Complexity and contingency

One of the more intriguing currents of social science research today is the field of complexity theory. Scientists like John Holland (Complexity: A Very Short Introduction), John Miller and Scott Page (Complex Adaptive Systems: An Introduction to Computational Models of Social Life), and Joshua Epstein (Generative Social Science: Studies in Agent-Based Computational Modeling) make bold and interesting claims about how social processes embody the intricate interconnectedness of complex systems.

John Holland describes some of the features of behavior of complex systems in these terms in Complexity:

  • self-organization into patterns, as occurs with flocks of birds or schools of fish  
  • chaotic behaviour where small changes in initial conditions (‘ the flapping of a butterfly’s wings in Argentina’) produce large later changes (‘ a hurricane in the Caribbean’)  
  • ‘fat-tailed’ behaviour, where rare events (e.g. mass extinctions and market crashes) occur much more often than would be predicted by a normal (bell-curve) distribution  
  • adaptive interaction, where interacting agents (as in markets or the Prisoner’s Dilemma) modify their strategies in diverse ways as experience accumulates. (p. 5)

In CAS the elements are adaptive agents, so the elements themselves change as the agents adapt. The analysis of such systems becomes much more difficult. In particular, the changing interactions between adaptive agents are not simply additive. This non-linearity rules out the direct use of PDEs in most cases (most of the well-developed parts of mathematics, including the theory of PDEs, are based on assumptions of additivity). (p. 11)

Miller and Page put the point this way:

One of the most powerful tools arising from complex systems research is a set of computational techniques that allow a much wider range of models to be explored. With these tools, any number of heterogeneous agents can interact in a dynamic environment subject to the limits of time and space. Having the ability to investigate new theoretical worlds obviously does not imply any kind of scientific necessity or validity— these must be earned by carefully considering the ability of the new models to help us understand and predict the questions that we hold most dear. (Complex Adaptive Systems, kl 199)

Much of the focus of complex systems is on how systems of interacting agents can lead to emergent phenomena. Unfortunately, emergence is one of those complex systems ideas that exists in a well-trodden, but relatively untracked, bog of discussion. The usual notion put forth underlying emergence is that individual, localized behavior aggregates into global behavior that is, in some sense, disconnected from its origins. Such a disconnection implies that, within limits, the details of the local behavior do not matter to the aggregate outcome. Clearly such notions are important when considering the decentralized systems that are key to the study of complex systems. Here we discuss emergence from both an intuitive and a theoretical perspective. 

(Complex Adaptive Systems, kl 832)

As discussed previously, we have access to some useful “emergence” theorems for systems that display disorganized complexity. However, to fully understand emergence, we need to go beyond these disorganized systems with their interrelated, helter-skelter agents and begin to develop theories for those systems that entail organized complexity. Under organized complexity, the relationships among the agents are such that through various feedbacks and structural contingencies, agent variations no longer cancel one another out but, rather, become reinforcing. In such a world, we leave the realm of the Law of Large Numbers and instead embark down paths unknown. While we have ample evidence, both empirical and experimental, that under organized complexity, systems can exhibit aggregate properties that are not directly tied to agent details, a sound theoretical foothold from which to leverage this observation is only now being constructed. 

(Complex Adaptive Systems, kl 987)

And here is Joshua Epstein’s description of what he calls “generative social science”:

The agent-based computational model— or artificial society— is a new scientific instrument. 1 It can powerfully advance a distinctive approach to social science, one for which the term “generative” seems appropriate. I will discuss this term more fully below, but in a strong form, the central idea is this: To the generativist, explaining the emergence2 of macroscopic societal regularities, such as norms or price equilibria, requires that one answer the following question:  

The Generativist’s Question 

*     How could the decentralized local interactions of heterogeneous autonomous agents generate the given regularity?  

The agent-based computational model is well-suited to the study of this question since the following features are characteristics. (5)

Here Epstein refers to the characteristics of heterogeneity of actors, autonomy, explicit space, local interactions, and bounded rationality. And he believes that it is both possible and mandatory to show how higher-level social characteristics emerge from the rule-governed interactions of the agents at a lower level.
 
There are differences across these approaches. But generally these authors bring together two rather different ideas — the curious unpredictability of even fairly small interconnected systems familiar from chaos theory, and the idea that there are simple higher level patterns that can be discovered and explained based on the turbulent behavior of the constituents. And they believe that it is possible to construct simulation models that allow us to trace out the interactions and complexities that constitute social systems.

So does complexity science create a basis for a general theory of society? And does it provide a basis for understanding the features of contingency, heterogeneity, and plasticity that I have emphasized throughout? I think these questions eventually lead to “no” on both counts.

Start with the fact of social contingency. Complexity models often give rise to remarkable and unexpected outcomes and patterns. Does this mean that complexity science demonstrates the origin of contingency in social outcomes? By no means; in fact, the opposite is true. The outcomes demonstrated by complexity models are in fact no more than computational derivations of the consequences of the premises of these models. So the surprises created by complex systems models only appear contingent; in fact they are generated by the properties of the constituents. So the surprises produced by complexity science are simulacra of contingency, not the real thing.

Second, what about heterogeneity? Does complexity science illustrate or explain the heterogeneity of social things? Not particularly. The heterogeneity of social things — organizations, value systems, technical practices — does not derive from complex system effects; it derives from the fact of individual actor interventions and contingent exogenous influences.

Finally, consider the feature of plasticity — the fact that social entities can “morph” over time into substantially different structures and functions. Does complexity theory explain the feature of social plasticity? It does not. This is simply another consequence of the substrate of the social world itself: the fact that social structures and forces are constituted by the actors that make them up. This is not a systems characteristic, but rather a reflection of the looseness of social interaction. The linkages within a social system are weak and fragile, and the resulting structures can take many forms, and are subject to change over time.

The tools of simulation and modeling that complexity theorists are in the process of developing are valuable contributions, and they need to be included in the toolbox. However, they do not constitute the basis of a complete and comprehensive methodology for understanding society. Moreover, there are important examples of social phenomena that are not at all amenable to treatment with these tools.

This leads to a fairly obvious conclusion, and one that I believe complexity theorists would accept: that complexity theories and the models they have given rise to are a valuable contribution; but they are only a partial answer to the question, how does the social world work?

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Designing and managing large technologies

What is involved in designing, implementing, coordinating, and managing the deployment of a large new technology system in a real social, political, and organizational environment? Here I am thinking of projects like the development of the SAGE early warning system, the Affordable Care Act, or the introduction of nuclear power into the civilian power industry.

Tom Hughes described several such projects in Rescuing Prometheus: Four Monumental Projects That Changed the Modern World. Here is how he describes his focus in that book:

Telling the story of this ongoing creation since 1945 carries us into a human-built world far more complex than that populated earlier by heroic inventors such as Thomas Edison and by firms such as the Ford Motor Company. Post-World War II cultural history of technology and science introduces us to system builders and the military-industrial-university complex. Our focus will be on massive research and development projects rather than on the invention and development of individual machines, devices, and processes. In short, we shall be dealing with collective creative endeavors that have produced the communications, information, transportation, and defense systems that structure our world and shape the way we live our lives. (kl 76)

The emphasis here is on size, complexity, and multi-dimensionality. The projects that Hughes describes include the SAGE air defense system, the Atlas ICBM, Boston’s Central Artery/Tunnel project, and the development of ARPANET. Here is an encapsulated description of the SAGE process:

The history of the SAGE Project contains a number of features that became commonplace in the development of large-scale technologies. Transdisciplinary committees, summer study groups, mission-oriented laboratories, government agencies, private corporations, and systems-engineering organizations were involved in the creation of SAGE. More than providing an example of system building from heterogeneous technical and organizational components, the project showed the world how a digital computer could function as a real-time information-processing center for a complex command and control system. SAGE demonstrated that computers could be more than arithmetic calculators, that they could function as automated control centers for industrial as well as military processes. (kl 285)

Mega-projects like these require coordinated efforts in multiple areas — technical and engineering challenges, business and financial issues, regulatory issues, and numerous other areas where innovation, discovery, and implementation are required. In order to be successful, the organization needs to make realistic judgments about questions for which there can be no certainty — the future development of technology, the needs and preferences of future businesses and consumers, and the pricing structure that will exist for the goods and services of the industry in the future. And because circumstances change over time, the process needs to be able to adapt to important new elements in the planning environment.

There are multiple dimensions of projects like these. There is the problem of establishing the fundamental specifications of the project — capacity, quality, functionality. There is the problem of coordinating the efforts of a very large team of geographically dispersed scientists and engineers, whose work is deployed across various parts of the problem. There is the problem of fitting the cost and scope of the project into the budgetary envelope that exists for it. And there is the problem of adapting to changing circumstances during the period of development and implementation — new technology choices, new economic circumstances, significant changes in demand or social need for the product, large shifts in the costs of inputs into the technology. Obstacles in any of these diverse areas can lead to impairment or failure of the project.

Most of the cases mentioned here involve engineering projects sponsored by the government or the military. And the complexities of these cases are instructive. But there are equally complex cases that are implemented in a private corporate environment — for example, the development of next-generation space vehicles by SpaceX. And the same issues of planning, coordination, and oversight arise in the private sector as well.

The most obvious thing to note in projects like these — and many other contemporary projects of similar scope — is that they require large teams of people with widely different areas of expertise and an ability to collaborate across disciplines. So a key part of leadership and management is to solve the problem of securing coordination around an overall plan across the numerous groups; updating plans in face of changing circumstances; and ensuring that the work products of the several groups are compatible with each other. Moreover, there is the perennial challenge of creating arrangements and incentives in the work environment — laboratory, design office, budget division, logistics planning — that stimulate the participants to high-level creativity and achievement.

This topic is of interest for practical reasons — as a society we need to be confident in the effectiveness and responsiveness of the planning and development that goes into large projects like these. But it is also of interest for a deeper reason: the challenge of attributing rational planning and action to a very large and distributed organization at all. When an individual scientist or engineer leads a laboratory focused on a particular set of research problems, it is possible for that individual (with assistance from the program and lab managers hired for the effort) to keep the important scientific and logistical details in mind. It is an individual effort. But the projects described here are sufficiently complex that there is no individual leader who has the whole plan in mind. Instead, the “organizational intentionality” is embodied in the working committees, communications processes, and assessment mechanisms that have been established.

It is interesting to consider how students, both undergraduate and graduate, can come to have a better appreciation of the organizational challenges raised by large projects like these. Almost by definition, study of these problem areas in a traditional university curriculum proceeds from the point of view of a specialized discipline — accounting, electrical engineering, environmental policy. But the view provided from a discipline is insufficient to give the student a rich understanding of the complexity of the real-world problems associated with projects like these. It is tempting to think that advanced courses for engineering and management students could be devised making extensive use of detailed case studies as well as simulation tools that would allow students to gain a more adequate understanding of what is needed to organize and implement a large new system. And interestingly enough, this is a place where the skills of humanists and social scientists are perhaps even more essential than the expertise of technology and management specialists. Historians and sociologists have a great deal to add to a student’s understanding of these complex, messy processes.

Critical points in history and social media

Recent posts have grappled with the interesting topic of phase transitions in physics (link, link, link). One reason for being interested in this topic is its possible relevance to the social world, where abrupt changes of state in the social plenum are rare but known occurrences. The eruption of protest in numerous countries across the Middle East and North Africa during the Arab Spring is one example. Essentially we can describe these incidents as moments when ordinary citizens are transformed from quiescent members of civil society, pursuing their private lives as best they can, to engaged activists assembling at great risk in large demonstrations. Is this an example of a phase transition? And are there observable indicators that might allow researchers to explain and sometimes anticipate such critical points?

There is a great deal of interesting research underway on these topics in the field of complex systems and communications theory. The processes and phenomena that researchers are identifying appear to have a great deal of importance both for understanding current social dynamics and potentially for changing undesirable outcomes.

Researchers on the dynamics of mass social media have addressed the question of critical transitions. Kuehn, Martens, and Romero (2014) provide an interesting approach in their article, “Critical transitions in social network activity” (link). Also of interest is Daniel Romero’s “An epidemiological approach to the spread of political third parties”, co-authored with Christopher Kribs-Zaleta, Anuj Mubayi, and Clara Orbe (link).

Here is the abstract for “Critical transitions”:

A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the dynamical state of the system abruptly changes. For exam- ple, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that detectable warning signs may precede some of these drastic events. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether such stochastic scaling laws used as warning signs for a priori unknown events in society are present in social networks is an exciting open problem, to which at present only highly speculative answers can be given. Here, we instead provide a first step towards tackling a simpler question by focusing on a priori known events and analyse a social media data set with a focus on classical variance and autocorrelation warning signs. Our results thus pertain to one absolutely fundamental question: Can the stochastic warning signs known from other areas also be detected in large-scale social media data? We answer this question affirmatively as we find that several a priori known events are preceded by variance and autocorrelation growth. Our findings thus clearly establish the necessary starting point to further investigate the relationship between abstract mathematical theory and various classes of critical transitions in social networks.

They use the idea of a tipping point rather than a phase transition, but there seems to be an important parallel between the two ideas. (Here are a few prior posts on continuity and tipping points; link, link.) Here is they define the idea of a critical transition: “A critical transition may informally be defined as a rapid and drastic change of a time-dependent dynamical system” (2). The warning signs they consider are formal and statistical rather than substantive: increasing variance and rising auto-correlation:

Two of the most classical warning signs are rising variance and rising auto-correlation before a critical transition [10,28]. The theory behind these warning signs is described in more detail in Appendix A. The basic idea is that if a drastic change is induced by a critical (bifurcation) point, then the underlying deterministic dynamics becomes less stable. Hence, the noisy fluctuations become more dominant as the decay rate decreases close to the critical transition. As a result, (a) the variance in the signal increases, due to the stronger fluctuations and (b) the system’s state memory (i.e., auto-correlation) increases, due to smaller deterministic contraction onto a single state [10,11]. It can be shown that both warning signs are related via a suitable fluctuation–dissipation relation [29]. (2)

Below are the data they present showing statistical associations of hashtag frequencies for impending known events — Halloween, Thanksgiving, and Christmas. The X panels represent the word frequency of the hashtag; the V panels represent the variance, and R represents autocorrelation on the time series of word frequency.

It is plain from the graphs of these variables that the frequency, variance, and autocorrelation statistics for the relevant hashtags demonstrate a rising trend as they approach the event and fall off steeply following the event; so these statistics post-dict the event effectively. But of course there is no value in predicting the occurrence of Halloween based on the frequency of #halloween earlier in October; we know that October 31 will soon occur. The difficult research question posed here is whether it is possible to identify warning signs for unknown impending events. The authors do not yet have an answer to this question, but they offer a provocative hypothesis: “These time series illustrate that there is a variety of potentially novel dynamical behaviors in large-scale social networks near large spikes that deserve to be investigated in their own right.” (4). This suggests several questions for future investigation:

  • How do we define when a critical transition occurs in the data for an a priori unknown event? 
  • For a priori unknown events, is there a possibility to identify hashtags or other aspects of the message which allow us to determine the best warning sign? 
  • Can we link warning signs in social networks to a priori unknown critical transitions outside a social network? 
  • Which models of social networks can re-produce critical transitions observed in data? 
Also of interest for issues raised previously in Understanding Society is Romero, Kribs-Zaleta, Mubayi, and Orbe’s “An epidemiological approach to the spread of political third parties” (link). This paper is relevant to the topic of the role of organizations in the spread of social unrest considered earlier (link, link). Their paper uses the example of Green Party activism as an empirical case. Here is their abstract:

Abstract. Third political parties are influential in shaping American politics. In this work we study the spread of a third party ideology in a voting population where we assume that party members/activists are more influential in recruiting new third party voters than non-member third party voters. The study uses an epidemiological metaphor to develop a theoretical model with nonlinear ordinary differential equations as applied to a case study, the Green Party. Considering long-term behavior, we identify three threshold parameters in our model that describe the different possible scenarios for the political party and its spread. We also apply the model to the study of the Green Party’s growth using voting and registration data in six states and the District of Columbia to identify and explain trends over the past decade. Our system produces a backward bifurcation that helps identify conditions under which a sufficiently dedicated activist core can enable a third party to thrive, under conditions which would not normally allow it to arise. Our results explain the critical role activists play in sustaining grassroots movements under adverse conditions.

And here is the basic intuition underlying the analysis of this paper:

We use an epidemiological paradigm to translate third party emergence from a political phenomenon to a mathematical one where we assume that third parties grow in a similar manner as epidemics in a population. We take this approach following in the steps of previous theoretical studies that model social issues via such methods. The epidemiological metaphor is suggested by the assumption that individuals’ decisions are influenced by the collective peer pressure generated by others’ behavior; the “contacts” between these two groups’ ideas are analogous to the contact processes that drive the spread of infectious diseases. (2)

Their approach makes use of a system of differential equations to describe the behavior of the population as a whole based on specific assumptions. It would seem that the problem could be approached using an agent-based model as well. This paper is relevant to the general topic of critical points in social behavior as well, since it attempts to discover the conditions under which a social movement like third-party mobilization will accelerate rather than decay.

Also of interest to the topic of large dynamic social processes and social media is R. Kelly Garrett and Paul Resnick, “Resisting political fragmentation on the Internet” (link). Here is their abstract:

Abstract: Must the Internet promote political fragmentation? Although this is a possible outcome of personalized online news, we argue that other futures are possible and that thoughtful design could promote more socially desirable behavior. Research has shown that individuals crave opinion reinforcement more than they avoid exposure to diverse viewpoints and that, in many situations, hearing the other side is desirable. We suggest that, equipped with this knowledge, software designers ought to create tools that encourage and facilitate consumption of diverse news streams, making users, and society, better off. We propose several techniques to help achieve this goal. One approach focuses on making useful or intriguing opinion-challenges more accessible. The other centers on nudging people toward diversity by creating environments that accentuate its benefits. Advancing research in this area is critical in the face of increasingly partisan news media, and we believe these strategies can help.

This research too is highly relevant to the dynamic social processes through which largescale social changes occur, and particularly so in the current climate of fake news and deliberate political polarization.

(It is interesting that social media and the Internet come into this story in several different ways. Google employee and Egyptian activist Wael Ghonim played a central role in the early stages of activation of the uprisings in Cairo in 2011. His book, Revolution 2.0: The Power of the People Is Greater Than the People in Power: A Memoir, is a fascinating exposure to some of the details of these events, and the short book Wael Ghonim… Facebook and The Uprising in Egypt by Dhananjay Bijale specifically addresses the role that Ghonim and FaceBook played in the mobilization of ordinary young Egyptians.)

Systems management and the War on Poverty

 

One of the important developments in engineering and management thinking since World War II is the value of approaching large problems as systems rather than simply as a sum of separable components. Designing a ballpoint pen is very different from designing an aircraft or a fire control system; in the latter cases there are multiple functionalities and components that need to be incorporated, each associated with specific engineering and material disciplines. It was recognized during World War II that it is much more effective to treat the product and the design and manufacturing efforts as systems so that it is possible to conform components to synergistic and mutually supportive inter-relationships.

Agatha Hughes and Thomas Hughes organized a group of leading researchers to reflect upon the history of systems engineering and management, and the chief results are included in their 2000 volume, Systems, Experts, and Computers: The Systems Approach in Management and Engineering, World War II and After. The contributors include experts (and participants) in the history of the development of complex military systems during World War II — for example, radar-controlled fire control systems for anti-aircraft use (David Mindell); experts like Donald MacKenzie on the incorporation of computing into the control of complex technologies (for example, the pathbreaking SABRE system for airline reservations); and experts on expertise such as Gabrielle Hecht, who provides an essay on post-war French technology management.

Here is how Hughes and Hughes describe the systems approach in their introduction to the volume:

Practitioners and proponents embrace a holistic vision. They focus on the interconnections among subsystems and components, taking special note of the interfaces among the various parts. What is significant is that system builders include heterogeneous components, such as mechanical, electrical, and organizational parts, in a single system. Organizational parts might be managerial structures, such as a military command, or political entities, such as a government bureau. Organizational components not only interact with technical ones but often reflect their characteristics. For instance, a management organization for presiding over the development of an intercontinental missile system might be divided into divisions that mirror the parts of the missile being designed. (2)
Hughes and Hughes provide a narrative that is intended to show the origins of systems engineering in operations research during World War II, and in the rapid development of highly complex technology systems needed for weaponry during the war (automated fire control, for example). In their telling of the story, the development of the digital computer during and after the war was a critical component of the development of the systems approach and the increasingly complex technologies and systems that the approach stewarded into existence. (See earlier posts on the development of ENIAC; linklink.) Much of this research took place within government and military organizations such as OSRD (Office of Scientific Research and Development); but private companies like RAND and MITRE soon emerged to take on contracts from military agencies for large-scale systems projects (5). And the research and development process itself came to be treated as a “system”, with new software developed to support project planning and management. One important example was the PERT (Program Evaluation Review Technique) software system, developed by Booz, Allen & Hamilton (10).

Of particular interest here is the light the volume sheds on the efforts by the Johnson administration to apply systems thinking to the large social problems the country faced in the early 1960s, including especially poverty and urban problems (16) (link). David Jardini’s essay “Out of the blue yonder: The transfer of systems thinking from the Pentagon to the Great Society, 1961-1965” explores this effort to transfer these systems methods to the social field. “[The chapter] argues that the construction and implementation of the Great Society social welfare programs and their analytical methods can be found at the core of Great Society policy making” (312). 
 
It emerges that a central political and policy disagreement that determined the course of events was a fundamental disagreement about centralization versus community involvement in social welfare policy. Policy leaders like Robert McNamara preferred to see the nation’s social welfare policies to be managed and monitored centrally; affected communities, on the other hand, wanted to have greater control over the programs that would affect them. These disagreements converged on the question of the role of CAPs (Community Action Program) in the implementation and management of policy initiatives on the ground. Should CAPs serve as effective venues for local opinions and demands, or should they be sidelined in favor of a more top-down administrative organization?

The first CAP program guide, for example, suggested that local organizations provide “meaningful opportunities for residents, either as individuals or in groups, to protest or to propose additions to or changes in the ways in which a Community Action Program is being planned or undertaken.” In fact, protest and confrontation were viewed by many CAP organizers as at least therapeutic means for the poor to vent their frustrations. (339)

But Johnson’s administration was not interested in providing a venue for community advocacy and protest, and quickly sought to find ways of managing social welfare programs to reduce the level of activism they stimulated. The solution was the extension of the PPB (Planning-Programming-Budgeting) model from defense systems administration to the Great Society. But, as Jardini observes, this hierarchical system of control is poorly adapted to the problem of designing and administering programs that affect vast groups of people who can see its effects and can have very different ideas about the appropriateness of the policies being conveyed. “In this sense, the DOD is a poor model for the democratic ideal many Americans hold for their government institutions” (341).

This example illustrates an important tension that runs through many of the essays in the volume concerning the political significance of systems engineering and management. The volume gives support to the idea that systems management is an expert-driven and non-democratic way of organizing complicated human activities. What Robert McNamara brought to Ford Motor Company and the Department of Defense was a hierarchical, analytical, expert-driven system of management that sought to replace decentralized decision-makers with an orderly process driven from the top. For some purposes this may be a reasonably effective way of organizing a large effort involving thousands of agents. But for purposes like social reform it has a fatal flaw; it makes it almost impossible to create the level of buy-in at the local level that will be crucial for the success of a large project.

(I remember asking Tom Hughes in 1999 or so what he thought about the massive “Big Dig” project in Boston, then approaching completion and affecting many neighborhoods and thousands of residents. He commented that he felt that we should not judge the success of the project on the basis of whether it came in under budget; in fact, he suggested that this would show that the project designers and managers had not done enough to modify and adapt the project to gain support from the communities that the project affected.)

Von Neumann on the brain


 
image: representation of a mammalian brain neural network 

After World War II John von Neumann became interested in the central nervous system as a computing organ. Ironically, more was probably known about neuroanatomy than about advanced digital computing in the 1940s; that situation has reversed, of course. Now we know a great deal about calculating, recognizing, searching, and estimating in silicon; but relatively less about how these kinds of processes work in the setting of the central nervous system. At the time of his final illness von Neumann was preparing a series of Silliman Lectures at Yale University that focused on the parallels that exist between the digital computer and the brain; these were published posthumously as The Computer and the Brain (CB) in 1958. This topic also comes in for substantial discussion in Theory Of Self Reproducing Automata (TSRA) (edited and published posthumously by Arthur Burks in 1966). It is very interesting to see how vB sought to analyze this problem on the basis of the kinds of information available to him in the 1950s.

Much of CB takes the form of a rapid summary of the state of knowledge about digital computing machines that existed in the 1950s, from Turing to ENIAC. Almost all computers today possess the “von Neumann” architecture along these lines.

Alan Turing provided some of the mathematical and logical foundations of modern digital computing (link). He hypothesized a very simple computing device that consisted of a tape of indefinite length, a  tape drive mechanism that permitted moving the tape forwards or backwards one space, and a read-write mechanism that could read the mark in a tape location or erase and re-write the mark in that location. Here is a diagram of a Turing machine:

 
(Fascinatingly, here is a photo of a working model of a Turing machine (link):)

 

 
Turing’s fundamental theorem is that any function that is computable at all is computable on a Turing machine; so a Turing machine is a universal computing machine. The von Neumann architecture and the computing machines that it spawned — ENIAC and its heirs — are implementations of a universal computing machine. 
 
From the time of Frege it has been understood that mathematical operations can be built up as compounds of several primitive operations — addition, subtraction, etc.; so, for example, multiplication can be defined in terms of a sequence of additions. Programming languages and libraries of subroutines take advantage of this basic logic: new functions are defined as series of more elementary operations embodied in machine states. As von Neumann puts the point in CB:

More specifically: any computing machine that is to solve a complex mathematical problem must be “programmed” for this task. This means that the complex operation of solving that problem must be replaced by a combination of the basic operations of the machine. Frequently it means something even more subtle: approximation of that operation—to any desired (prescribed) degree—by such combinations. (5)

Key questions about the capacities of a computing machine, either electro-mechanical or biological, have to do with estimating its dimensionality: how much space does it occupy, how much energy does it consume, and how much time does it take to complete a given calculation? And this is where vB’s analysis took its origin. Von Neumann sought to arrive at realistic estimates of the size and functionality of the components of these two kinds of computation machines. The differences in scale are enormous, whether we consider speed, volume, or energy consumption. Fundamentally, neurons are more numerous by orders of magnitude (10^10 versus 10^4); slower by orders of magnitude (5 msec vs. 10^-3 msec); less energy-intensive by orders of magnitude (10^-3 ergs vs.10^2 ergs); and computationally less precise by orders of magnitude. (Essentially he estimates that a neural circuit, either analog or digital, is capable of precision of only about 1%.) And yet von Neumann concludes that brains accomplish  computational problems faster than digital computers because of their massively parallel structure — in spite of the comparative slowness of the individual elements of computation (neurons). This implies that the brain embodies a structurally different architecture than sequential digital computing embodied in the von Neumann model.
 
Von Neumann takes the fundamental operator of the brain to be the neuron, and he represents the neuron as a digital device (in spite of its evident analog electrochemical properties). A neuron transmits a pulse. “The nervous pulses can clearly be viewed as (two-valued) markers…. The absence of a pulse then represents one value (say, the binary digit 0), and the presence of one represents the other (say, the binary digit 1)” (42). “The nervous system has a prima facie digital character” (44).
 
In their introduction to the second edition of CB the Churchlands summarize von Neumann’s conclusion somewhat differently by emphasizing the importance of the analog features of the brain: “If the brain is a digital computer with a von Neumann architecture, it is doomed to be a computational tortoise by comparison… [But] the brain is neither a tortoise nor a dunce after all, for it was never a serial, digital machine to begin with: it is a massively parallel analog machine” (kl 397). However, it appears to me that they overstate the importance of analog neural features in von Neumann’s account. Certainly vN acknowledges the analog electro-chemical features of neural activity; but I don’t find him making a strong statement in this book to the effect that analog features contribute to the better-than-expected computational performance of the brain. This seems to correspond more to a view of the Churchlands than to von Neumann’s analysis in the 1950s. Here is their view as expressed in “Could a Machine Think?” in Scientific American in 1990:

First, nervous systems are parallel machines, in the sense that signals are processed in millions of different pathways simultaneously. The retina, for example, presents its complex input to the brain not in chunks of eight, 16 or 32 elements, as in a desktop computer, but rather in the form of almost a million distinct signal elements arriving simultaneously at the target of the optic nerve (the lateral geniculate nucleus), there to be processed collectively, simultaneously and in one fell swoop. Second, the brain’s basic processing unit, the neuron, is comparatively simple. Furthermore, its response to incoming signals is analog, not digital, inasmuch as its output spiking frequency varies continuously with its input signals. Third, in the brain axons projecting from one neuronal population to another are often matched by axons returning from their target population. These descending or recurrent projections allow the brain to modulate the character of its sensory processing. (

link

, 35)

In considering the brain von Neumann reached several fundamental observations. First, the enormous neural network of the central nervous system is itself a universal computing machine. Von Neumann worked on the assumption that the CNS could be “programmed” to represent the fundamental operations of arithmetic and logic; and therefore it has all the power of a universal computational machine. But second, von Neumann believes his analysis demonstrates that its architecture is fundamentally different from the standard von Neumann architecture. This observation is the more fundamental. It derives from von Neumann’s estimates of the base speed rate of calculation available to neurons in comparison to vacuum tubes; a von Neumann machine with components of this time scale would take eons to complete the calculations that the brain performs routinely. And so this underlines the importance of the massively parallel computing that is accomplished by the biological neural network. Ironically, however, it has proven challenging to emulate massively parallel neural nets in digital computing environments; here is an interesting technical report by Paul Fox that identifies communication bandwidth as being the primary limiting factor for such emulations (link). 
 
(Tsutomu Miki explores some of these issues in Brainware : Bio-Inspired Architecture and Its Hardware Implementation.)

International relations and complexity theory

 

Hilton Root has published some very interesting ideas about systems thinking in international relations theory in Dynamics among Nations: The Evolution of Legitimacy and Development in Modern States. Here he offers an approach to social, political, and economic change through a set of ideas that are not yet strongly integrated into IR theory — the perspective of complexity theory, worked out in a clear and useable form.

The three sources of theoretical argument which he introduces — complexity theory, social network theory, and evolutionary ecology — represent a significant innovation in comparative history. The novel approach Root takes consists of three large ideas: that social systems at all levels display “adaptive complexity”; that the structure of the social networks (governance systems, information systems, economic inter-dependencies) that are embedded in a specific society have important and unexpected consequences for the behavior of the system; and that complex social developments have much in common with “landscape ecology”, by which he means that there are multiple next steps that can be taken at any point leading to an improvement of performance.

His fundamental claim is that communities, states, and international systems need to be understood as dynamic systems with emergent properties. A society is not simply the linear sum of the behaviors of its component systems.

The system of international relations, like most complex ecosystems, such as the nervous system or a rain forest, is yielding to its rules of complexity. In complex systems, a central administrator rarely guides the collective behaviors that characterize development processes. The system itself has a collective behavior that depends on all its parts. Rather than convergence toward a dominant model, or “global optimum,” the interactive dynamics are coevolutionary; their interactions result in reciprocal and evolving change. (2)

One consequence of these ideas is that international relations and economic and political development processes show substantial path dependency and contingency. Another consequence is that some leading metaphors for large-scale historical change are implausible and misleading: in particular, modernization theory, “uniqueness of the West,” and “end of history.” Finally, Root argues that we should expect substantial variation in the strategies and structures that nations choose, given their own geopolitical environments.

Competition in highly interdependent global environments produces far greater local variation and diversity of structures and strategies than modernization theory ever anticipated. (3)

The book uses numerous episodes from the political, military, and economic histories of Europe and Asia to illustrate and validate the approach he takes. As a particularly interesting example of this, Root interprets Napoleon’s decision to invade Russia, not as folly, but as an intuition of the nodal character of the traditional European state system (126 ff.). He also makes repeated use of periods in Chinese imperial history to illustrate his notion that system dynamics and the structure of the governance network create very powerful obstacles to innovation and change.

So what does Root mean by “complexity”? His central concept is that of a “complex interactive adaptive system” (CIAS) within a heterogeneous environment. Here is a useful description of international relations through the lens of CIAS theory.

A network is comprised of agents. The agents interact according to shared and evolving rules of behavior that in turn define the larger environment or system. That behavior generates continuous feedback loops that enable agents to learn and to adjust their behaviors to others’ actions, thereby re-creating the system in which they operate. Complex adaptive systems are created by interactions and communications of self-adjusting agents. Continuous “feedback” motivates agents to re-evaluate their positions. Because agents are constantly reacting to other agents’ behaviors, nothing in the environment is ever fixed or finite. In order to fully understand the impacts of these agents, their behaviors must be understood as they interact with the broader system. (16)

A key analytical idea the author brings forward repeatedly is the notion of “co-evolution”. This concept captures one important aspect of a complex interactive adaptive system. CIAS’s show two types of unpredictability. First, the mutual interactions of the parts lead to “chaotic” courses of development of the system, as A, B, and C interact to produce unexpected outcome D. But second, the “adaptive” part introduces another kind of indeterminacy, as organisms, actors, and institutions change their characteristics in face of changes in the environment. So the properties of A, B, and C are not fixed over time; rather, selection and purposive adaptation lead to organisms and actors who respond differently over time to ecological opportunities and threats.

Features of uncertainty, time framing, rule change, and novel behavior all contribute to a set of system characteristics: unpredictability, path dependency, and sensitivity to initial conditions. And Root believes that these factors have important implications about the feasibility of reducibility or micro- to macro- reconstruction:

When a state’s interactions shift from being locally based to being regionally or nationally based, its behaviors change across the network and the greater system. Thus a general theory of the system cannot be deduced from the properties of its constituent parts, just as the universe cannot be reconstructed from the fundamental laws of physics. (31)

Root’s treatment of “New Institutional Economics” in Chapter 5 is important for several reasons. Most important, he demonstrates the harm that comes from incorporating a questionable theory of change into a comprehensive agenda for policy. The guiding idea of “creating institutions of good governance” as a panacea for slow economic growth and widespread poverty led policy makers to ignore other important causal factors, including locally rational but myopic strategies pursued by sub-actors. Root seems to agree with Dani Rodrik in concluding that NIC is limited when it comes to serving as a guide for positive policy design:

Assessing the legacy of new institutional economics, Harvard economist Dani Rodrik concludes that beyond “a very aggregate level of generality,” these ideas do not provide much policy guidance. (81)

Instead of looking for a general theory that can be used by centralized planning ministries to guide their economic and social policies, Root favors a more evolutionary approach: allow for a diversity of development experiments at the middle level of society, and then favor those experiments that appear to have the best results.

Chinese planners never attained the celebrity status of their Indian peers, but by trying multiple paths and starting with smaller interventions from the top, they found a better way to determine what worked. After Deng declared the opening of the Chinese economy, he instituted a multi-level process that facilitated both change and stability, and strengthened social organization and social learning through local experimentation. (108-109)

(Contrast this with the “single experiment” approach associated with land collectivization in the 1950s, resulting in massive agricultural failure and famine during the Great Leap Forward.)

Root’s treatment of Imperial China’s history is intriguing but controvertible. His central premise is that China’s Imperial system was a hierarchical network of control, and systems like this are substantially less resilient and open to change than multi-nodal networks. The interpretation is reminiscent of the theory of Oriental despotism: an all-powerful imperial system suppressed both challengers and change-agents. But contemporary China historians would probably give the Imperial system more credit in terms of its degree of flexibility in face of challenges. Take peasant uprisings. The state was generally successful in its response to large peasant rebellions, even if the military response was often flat-footed. The Taiping Rebellion is an example that probably supports the author’s interpretation best, since it was local militias organized and funded by local gentry which were most successful in opposing the Taipings. But China’s history is littered with hundreds of peasant and ethnic uprisings, and its military eventually prevailed in most of them.

One way of reading Root’s book is as a guidebook for administrators in a time of complexity. Root correctly emphasizes the difficulty or impossibility of “solving” a set of social and political problems simultaneously, and the parallel difficulty of making confident predictions about medium- or long-term consequences of various policy interventions. Second best, in his account, is an evolutionary approach: try a diversity of approaches, and cautiously increase the volume of those approaches that seem to work best. But even this approach is uncertain; evolutionary processes lead to dead-ends that are unforeseen in earlier stages of the process.

(See this post about decision-making under conditions of deep uncertainty; link. And here is a series of earlier posts about social complexity; link.)

Simon on complexity

Herbert Simon’s The Sciences of the Artificial – 3rd Edition provided an alternative model for thinking about society. We can think of social institutions as partially designed and selected for their organizational properties; so they are different from proteins and planetary systems.  Simon is also an important contributor to the study of complexity. So his new chapter in the 1996 edition of the book, “Alternative Views of Complexity,” is worth reading carefully. Here is how he motivates this new chapter in SA:

The preceding chapters of this book have discussed several kinds of artificial systems. The examples we have examined — in particular, economic systems, the business firm, the human mind, sophisticated engineering designs, and social plans — range from the moderately to the exceedingly complex (not necessarily in the order in which I have just listed them). These final two chapters address the topic of complexity more generally, to see what light it casts on the structure and operation of these and other large systems that are prominent in our world today. (169)

It turns out that there isn’t much new in the 1996 chapter, however. In fact, most of its content is taken from his pathbreaking 1962 article, “The Architecture of Complexity” (link). The new chapter 7 and renumbered chapter 8 largely incorporate the content and sometimes the language of the 1962 article. And this is interesting, because it implies that Simon’s primary ideas about reduction, composition, and inter-level interactions were largely already formed in 1962.

There are a few ideas and themes that are new to the 1996 version. One is a more specific periodization of thinking about complexity theory in the twentieth century.  The 1996 version identifies three phases of theorizing about complexity and “whole systems”.

  1. Biological emergence theory (post World War I)
  2. Cybernetics and systems theory (post World War II)
  3. Contemporary complexity theory (post 1960s)

Simon is skeptical about the tendency towards irreducible holism that was associated with the earlier two phases of thinking in both versions; in the 1996 chapter he favors a “weak” interpretation of emergence: a commitment to …

… reductionism in principle even though it is not easy (often not even computationally feasible) to infer rigorously the properties of the whole from knowledge of the properties of the parts. In this pragmatic way, we can build nearly independent theories for each successive level of complexity, but at the same time, build bridging theories that show how each higher level can be accounted for in terms of the elements and relations of the next level down. (172)

This “pragmatic holism” is already contained in the 1962 version (link). So this doesn’t represent new ground in 1996. But Simon’s use of this idea to criticize several false starts in the field of complexity research is valuable.

Simon finds some of the central concepts of the third phase to be more promising for the study of social phenomena. The mathematics and physics of chaotic behavior (where simple low-level processes can aggregate to wildly variant higher-level outcomes), simulations of evolution through computational models (genetic algorithms), and the exploration of cellular autonoma (the game of life) all come in for favorable comments. (The Lorenz attractor illustrated here is a common example of chaotic behavior.)

One idea that is not contained in the 1962 version is that of causal non-linearity. Non-linearity is a problem for the “near decomposability” view that Simon wanted to take of complexity in the 1962 version, because it casts doubt on the ability to disentangle causal influences deriving from inter-connected subsystems. Small differences in initial conditions can lead to large differences in outcome. This is a key aspect of chaos theory and the varieties of turbulent phenomena that provide the best examples of chaotic systems. And this casts some doubt on one of the central conclusions of the 1962 paper:

The fact, then, that many complex systems have a nearly decomposable, hierarchic structure is a major facilitating factor enabling us to understand, to describe, and event to “see” such systems and their parts. Or perhaps the proposition should be put the other way round. If there are important systems in the world that are complex without being hierarchic, they may to a considerable extent escape our observation and our understanding. (477)

This is a decidedly pre-chaos understanding of the nature of complex systems. I have the impression that many contemporary complexity theorists would reject the idea that social processes are commonly the result of “nearly decomposable, hierarchic structures”. So it is a genuine change for the mathematics of chaos theory to be included in the 1996 version. Complexity research has moved forward since 1962, and Simon recognizes this in the 1996 chapter.

What we don’t find here is any discussion of whether actual social processes and systems display chaotic behavior in this well defined sense. And we don’t see Simon shifting his position on “nearly decomposable” systems.

Are there examples of social processes and phenomena that display chaotic characteristics over time? Take the occurrence of massive street demonstrations as an example; are there aspects of chaos in the technical sense involved in the outbreak of street mobilization? Do small, apparently random events have large effects on the eventual outcome?

It would appear that this is the case when we look at the cases of uprising and passivity in different cities during the Arab Spring of 2011. Some social scientists have tried to understand the likelihood of uprising as an increasing function of economic crisis, regime weakness, and regime brutality. This implies a linear assumption about the causal role of these three forces. But it seems plausible to speculate that random events like a broken phone chain, an Internet outage, or the defection of a key leader could push the process of mobilization into a different direction. Moreover, it seems that contemporary research on social complexity pays a lot of attention to non-linearity, path-dependency, and sequential processes of social mobilization — leaving a lot of room for the kinds of turbulent effects that are observed in traffic flow, storm generation, and water dripping from a leaking tap. This is the kind of work that is described in Scott Page and John Miller, Complex Adaptive Systems: An Introduction to Computational Models of Social Life.

So oddly enough, it seems that one could fairly say that Simon’s views of social complexity — as expressed in the 1996 third edition of  The Sciences of the Artificial as well as in his groundbreaking “Architecture of Complexity” in 1962 — are significantly incomplete, given the way that complexity theorists are now thinking about social processes. Simon did not incorporate the guiding assumptions of “complex adaptive systems theory” into his own thinking, and remained convinced of the adequacy of the ideas of hierarchical systems and nearly decomposable systems as late at 1996.  His own approach to social complexity remains a phase two approach, not a phase three approach.

(The graph at the top of this post is offered as an interpretation of a highly path-dependent social process. The reader is asked to consider each path as a hypothetical development from a common origin, with small stochastic variations in the situation occurring over time. Imagine the starting position is “large city, economic hardship, weak state, lots of repression”, time is the x axis, and the y axis measures civil unrest. Some of those variations push the path towards a high outcome (blue), and some towards a low outcome (magenta). The great majority of outcomes fall within a short distance of the starting position. So the most likely outcome is “not much change”, but there are unlikely but diametrically different outcomes possible as well.)

Complex systems

Social complexity

Social ensembles are often said to be “complex”. What does this mean?

Herbert Simon is one of the seminal thinkers in the study of complexity. His 1962 article, “The Architecture of Complexity” (link), put forward several ideas that have become core to the conceptual frameworks of people who now study social complexity. So it is worthwhile highlighting a few of the key ideas that were put forward in that article. Here is Simon’s definition of complexity:

Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole. In the face of complexity, an in-principle reductionist may be at the same time a pragmatic holist. (468)

Notice several key ideas contained here, as well as several things that are not said. First, the complexity of a system derives from the “nonsimple” nature of the interaction of its parts (subsystems). A watch is a simple system, because it has many parts but the behavior of the whole is the simple sum of the direct mechanical interactions of the parts. The watchspring provides an (approximately) constant impulse to the gearwheel, producing a temporally regular motion in the gears. This motion pushes forward the time registers (second, minute, hour) in a fully predictable way. If the spring’s tension influenced not only the gearwheel, but also the size of the step taken by the minute hand; or if the impulse provided by the spring varied significantly according to the alignment of the hour and second hands and the orientation of the spring — then the behavior of the watch would be “complex”. It would be difficult or impossible to predict the state of the time registers by counting the ticks in the watch gearwheel. So this is a first statement of the idea of complexity: the fact of multiple causal interactions among the many parts (subsystems) that make up the whole system.

A second main idea here is that the behavior of the system is difficult to predict as a result of the nonsimple interactions among the parts. In a complex system we cannot provide a simple aggregation model of the system that adds up the independent behaviors of the parts; rather, the parts are influenced in their behaviors by the behaviors of other components. The state of the system is fixed by interdependent subsystems; which implies that the system’s behavior can oscillate wildly with apparently similar initial conditions. (This is one explanation of the Chernobyl nuclear meltdown: engineers attempted to “steer” the system to a safe shutdown by manipulating several control systems at once; but these control systems had complex effects on each other, with the result that the engineers catastrophically lost control of the system.)

A third important point here is Simon’s distinction between “metaphysical reducibility” and “pragmatic holism.” He accepts what we would today call the principle of supervenience: the state of the system supervenes upon the states of the parts. But he rejects the feasibility of performing a reduction of the behavior of the system to an account of the properties of the parts. He does not use the concept of “emergence” here, but this would be another way of putting his point: a metaphysically emergent property of a system is one that cannot in principle be derived from the characteristics of the parts. A pragmatically emergent property is one that supervenes upon the properties of the parts, but where it is computationally difficult or impossible to map the function from the state of the parts to the state of the system. This point has some relevance to the idea of “relative explanatory autonomy” mentioned in an earlier posting (link). The latter idea postulates that we can sometimes discover system properties (causal powers) of a complex system that are in principle fixed by the underlying parts, but where it is either impossible or unnecessary to discover the specific causal sequences through which the system’s properties come to be as they are.

Another key idea in this article is Simon’s idea of a hierarchic system.

By a hierarchic system, or hierarchy, I mean a system that is composed of interrelated subsystems, each of the latter being, in turn, hierarchic in structure until we reach some lowest level of elementary subsystem. (468)

I have already given an example of one kind of hierarchy that is frequently encountered in the social sciences: a formal organization. Business firins, governments, universities all have a clearly visible parts-within-parts structure. (469)

Here the idea is also an important one. It is a formal specification of a particular kind of ensemble in which structures at one level of aggregation are found to be composed separately of structures or subsystems at a lower level of aggregation. Simon offers the example of a biological cell that can be analyzed into a set of exhaustive and mutually independent subsystems nested within each other. It is essential that there is a relation of enclosure as we descend the hierarchy of structures: the substructures of level S are entirely contained within it and do not serve as substructures of some other system S’.

It is difficult to think of biological examples that violate the conditions of hierarchy — though we might ask whether an organism and its symbiote might be best understood as a non-hierarchical system. But examples are readily available in the social world. Labor unions and corporate PACs play significant causal roles in modern democracies. But they are not subsystems of the political process in a hierarchical sense: they are not contained within the state, and they play roles in non-state systems as well. (A business lobby group may influence both the policies chosen by a unit of government and the business strategy of a healthcare system.)

Simon appears to believe that hierarchies reduce the complexity of systems; and they support the feature of what we would now call “modularity”, where we can treat the workings of a subsystem as a self-enclosed unit that works roughly the same no matter what changes occur in other subsystems.

Simon puts this point in his own language of “decomposability.” A system is decomposable if we can disaggregate its behavior onto the sum of the independent behaviors of its parts. A system is “nearly decomposable” if the parts of the system have some effects on each other, but these effects are small relative to the overall workings of the system.

At least some kinds of hierarchic systems can be approximated successfully as nearly decomposable systems. The main theoretical findings from the approach can be summed up in two propositions:

(a) in a nearly decomposable system, the short-run behavior of each of the component subsystems is approximately independent of the short-run behavior of the other components; (b) in the long run, the behavior of any one of the components depends in only an aggregate way on the behavior of the other components. (474)

He illustrates this point in the case of social systems in these terms:

In the dynamics of social systems, where members of a system communicate with and influence other members, near decomposability is generally very prominent. This is most obvious in formal organizations, where the formal authority relation connects each member of the organization with one immediate superior and with a small number of subordinates. Of course many communications in organizations follow other channels than the lines of formal authoritv. But most of these channels lead from any particular individual to a very limited number of his superiors, subordinates, and associates. Hence, departmental boundaries play very much the same role as the walls in our heat example. (475)

And in summary:

We have seen that hierarchies have the property of near-decomposability. Intra-component linkages are generally stronger than intercomponent linkages. This fact has the effect of separating the high-frequency dynamics of a hierarchy — involving the internal structure of the components– from the low frequency dynamics-involving interaction among components. (477)

So why does Simon expect that systems will generally be hierarchical, and hierarchies will generally be near-decomposable?  It turns out that this is an expectation that derives from the notion that systems were created by designers (who would certainly favor these features because they make the system predictable and understandable) or evolved through some process of natural selection from simpler to more complex agglomerations.  So we might expect that hydroelectric plants and motion detector circuits in frogs’ visual systems are hierarchical and near-decomposable.
But here is an important point about social complexity.  Neither of these expectations is likely to be satisfied in the case of social systems.  Take the causal processes (sub-systems) that make up a city. And consider some aggregate properties we may be interested in — emigration, resettlement, crime rates, school truancy, real estate values.  Some of the processes that influence these properties are designed (zoning boards, school management systems), but many are not.  Instead, they are the result of separate and non-teleological processes leading to the present.  And there is often a high degree of causal interaction among these separate processes.  As a result, it might be more reasonable to expect, contrary to Simon’s line of thought here, that social systems are likely to embody greater complexity and less decomposability than the systems he uses as examples.
(A recent visit to the Center for Social Complexity at George Mason University (link) was very instructive for me.  There is a great deal of very interesting work underway at the Center using agent-based modeling techniques to understand large, complicated social processes: population movements, housing markets, deforestation, and more.  Particularly interesting is a blog by Andrew Crooks at the Center on various aspects of agent-based modeling of spatial processes.)

Revisiting Popper


Karl Popper’s most commonly cited contribution to philosophy and the philosophy of science is his theory of falsifiability (The Logic of Scientific Discovery, Conjectures and Refutations: The Growth of Scientific Knowledge). (Stephen Thornton has a very nice essay on Popper’s philosophy in the Stanford Encyclopedia of Philosophy.) In its essence, this theory is an alternative to “confirmation theory.” Contrary to positivist philosophy of science, Popper doesn’t think that scientific theories can be confirmed by more and more positive empirical evidence. Instead, he argues that the logic of scientific research is a critical method in which scientists do their best to “falsify” their hypotheses and theories. And we are rationally justified in accepting theories that have been severely tested through an effort to show they are false — rather than accepting theories for which we have accumulated a body of corroborative evidence. Basically, he argues that scientists are in the business of asking this question: what is the most unlikely consequence of this hypothesis? How can I find evidence in nature that would demonstrate that the hypothesis is false? Popper criticizes theorists like Marx and Freud who attempt to accumulate evidence that corroborates their theories (historical materialism, ego transference) and praises theorists like Einstein who honestly confront the unlikely consequences their theories appear to have (perihelion of Mercury).

At bottom, I think many philosophers of science have drawn their own conclusions about both falsifiability and confirmation theory: there is no recipe for measuring the empirical credibility of a given scientific theory, and there is no codifiable “inductive logic” that might replace the forms of empirical reasoning that we find throughout the history of science. Instead, we need to look in greater detail at the epistemic practices of real research communities in order to see the nuanced forms of empirical reasoning that are brought forward for the evaluation of scientific theories. Popper’s student, Imre Lakatos, makes one effort at this (Methodology of Scientific Research Programmes; Criticism and the Growth of Knowledge); so does William Newton-Smith (The Rationality of Science), and much of the philosophy of science that has proceeded under the rubrics of philosophy of physics, biology, or economics is equally attentive to the specific epistemic practices of real working scientific traditions. So “falsifiability” doesn’t seem to have a lot to add to a theory of scientific rationality at this point in the philosophy of science. In particular, Popper’s grand critique of Marx’s social science on the grounds that it is “unfalsifiable” just seems to miss the point; surely Marx, Durkheim, Weber, Simmel, or Tocqueville have important social science insights that can’t be refuted by deriding them as “unfalsifiable”. And Popper’s impatience with Marxism makes one doubt his objectivity as a sympathetic reader of Marx’s work.

Of greater interest is another celebrated idea that Popper put forward, his critique of “historicism” in The Poverty of Historicism (1957). And unlike the theory of falsifiability, I think that there are important insights in this discussion that are even more useful today than they were in 1957, when it comes to conceptualizing the nature of the social sciences. So people who are a little dismissive of Popper may find that there are novelties here that they will find interesting.

Popper characterizes historicism as “an approach to the social sciences which assumes that historical prediction is their principal aim, and which assumes that this aim is attainable by discovering the ‘rhythms’ or the ‘patterns’, the ‘laws’ or the ‘trends’ that underlie the evolution of history” (3). Historicists differ from naturalists, however, in that they believe that the laws that govern history are themselves historically changeable. So a given historical epoch has its own laws and generalizations – unlike the laws of nature that are uniform across time and space. So historicism involves combining two ideas: prediction of historical change based on a formulation of general laws or patterns; and a recognition that historical laws and patterns are themselves variable over time, in reaction to human agency.

Popper’s central conclusion is that large predictions of historical or social outcomes are inherently unjustifiable — a position taken up several times here (post, post). He finds that “holistic” or “utopian” historical predictions depend upon assumptions that simply cannot be justified; instead, he prefers “piecemeal” predictions and interventions (21). What Popper calls “historicism” amounts to the aspiration that there should be a comprehensive science of society that permits prediction of whole future states of the social system, and also supports re-engineering of the social system if we choose. In other words, historicism in his description sounds quite a bit like social physics: the aspiration of finding a theory that describes and predicts the total state of society.

The kind of history with which historicists wish to identify sociology looks not only backwards to the past but also forwards to the future. It is the study of the operative forces and, above all, of the laws of social development. (45)

Popper rejects the feasibility or appropriateness of this vision of social knowledge, and he is right to do so. The social world is not amenable to this kind of general theoretical representation.

The social thinker who serves as Popper’s example of this kind of holistic social theory is Karl Marx. According to Popper, Marx’s Capital (Marx 1977 [1867]) is intended to be a general theory of capitalist society, providing a basis for predicting its future and its specific internal changes over time. And Marx’s theory of historical materialism (“History is a history of class conflict,” “History is the unfolding of the contradictions between the forces and relations of production”; (Communist Manifesto, Preface to a Contribution to Political Economy)) is Popper’s central example of a holistic theory of history. And it is Marx’s theory of revolution that provides a central example for Popper under the category of utopian social engineering. In The Scientific Marx I argue that Popper’s representation of Marx’s social science contribution is flawed; rather, Marx’s ideas about capitalism take the form of an eclectic combination of sociology, economic theory, historical description, and institutional analysis. It is also true, however, that Marx writes in Capital that he is looking to identify the laws of motion of the capitalist mode of production.

Whatever the accuracy of Popper’s interpretation of Marx, his more general point is certainly correct. Sociology and economics cannot provide us with general theories that permit the prediction of large historical change. Popper’s critique of historicism, then, can be rephrased as a compelling critique of the model of the natural sciences as a meta-theory for the social and historical sciences. History and society are not law-governed systems for which we might eventually hope to find exact and comprehensive theories. Instead, they are the heterogeneous, plastic, and contingent compound of actions, structures, causal mechanisms, and conjunctures that elude systematization and prediction. And this conclusion brings us back to the centrality of agent-centered explanations of historical outcomes.

I chose the planetary photo above because it raises a number of complexities about theoretical systems, comprehensive models, and prediction that need sorting out. Popper observes that metaphors from astronomy have had a great deal of sway with historicists: “Modern historicists have been greatly impressed by the success of Newtonian theory, and especially by its power of forecasting the position of the planets a long time ahead” (36). The photo is of a distant planetary system in the making. The amount of debris in orbit makes it clear that it would be impossible to model and predict the behavior of this system over time; this is an n-body gravitational problem that even Newton despaired to solve. What physics does succeed in doing is identifying the processes and forces that are relevant to the evolution of this system over time — without being able to predict its course in even gross form. This is a good example of a complex, chaotic system where prediction is impossible.

Policy, treatment, and mechanism

Policies are selected in order to bring about some desired social outcome or to prevent an undesired one. Medical treatments are applied in order to cure a disease or to ameliorate its effects. In each case an intervention is performed in the belief that this intervention will causally interact with a larger system in such a way as to bring about the desired state. On the basis of a body of beliefs and theories, we judge that T in circumstances C will bring about O with some degree of likelihood. If we did not have such a belief, then there would be no rational basis for choosing to apply the treatment. “Try something, try anything” isn’t exactly a rational basis for policy choice.

In other words, policies and treatments depend on the availability of bodies of knowledge about the causal structure of the domain we’re interested in — what sorts of factors cause or inhibit what sorts of outcomes. This means we need to have some knowledge of the mechanisms that are at work in this domain. And it also means that we need to have some degree of ability to predict some future states — “If you give the patient an aspirin her fever will come down” or “If we inject $700 billion into the financial system the stock market will recover.”

Predictions of this sort could be grounded in two different sorts of reasoning. They might be purely inductive: “Clinical studies demonstrate that administration of an aspirin has a 90% probability of reducing fever.” Or they could be based on hypotheses about the mechanisms that are operative: “Fever is caused by C; aspirin reduces C in the bloodstream; therefore we should expect that aspirin reduces fever by reducing C.” And ideally we would hope that both forms of reasoning are available — causal expectations are born out by clinical evidence.

Implicitly this story assumes that the relevant causal systems are pretty simple — that there are only a few causal pathways and that it is possible to isolate them through experimental studies. We can then insert our proposed interventions into the causal diagram and have reasonable confidence that we can anticipate their effects. The logic of clinical trials as a way of establishing efficacy depends on this assumption of causal simplicity and isolation.

But what if the domain we’re concerned with isn’t like that? Suppose instead that there are many causal factors and a high degree of causal interdependence among the factors. And suppose that we have only limited knowledge of the strength and form of these interdependencies. Is it possible to make rationally justified interventions within such a system?

This description comes pretty close to what are referred to as complex systems. And the most basic finding in the study of complex systems is the extreme difficulty of anticipating future system states. Small interventions or variations in boundary conditions produce massive variations in later system states. But this is bad news for policy makers who are hoping to “steer” a complex system towards a more desirable state. There are good analytical reasons for thinking that they will not be able to anticipate the nature or magnitude or even direction of the effects of the intervention.

The study of complex systems is a collection of areas of research in mathematics, economics, and biology that attempt to arrive at better ways of modeling and projecting the behavior of systems with these complex causal interdependencies. This is an exciting field of research at places like the Santa Fe Institute and the University of Michigan. One important tool that had been extensively developed is the theory of agent-based modeling — essentially, the effort to derive system properties as the aggregate result of the activities of independent agents at the micro-level. And a fairly durable result has emerged: run a model of a complex system a thousand times and you will get a wide distribution of outcomes. This means that we need to think of complex systems as being highly contingent and path-dependent in their behavior. The effect of an intervention may be a wide distribution of future states.

So far the argument is located at a pretty high level of abstraction. Simple causal systems admit of intelligent policy intervention, whereas complex, chaotic systems may not. But the important question is more concrete: which kind of system are we facing when we consider social policy or disease? Are social systems and diseases examples of complex systems? Can social systems be sufficiently disaggregated into fairly durable subsystems that admit of discrete causal analysis and intelligent intervention? What about diseases such as solid tumors? Can we have confidence in interventions such as chemotherapy? And, in both realms, can the findings of complexity theory be helpful by providing mathematical means for working out the system effects of various possible interventions?

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