can generate up to 4,999,950,000! The interactions are not usually significant if there are only two agents. When there are three, interactions can become a factor. And from four on up, interactions increasingly become the things that count.
In fact, the emergent quality of nonlinearity is attributed to the interactions between the agents within a system, and not the agents themselves. Graham T. Allison, back in 1971, described this proposition with little, if any, knowledge of nonlinearity.
- [T]he Governmental (or Bureaucratic) Politics Model sees no unitary actor but rather many actors as players-players who focus not on a single strategic issue but on many diverse international problems as well; players who act in terms of no consistent set of strategic objectives but rather according to various conceptions of national, organizational, and personal goals; players who make government decisions not by a single, rational choice but by the pulling and hauling that is politics. (3)
Steven Rinaldi, a physicist and Air Force officer who is often cited in this book, perceptively adds,
- According to this model, the global emergent properties (the strategic decisions) of the government come about not because of the personal, organizational, and national goals of the agents (players), but rather because of the interactions (political maneuvering) between the agents within the governmental hierarchy. And a prior knowledge of the agents does not suffice in comprehending the emergent decisions of a government. (4)
Obviously, the more that interactions count, which is a function of the number of agents/objects, the less linear reductionism does. And the number of agents/objects are globally increasing over time because there is an absolute growth in nonlinearity. Below are three views of this growth:
W. Brian Arthur, member of the Santa Fe Institute (the leading Complexity theory "think tank") and prominent nonlinear economist, believes that,
- there is a general law: complexity tends to increase as functions and modifications are added to a system to break through limitations, handle exceptional circumstances or adapt to a world itself more complex. This applies, if you think about it, not just to technologies and biological organisms but also to legal systems, tax codes, scientific theories, even successive releases of software programs. Where forces exist to weed out useless functions, increased complexity delivers a smooth, efficient machine. Where they do not, it merely encumbers. (5)
Murray Gell-Mann, nobel laureate says that,
- As the universe grows older and frozen accidents pile up [i.e., the net increase in saved bifurcations over historical time], the opportunities for effective complexity to increase keep accumulating as well. Hence there is a tendency for the envelope of complexity to expand, even though any given entity may either increase or decrease its complexity during a given time period. (6)
LtGen Erwin Rokke, USAF (Ret.), former president of the National Defense University, sees a technological basis for the increase in nonlinearity. Speed and feedback loops are attributes of nonlinearity. Hence, new information technologies such as the Internet, e-mail, and CNN increase the nonlinearity of both information exchanges and the events and processes they cover.
Increasing the overall level of complexity does not change the size of the complexity region. But it does increase the population of the agents/objects within it, and, therefore, disproportionately, the potential number of interactions. One result is to make predictability even more difficult. Another, effect however, is that
- diversity and sheer complexity have also made the economy more rugged, distributing shocks across a greater number of smaller businesses and an ever-denser web of commercial relationships. 'Rather than multiply a decline [economic recessions], these wider networks are far more likely to cushion that decline....' (7)
In fact, this increase in complexity may help to account for the amazing (1992-199?) "bull" stock market. The effect is, of course, not limited to the economy, but extends to networks of all kinds and to social interactions.
Yet,
- We can't study most individual interactions because they are either too small, or we can't separate them from all the other interactions...This is one of the main reasons why we don't have effective explanations in ecology, epidemiology, or economics. The new area of complexity theory pays a lot of attention to just these areas, searching for a better approach. Despite intense study of AIDS, we cannot confidently predict the number of people who will be infected in twenty years' time. Nobody knows how to predict stock-market crashes. There are no big areas of reductionist causality in social science or management studies. When we find an explanation that seems convincing, it always turns out that for every expert there is an equal and opposite expert who can convince us of the reverse story. Nobel prizes have been awarded to economists whose theories flatly contradict each other. (8)
Therefore, it is usual that imposing linear expectations on the agents within a nonlinear system will backfire in the form of unintended consequences caused by those slippery interactions.
The neverending consequences of these interactions led Robert Jervis to explore the nature of these unintended results in diplomacy and security policy in his Complex Systems: The Role of Interactions (9), which is found in the Appendix. Jervis, who is an Adlai E. Stevenson professor of international affairs at Columbia University, writes:
- We can never do merely one thing. Wishing to kill insects, we may put an end to the singing of birds. Wishing to 'get there' faster we insult our lungs with smog. Seeking to protect the environment by developing non-polluting sources of electric power, we build windmills that kill hawks and eagles that fly into the blades; cleaning the water in our harbors allows the growth of mollusks and crustaceans that destroy wooden piers and bulkheads; adding redundant safety equipment make some accidents less likely, but increases the chances of others due to the operators' greater confidence and the interaction effects among the devices; placing a spy in the adversary's camp not only gains valuable information, but leaves the actor vulnerable to deception if the spy is discovered; eliminating rinderpest in East Africa paved the way for canine distemper in lions because it permitted the accumulation of cattle, which required dogs to herd them, dogs which provided a steady source for the virus that could spread to lions; releasing fewer fine particles and chemicals into the atmosphere decreases pollution but also is likely to accelerate global warming; pesticides often destroy the crops that they are designed to save by killing the pests' predators; removing older and dead trees from forests leads to insect epidemics and an altered pattern of regrowth; allowing the sale of an anti-baldness medicine without a prescription may be dangerous because people no longer have to see a doctor, who in some cases would have determined that the loss of hair was a symptom of a more serious problem; flying small formations of planes over Hiroshima to practice dropping the atomic bomb accustomed the population to air raid warnings that turned out to be false alarms, thereby reducing the number of people who took cover on August 6.
Additionally, Jervis further identifies these interactions as one of three unique types that lead to unintended consequences, and relate directly to our understanding of the nature of complexity and national security:
- Interactions in Which the Results Cannot be Predicted From the Separate Actions
- The effect of one variable frequently depends on the state of another, as we often see in everyday life: each of two chemicals alone may be harmless but exposure to both could be fatal; patients have suffered from taking combinations of medicines that individually are helpful. So research tries to test for interaction effects and much of modern social science is built on the understanding that social and political outcomes are not simple aggregations of the actors' preferences because very different results are possible depending on how choices are structured and how actors move strategically.
- Interactions in Which Strategies Depend On the Strategies of Others
- Further complexities are introduced when we look at the interactions that occur between strategies when actors consciously react to others and anticipate what they think others will do. Obvious examples are provided by many diplomatic and military surprises: a state believes that the obstacles to a course of action are so great that the adversary could not undertake it; the state therefore does little to block or prepare for that action; the adversary therefore works especially hard to see if he can make it succeed. As an 18th century general explained, "In war it is precisely the things which are thought impossible which most often succeed, when they are well conducted." In the war in Vietnam, the US Air Force missed this dynamic and stopped patrolling sections of the North's supply lines when reconnaissance revealed that the number of targets had greatly diminished: after the attacks ceased the enemy resumed use of the route.
- Interactions in Which Behavior Changes the Environment
- Initial behaviors and outcomes often influence later ones, producing powerful dynamics that explain change over time and that cannot be captured by labeling one set of elements "causes" and other "effects." Although learning and thinking play a large role in political and social life, they are not necessary for this kind of temporal interaction. Indeed, it characterizes the operation of evolution in nature. We usually think of individuals and species competing with one another within the environment, thus driving evolution through natural selection. In fact, however, there is coevolution: plants and animals not only adapt to the environment, they change it. As a result, it becomes more hospitable to some life forms and less hospitable to others.
The challenge for security policy and military affairs, arising from the unintended consequences of interactions, lies in rethinking "ends and means" as we conventionally linearly view them. We must take these identified interaction types consciously into account.
One of the best examples of what happens when linearity meets nonlinearity in this century took place in Vietnam, and is described in the excerpt of the chapter of Martin L. Van Creveld's book, Command in War (10) in the appendix. During Vietnam, the United States was led by perhaps the most linear leadership in its history. Van Creveld illustrates the shortcomings of linear reductionism in warfare-especially the imperative to control, through quantification and centralization-and the susceptibility to the thrall of technology that marked the war. Van Creveld's observations on the use of statistics are especially pertinent to our discussion of the effects of interactions within systems.
- Since the patterns that form the objective of statistical analysis only become visible at fairly high levels in the hierarchy (further down, the figures are by definition meaningless), reliance on such analysis is itself a contribution toward centralization and the information pathologies of which centralization can be a cause. Statistics may have been the only way to handle the flood of incoming messages-running, at the Pentagon level, into the hundreds of thousands per day-but in the process, statistics reduced the content of those messages to the lowest common denominator. Finally, statistics constitute one of the most abstract forms of information known to man; although they can possibly present a good picture of a whole phenomenon the relevance of any given set of figures to this or that particular event at this or that particular place may well be next to zero.
There are severe limits to linearity's promise of control, even to those who faithfully practice its arts and follow its form. Linear reductionism will not be succeeded, but will be combined with nonlinear reductionism to form a more robust, versatile, and effective means, not to control, but to cope. The fiction of control will go down hard, while the considerable virtues of coping will just have to be learned to be appreciated.
| Coping with the Bounds Index | Foreword | Acknowledgments | Introduction | Part One Introduction | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Part Two Introduction | Chapter 5 | Chapter 6 | Chapter 7 | Chapter 8 | Chapter 9 | Chapter 10 | Conclusion | Appendix 1 | Appendix 2 | Appendix 3 | Appendix 4 | Appendix 5 | Appendix 6 | Notes |