## Bill McKelvey.org

## Publications

#### Complexity/Order - Creation Science

**Complexity/Order Home**- Papers
- Selected Bibliography

There is no doubt that Stewart Kauffman’s book, The Origins of Order, has profoundly influenced me. Papers 2, 8, 10, 11, 16, and 22 are quite Kauffmanesque. I translate Kauffman’s NK model of coevolutionary complexity into an organizational context by using value chain competencies as “parts” of firms. ‘Multilevel coevolutionary complexity’ is a function of the extent complexity plays a part in the nature and fitness of coevolutionary interdependencies (1) among parts within a firm; and (2) between the parts of a firm and the parts of its opponents. In this conceptualization, “parts” are further reduced to discrete random behavioral events, each of which is governed by a ‘microagent’. This approach substitutes stochastic nonlinear numerical simulation models in place of the linear deterministic event history models and case studies heretofore used to study coevolution (for more detail on managing coevolution see paper # 24). Specifically, my translation of questions bearing on organizational complexity to fit Kauffman’s simulation models appears to be a useful alternative for exploring such questions as: (1) What intrafirm levels of integrative complexity affect competitive advantage? (2) What levels of integrative complexity influence how rapidly firms in coevolutionary groups reach equilibrium fitness levels, if they do so? (3) What complexity factors might affect competitive advantage? and (4) What levels of integrative complexity might affect the overall adaptive success of firms comprising a coevolving system?

Kauffman’s theory does have some parallels with Burt’s structural holes theory and computer simulation studies of emergent behavior in social movements. Kauffman’s theory allows the interweaving of network sociology studies with Michael Porter’s coevolutionary pocket and value chain “unique activities” theories, the resource- and competence-based views, and multicoevolutionary views in organization science.

The world of complexity science scholarship seems to be divided into the European and American Schools. The European group consists of Prigogine, Haken, Nicolis, Cramer, Kaye, and Mainzer, among others. The American group consists largely of those associated with the Santa Fe Institute. While one could gloss over the differences, I think it is worth not doing so. Europeans emphasize critical values and phase transitions, drawing more from the physical sciences. Americans emphasize coevolution, complexity cascades, and power laws, drawing more from the life and social sciences.

Certainly, a part of the “separation” is due to differing interpretations of the role of the 2nd Law of Thermodynamics. Prigogine quotes Max Born as saying, “irreversibility is the effect of the introduction of ignorance into the basic laws of physics” and he quotes Gell-Mann as essentially saying the same thing. Prigogine’s entire body of work over 50 years is based on irreversibility and Eddington’s “arrow of time.” Phase transitions are significant events that occur at the 1st critical value, Rc1, of R, the fluid dynamicists’ Reynolds number. Further, it is clear that phase transitions, especially at Rc1, (the Rayleigh number) are fundamental in the European view. Phase transitions are, thus, dramatic events, far removed from the chaos theorists’ minute, random “butterfly” effects (that set off “self-organized criticality” and complexity cascades), and strange attractors.

The Europeans typically begin with Bénard cells. In a Bénard process, “critical values” in the energy differential (measured as a change in temperature) between warmer and cooler surfaces of a container affect the velocity, R, of the fluid flow, which correlates with the change in temperature. For example, if the surfaces of the container represent the hot surface of the earth and the cold upper atmosphere, the critical values divide the velocity of airflow in the atmosphere into three kinds:

- Below Rc1 heat transfer occurs via conduction—gas molecules transfer energy by vibrating more vigorously against each other while remaining essentially in the same place;
- Between Rc1 and the 2nd critical value, Rc2, heat transfer occurs via a bulk movement of air in which the gas molecules move between the earth’s surface and the upper atmosphere in a circulatory pattern—the emergent Bénard cells appear as storm cells. We encounter these in aircraft as up- and down-drafts; and
- Above Rc2 a transition to chaotically moving gas molecules is observed—we see tornadoes periodically appearing and disappearing.

Since Bénard’s doctoral dissertation, published in 1901, fluid dynamicists’ have focused on Rc1, that separates laminar from turbulent flows. Below Rc1 viscous damping dominates so self-organized emergent (new) order does not occur; above Rc1 a number emergent inertial fluid motion dynamics occur. Ashby, in his book, Design for a Brain, describes functions that, after a certain critical value is reached, jump into a new family of differential equations, or as Prigogine would put it, jump from one family of “Newtonian” linear differential equations describing a dissipative structure to another family. Lorenz, followed by complexity scientists, added the second critical value, Rc2. This one separates the region of emergent complexity from deterministic chaos—the so-called “edge of chaos.” Together, the 1st and 2nd critical values define three kinds of complexity. These perspectives are detailed in papers 11, 20, and 22.

Since Bénard’s doctoral dissertation, published in 1901, fluid dynamicists’ have focused on Rc1, that separates laminar from turbulent flows. Below Rc1 viscous damping dominates so self-organized emergent (new) order does not occur; above Rc1 a number emergent inertial fluid motion dynamics occur. Ashby, in his book, Design for a Brain, describes functions that, after a certain critical value is reached, jump into a new family of differential equations, or as Prigogine would put it, jump from one family of “Newtonian” linear differential equations describing a dissipative structure to another family. Lorenz, followed by complexity scientists, added the second critical value, Rc2. This one separates the region of emergent complexity from deterministic chaos—the so-called “edge of chaos.” Together, the 1st and 2nd critical values define three kinds of complexity. These perspectives are detailed in papers 11, 20, and 22.

The Europeans seem to focus mostly on phase transitions at Rc1—the lower bound of the region of emergence complexity. American complexity scientists, in contrast, focus mostly on Rc2—the “edge of chaos.” What happens at Rc1 is better understood; what happens at Rc2 is more obscure. The “edge of chaos” is clearly a Santa Fe reference point, though now in disrepute.

What sets off bursts of order-creation via coevolution? The American complexity literature focuses on coevolution, power laws, and small instigating effects. Gleick details chaos theory and its focus on the so-called—very small indeed—butterfly effect (the fabled story of a butterfly, flapping its wings in Brazil, causing a storm in North America), ever since the founding paper by Lorenz. Bak reports on his discovery self-organized criticality—a power law event—in which small initial events can lead to complexity cascades of avalanche proportions. Arthur focuses on positive feedbacks stemming from initially small economic instigation events. Casti and Brock continue the focus on power laws. The rest of the Santa Fe story is told in Lewin’s book, Complexity: Life at the Edge of Chaos. In the Santa Fe vision, coevolution is the “engine” of complex system adaptation. I detail problems coevolutionary dynamics pose for managers in paper #24.

More specifically, managers need to figure out how to increase the rate of efficaciously adaptive coevolutions in their firms. The Red Queen race can be won only by speeding up coevolutionary processes. How?

- Managers can begin this process by focusing on the adaptive tension drivers—tensions highlighted by Jack Welch’s famous phrase, “Be #1 or 2 in market share in your industry or you will be fixed, sold, or closed,” and then decomposing it so that its effect extends down and through out a firm;
- Managers need to focus on creating the agent-level conditions that foster emergent self-organizing behaviors—the basic elements of coevolution events;
- Managers need to realize that they can originate, focus on, emphasize, select, and control only some of the tensions apt to set off coevolution events—once conditions are created to foster the nonlinear results of coevolution, the second part of the problem begins, to wit, the need for managing damping mechanisms. Since coevolutions pop up like weeds, this is a never-ending process!

I identify twelve kinds of damping mechanisms:

- Loss of Agent Heterogeneity
- Loss of Weak-tie Fields
- Failing Human Capital (Nodes)
- Senescence Due to Longevity
- Growing Complexity Catastrophe
- Loss of Coupled Dancing
- Separation from Contextual Drivers
- Disconnection from Adaptive Tension and Critical Values
- Corrupted Weak-tie Fields
- Boiled Frog Effects
- Self-organized Micro Defenses Against Coevolution
- Coevolution of Macro Driven Micro Defenses

The behaviors underlying some of these damping mechanisms have been well known since the early days of management and sociological research. Complexity scientists have more recently highlighted others. Any attempt to manage by becoming more aware of coevolutionary processes requires an immediate attention to what kinds of damping mechanisms are prevalent, what kinds of tensions are energizing them, and what coevolutionary processes they are aimed at inhibiting.