- When dealing with any nonlinear system, especially a complex one, it is not sufficient to think of the system in terms of parts or aspects identified in advance, then to analyze those parts or aspects separately, and finally to combine those analyses in an attempt to describe the entire system. Such an approach is not, by itself, a successful way to understand the behavior of the system. In this sense there is truth in the old adage that the whole is more than the sum of its parts...It is of crucial importance that we learn to supplement those specialized studies with what I call a crude look at the whole.
Murray Gell-Mann, Nobel Laureate
I resort to a whole, in importance, yet stunted, in length, chapter in order to emphasize the following point. Linear reductionism, as Tools of Analysis, alone is not sufficient to cope with today's and tomorrow's problems, just as it was not capable of solving all of yesterday's. Nor are nonlinear techniques in the form of Aids to Learning alone sufficient. Instead, we require an approach which calls for intertwining or meshing both linear and nonlinear reductionist techniques; that is, "tools of analysis" for linear techniques, blending to "aids to learning" for nonlinear approaches, depending on the environment involved. Further, linear subsystems might be connected in nonlinear ways, just as nonlinear subsystems might be interlinked in linear ways. There are these places where the use of appropriate techniques will have merit. Often we need a synthesis. One must become ambidextrous-a switch-hitter.
Of importance to this notional continuum of linear and nonlinear techniques is the idea of the "80/20" rule. It is widely accepted, not just in Western culture, but most if not all cultures, that typically the first part of an endeavor or task is relatively easy. It then gets progressively more difficult, and toward the end, gets hard to do. In fact, it is so common that it has not only been codified into a saying, but quantified-the 80/20 rule. For example, software developers routinely establish as a rule of thumb budgets and schedules which allocate 20 percent of the dollars and time to the first 80 percent of the project, and the remainder to the last fifth. Why? Because time and time again, from generation to generation, the phenomenon has persisted, whether in a blacksmith shop or a national central bank trying to control inflation.
Suppose that all that accumulated experience and wisdom tells us something with enough confidence to take a stab at pinning it down. If we measure the generalized playing field of complexity, we find that the "80 yard line" is located just beyond the second bifurcation point. See Figure 4.1.
We could postulate this to be the effective limit of linear reductionist techniques, which also marks the boundary of mild nonlinearity. After that point, Aids to Learning come into play because Tools of Analysis lose their power, especially to provide "good enough" internal models for complex adaptive systems (cas). In terms of bifurcation points, this is only halfway through the Period-Doubling Cascade. Further, we might assume that Aids to Learning can be a useful supplement, or substitute, even earlier. This would also tell the practitioner that when the system becomes sensitive to more than two ranges, oscillations, or feedbacks, when the environment begins to cloud judgment with more than two effective possibilities, that the commander or manager would go into "nonlinear mode," bringing to bear Aids to Learning in order to persevere.
Today's economy must be viewed as the situation requires-linearly, nonlinearly, and sometimes something in between. It therefore provides reinforcement for the argument that the meshing of Tools of Analysis and Aids to Learning is necessary in order to be effective, to succeed, or to subdue.
Many of you will vaguely remember the principle of diminishing returns from your Economics 101 course long ago. Basically, the gist went something like this: A farmer gets into peanuts early and starts to make a killing. But this is noticed by other farmers and they switch to peanuts, too, thereby increasing the supply and driving down prices. The farmer tries expanding, but the price of land increases, and sooner or later, he finds that he or she reaches a point where diminishing returns makes it senseless to increase production because it does not pay, and equilibrium sets in. That is classical economics and it is linear, caused by negative feedback.
Now consider a piece of software, say something called a web browser. The first copy may cost $1 million to develop, but the second and ensuing copies go for 99 cents to cover the cost of the floppy disk, packaging, advertising, and shipping and handling. But the developer is smart enough to give it away free, in order to establish a user base large enough to create a de facto standard, thereby creating "early lock-in." The strategy is to make money off of upgrades and bundled features. Essentially, you have increasing returns, because each unit of increased production faces none of the perils faced by the peanut farmer. Welcome to the world of nonlinear economics caused by positive feedback. The result is that the economy, as a whole, is becoming differentiated:
- Mechanisms of increasing returns exist alongside those of diminishing returns in all industries. But roughly speaking, diminishing returns hold sway in the traditional part of the economy-the processing industries. Increasing returns reign in the newer part-the knowledge-based industries. Modern economies have therefore bifurcated into two inter-related worlds of business corresponding to the two types of returns. The two worlds have different economics. They differ in behavior, style, and culture. They call for different management techniques, strategies, and codes of government regulation....Where do service industries such as insurance, restaurants, and banking fit in?...It would appear that such industries belong to the diminishing returns, processing part of the economy. . . [But] (t)hese industries, too, are subject to mild increasing returns. . . .In fact, the increasing returns character of service industries is steadily strengthening, One of the marks of our time is that in services....processing insurance claims, supplying and inventorying in retail, conducting paralegal searches for case precedents-are increasingly being handled by software....Services belong to both the processing and the increasing returns world. But their center of gravity is crossing over to the latter. (1)
The concept of increasing returns is the work of W. Brian Arthur of Stanford and the complexity theory think-tank, the Santa Fe Institute, who has again been passed over for the Nobel Prize. This year it went to a pair of individuals for devising stock market derivatives, of all things. The continuing anti-trust action by the Justice Department against Microsoft is to a great extent based on increasing returns. It is ironic that there is now case law based on nonlinearity, while its applications remain largely unrecognized in other realms. It is almost enough to make one say something nice about lawyers!
To recapitulate, the "meshing" framework for the economy looks like this:
Having now made my plea that both linear and nonlinear techniques are vital, and need to be used together, we can move on to the next section, where we will examine each of the six Aids to Learning individually. Of necessity, both their composition and application are still incomplete. While the Metaphor and Van Creveld's Rule are well tested, all remain in stages of development. Paradoxically, even when fully developed, each will remain, in Murray Gell-Mann's term, a "crude look at the whole," for that is what nonlinearity both requires and prizes.
| 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 |