Dynamics of medieval cities

 

Cities provide a good illustration of the ontology of the theory of assemblage (link). Many forms of association, production, logistics, governance, and population processes came together from independent origins and with different causal properties. So one might imagine that unexpected dynamics of change are likely to be found in all urban settings.

The medieval period is not known for its propensity for innovation, out-of-the-box thinking, or dynamic tendencies towards change. One thinks rather of the placid, continuing social relations of the English countryside, the French village, or the Italian town. There is the idea that a stultifying social order made innovation and change difficult. However, studies of medieval cities over the past century have cast some doubt on this stereotype. Henri Pirenne’s lectures on the medieval city in 1923 were collected in Medieval Cities: Their Origins and the Revival of Trade, and there are numerous clues indicating that Pirenne found ample features of dynamic change in the medieval city from the eleventh century forward. Here are a few examples:

The eleventh century, in fact, brings us face to face with a real commercial revival. This revival received its impetus from two centers of activity, one located in the south and the other in the north: Venice on one side and the Flemish coast on the other. (82) 

Trade was thus forced upon them [Venice] by the very conditions under which they lived. And they had the energy and the genius to turn to profit the unlimited possibilities which trade offered them. (83)

 Constantinople, even in the eleventh century, appears not only as a great city, but as the greatest city of the whole Mediterranean basin. Her population was not far from reaching the figure of a million inhabitants, and that population was singularly active. She was not content, as had been the population of Rome under the Republic and the Empire, to consume without producing. She gave herself over, with a zeal which the fiscal system shackled but did not choke, not only to trading but to industry. (84)

The geographical situation of Flanders, indeed, put her in a splendid position to become the western focus for the commerce of the seas of the north. It formed the natural terminus of the voyage for ships arriving from Northern England or which, having crossed the Sound after coming out of the Baltic, were on their way to the south. (97)

It was only in the twelfth century that, gradually but definitely, Western Europe was transformed. The economic development freed her from the traditional immobility to which a social organization, depending solely on the relations of man to the soil, had condemned her. Commerce and industry did not merely find a place alongside of agriculture; they reacted upon it…. The rigid confines of the demesnial system, which had up to now hemmed in all economic activity, were broken down and the whole social order was patterned along more flexible, more active and more varied lines. (101-102)

Large or small, [cities] were to be met everywhere; one was to be found, on the average, in every twenty-five square leagues of land. They had, in fact, become indispensable to society. They had introduced into it a division of labor which it could no longer do without. Between them and the country was established a reciprocal exchange of services. (102)

So trade, finance, manufacturing, and flexible labor led to a dynamic of change that resulted in real economic and urban development in medieval European cities. Pirenne emphatically does not give a rendering of the medieval city that features a rigid social order impeding social and economic change.

A recent study provides modern evidence that the stereotyped impression of social stasis in the urban world of the middle ages is incorrect (link). Rudolf Ceseretti and his co-authors of “Population-Area Relationship for Medieval European Cities” provide a strikingly novel view of the medieval city (link). Their key finding is that there is an unexpected similarity of behavior with modern urban centers that can be observed in the population and spatial characteristics of medieval cities. They have collected data on 173 medieval cities across Western Europe:

Here is how they frame their finding in the Introduction:

This research suggests that, at a fundamental level, cities consist of overlapping social and physical networks that are self-consistently bounded by settled physical space [55–57]. Here, we investigate whether the relationships between settlement population and settled land area predicted by scaling theory—and observed in contemporary cities—also characterized medieval European cities.

In this paper, we analyze the relationship between the extent of built-up area and resident populations of 173 settlements located in present-day Belgium, France, England, Switzerland, Germany, and Italy, ca. AD 1300. Previous scholarship has produced population estimates for a large number medieval European cities [58,59]. We build on this work by linking population estimates with estimates for the built-up area compiled from historical and archaeological sources.

The authors focus on a common belief about medieval cities — the idea that social interactions among residents are structured by powerful social institutions. Guilds, ethnicities, family groups, and religion provide examples of such institutions. If the net effect of social institutions like these is to reduce the likelihood of interaction of pairs of individuals, then medieval cities should display different patterns of spatial distribution of population and growth; if this effect is not significant, then medieval cities should resemble modern cities in these respects. This study finds the latter to be the case. Fundamentally they are interested in the topic of “scaling of settlement area with population size”. Here is a plot of area and population for the cities they studied, separated by region:

Their central finding is that the data about population density and spatial distribution do not support the hypothesis that medieval social institutions substantially inhibited social interactions to an extent that hindered urban growth and development. Rather, medieval cities look in their population and spatial structures to be very similar to modern cities.

Table 1 shows that the point estimates of the scaling coefficients for all four regional groups and for the pooled dataset fall within the 2/3 ≥

a

≥ 5/6 range predicted by the social reactor model… Thus, medieval cities across Western Europe exhibit, on average, economies of scale with respect to spatial agglomeration such that larger cities were denser on average. This pattern is similar to that observed for modern cities. 

Even though medieval cities were structured by hierarchical institutions that are ostensibly not so dominant today, we interpret this finding as excluding a strongly segregating role for medieval social institutions. This would suggest that the institutions of Western European urban systems ca. 1300 did not substantially constrain social mixing, economic integration, or the free flow of people, ideas, and information. We take these findings as an indication that the underlying micro-level social dynamics of medieval cities were fundamentally similar to those of contemporary cities. (discussion)

This study presents a fascinating contemporary test of a thesis that would surely have interested Pirenne almost a century ago: did medieval cities develop spatially in ways that reflect a reasonable degree of freedom of choice among residents about where they lived and worked? And the data seem to confirm a “yes” for this question.

(I haven’t attempted to summarize the methods used in this study, and the full article bears reading for anyone interested in the question of interpreting urban history from a quantitative point of view.)

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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?

ANT-style critique of ABM

A short recent article in the Journal of Artificial Societies and Social Simulation by Venturini, Jensen, and Latour lays out a critique of the explanatory strategy associated with agent-based modeling of complex social phenomena (link). (Thanks to Mark Carrigan for the reference via Twitter; @mark_carrigan.) Tommaso Venturini is an expert on digital media networks at Sciences Po (link), Pablo Jensen is a physicist who works on social simulations, and Bruno Latour is — Bruno Latour. Readers who recall recent posts here on the strengths and weaknesses of ABM models as a basis for explaining social conflict will find the article interesting (link). VJ&L argue that agent-based models — really, all simulations that proceed from the micro to the macro — are both flawed and unnecessary. They are flawed because they unavoidable resort to assumptions about agents and their environments that reduce the complexity of social interaction to an unacceptable denominator; and they are unnecessary because it is now possible to trace directly the kinds of processes of social interaction that simulations are designed to model. The “big data” available concerning individual-to-individual interactions permits direct observation of most large social processes, they appear to hold.

Here are the key criticisms of ABM methodology that the authors advance:

  • Most of them, however, partake of the same conceptual approach in which individuals are taken as discrete and interchangeable ‘social atoms’ (Buchanan 2007) out of which social structures emerge as macroscopic characteristics (viscosity, solidity…) emerge from atomic interactions in statistical physics (Bandini et al. 2009). (1.2)
  • most simulations work only at the price of simplifying the properties of micro-agents, the rules of interaction and the nature of macro-structures so that they conveniently fit each other. (1.4)
  • micro-macro models assume by construction that agents at the local level are incapable to understand and control the phenomena at the global level. (1.5)

And here is their key claim:

  • Empirical studies show that, contrarily to what most social simulations assume, collective action does not originate at the micro level of individual atoms and does not end up in a macro level of stable structures. Instead, actions distribute in intricate and heterogeneous networks than fold and deploy creating differences but not discontinuities. (1.11) 

This final statement could serve as a high-level paraphrase of actor-network theory, as presented by Latour in Reassembling the Social: An Introduction to Actor-Network-Theory. (Here is a brief description of actor-network theory and its minimalist social ontology; link.)

These criticisms parallel some of my own misgivings about simulation models, though I am somewhat more sympathetic to their use than VJ&L. Here are some of the concerns raised in earlier posts about the validity of various ABM approaches to social conflict (linklink):

  • Simulations often produce results that appear to be artifacts rather than genuine social tendencies.
  • Simulations leave out important features of the social world that are prima facie important to outcomes: for example, quality of leadership, quality and intensity of organization, content of appeals, differential pathways of appeals, and variety of political psychologies across agents.
  • The factor of the influence of organizations is particularly important and non-local.
  • Simulations need to incorporate actors at a range of levels, from individual to club to organization.
And here is the conclusion I drew in that post:
  • But it is very important to recognize the limitations of these models as predictors of outcomes in specific periods and locations of unrest. These simulation models probably don’t shed much light on particular episodes of contention in Egypt or Tunisia during the Arab Spring. The “qualitative” theories of contention that have been developed probably shed more light on the dynamics of contention than the simulations do at this point in their development.

But the confidence expressed by VJ&L in the new observability of social processes through digital tracing seems excessive to me. They offer a few good examples that support their case — opinion change, for example (1.9). Here they argue that it is possible to map or track opinion change directly through digital footprints of interaction (Twitter, Facebook, blogging), and this is superior to abstract modeling of opinion change through social networks. No doubt we can learn something important about the dynamics of opinion change through this means.

But this is a very special case. Can we similarly “map” the spread of new political ideas and slogans during the Arab Spring? No, because the vast majority of those present in Tahrir Square were not tweeting and texting their experiences. Can we map the spread of anti-Muslim attitudes in Gujarat in 2002 leading to massive killings of Muslims in a short period of time? No, for the same reason: activists and nationalist gangs did not do us the historical courtesy of posting their thought processes in their Twitter feeds either. Can we study the institutional realities of the fiscal system of the Indonesian state through its digital traces? No. Can we study the prevalence and causes of official corruption in China through digital traces? Again, no.

 
In other words, there is a huge methodological problem with the idea of digital traceability, deriving from the fact that most social activity leaves no digital traces. There are problem areas where the traces are more accessible and more indicative of the underlying social processes; but this is a far cry from the utopia of total social legibility that appears to underlie the viewpoint expressed here.
 
So I’m not persuaded that the tools of digital tracing provide the full alternative to social simulation that these authors assert. And this implies that social simulation tools remain an important component of the social scientist’s toolbox.
 

John von Neumann and stochastic simulations

source: Monte Carlo method (Wikipedia)

John von Neumann was one of the genuine mathematical geniuses of the twentieth century. A particularly interesting window onto von Neumann’s scientific work is provided by George Dyson in his  book, Turing’s Cathedral: The Origins of the Digital Universe. The book is as much an intellectual history of the mathematics and physics expertise of the Princeton Institute for Advanced Study as it is a study of any one individual, but von Neumann plays a key role in the story. His contribution to the creation of the general-purpose digital computer helped to lay the foundations for the digital world in which we now all live.

There are many interesting threads in von Neumann’s intellectual life, but one aspect that is particularly interesting to me is the early application of the new digital computing technology to the problem of simulating large complex physical systems. Modeling weather and climate were topics for which researchers sought solutions using the computational power of first-generation digital computers, and the research needed to understand and design thermonuclear devices had an urgent priority during the war and post-war years. Here is a description of von Neumann’s role in the field of weather modeling in designing the early applications of ENIAC  (P. Lynch, “From Richardson to early numerical weather prediction”; link):

John von Neumann recognized weather forecasting, a problem of both great practical significance and intrinsic scientific interest, as ideal for an automatic computer. He was in close contact with Rossby, who was the person best placed to understand the challenges that would have to be addressed to achieve success in this venture. Von Neumann established a Meteorology Project at the Institute for Advanced Study in Princeton and recruited Jule Charney to lead it. Arrangements were made to compute a solution of a simple equation, the barotropic vorticity equation (BVE), on the only computer available, the ENIAC. Barotropic models treat the atmosphere as a single layer, averaging out variations in the vertical. The resulting numerical predictions were truly ground-breaking. Four 24-hour forecasts were made, and the results clearly indicated that the large-scale features of the mid-tropospheric flow could be forecast numerically with a reasonable resemblance to reality. (Lynch, 9)

image: (link, 10)

A key innovation in the 1950s in the field of advanced computing was the invention of Monte Carlo simulation techniques to assist in the invention and development of the hydrogen bomb. Thomas Haigh, Mark Priestley, and Crispin Rope describe the development of the software supporting Monte Carlo simulations in the ENIAC machine in a contribution to the IEEE Annals of the History of Computing (link). Peter Galison offers a detailed treatment of the research communities that grew up around these new computational techniques (link). Developed first as a way of modeling nuclear fission and nuclear explosives, these techniques proved to be remarkably powerful for allowing researchers to simulate and calculate highly complex causal processes. Here is how Galison summarizes the approach:

Christened “Monte Carlo” after the gambling mecca, the method amounted to the use of random, numbers (a la roulette) to simulate the stochastic processes too complex to calculate in full analytic glory. But physicists and engineers soon elevated the Monte Carlo above the lowly status of a mere numerical calculation scheme; it came to constitute an alternative reality–in some cases a preferred one–on which “experimentation” could be conducted. (119) 

At Los Alamos during the war, physicists soon recognized that the central problem was to understand the process by which neutrons fission, scatter, and join uranium nuclei deep in the fissile core of a nuclear weapon. Experiment could not probe the critical mass with sufficient detail; theory led rapidly to unsolvable integro-differential equations. With such problems, the artificial reality of the Monte Carlo was the only solution–the sampling method could “recreate” such processes by modeling a sequence of random scatterings on a computer. (120)

The approach that Ulam, Metropolis, and von Neumann proposed to take for the problem of nuclear fusion involved fundamental physical calculations and statistical estimates of interactions between neutrons and surrounding matter. They proposed to calculate the evolution of the states of a manageable number of neutrons as they traveled from a central plutonium source through spherical layers of other materials. The initial characteristics and subsequent interactions of the sampled neutrons were assigned using pseudo-random numbers. A manageable number of sampled spaces within the unit cube would be “observed” for the transit of a neutron (127) (10^4 observations). If the percentage of fission calculated in the sampled spaces exceeded a certain value, then the reaction would be self-sustaining and explosive. Here is how the simulation would proceed:

Von Neumann went on to specify the way the simulation would run. First, a hundred neutrons would proceed through a short time interval, and the energy and momentum they transferred to ambient matter would be calculated. With this “kick” from the neutrons, the matter would be displaced. Assuming that the matter was in the middle position between the displaced position and the original position, one would then recalculate the history of the hundred original neutrons. This iteration would then repeat until a “self-consistent system” of neutron histories and matter displacement was obtained. The computer would then use this endstate as the basis for the next interval of time, delta t. Photons could be treated in the same way, or if the simplification were not plausible because of photon-matter interactions, light could be handled through standard diffusion methods designed for isotropic, black-body radiation. (129)

Galison argues that there were two fairly different views in play of the significance of Monte Carlo methods in the 1950s and 1960s. According to the first view, they were simply a calculating device permitting the “computational physicist” to calculate values for outcomes that could not be observed or theoretically inferred. According to the second view, Monte Carlo methods were interpreted realistically. Their statistical underpinnings were thought to correspond exactly to the probabilistic characteristics of nature; they represented a stochastic view of physics.

King’s view–that the Monte Carlo method corresponded to nature (got “back of the physics of the problem”) as no deterministic differential equation ever could–I will call

stochasticism

. It appears in myriad early uses of the Monte Carlo, and clearly contributed to its creation. In 1949, the physicist Robert Wilson took cosmic-ray physics as a perfect instantiation of the method: “The present application has exhibited how easy it is to apply the Monte Carlo method to a stochastic problem and to achieve without excessive labor an accuracy of about ten percent.” (146)

This is a very bold interpretation of a simulation technique. Rather than looking at the model as an abstraction from reality, this interpretation looks at the model as a digital reproduction of that reality. “Thus for the stochasticist, the simulation was, in a sense, of apiece with the natural phenomenon” (147).

One thing that is striking in these descriptions of the software developed in the 1950s to implement Monte Carlo methods is the very limited size and computing power of the first-generation general-purpose computing devices. Punch cards represented “the state of a single neutron at a single moment in time” (Haigh et al link 45), and the algorithm used pseudo-random numbers and basic physics to compute the next state of this neutron. The basic computations used third-order polynomial approximations (Haigh et al link 46) to compute future states of the neutron. The simulation described here resulted in the production of one million punched cards. It would seem that today one could use a spreadsheet to reproduce the von Neumann Monte Carlo simulation of fission, with each line being the computed result from the previous line after application of the specified mathematical functions to the data represented in the prior line. So a natural question to ask is — what could von Neumann have accomplished if he had Excel in his toolkit? Experts — is this possible?

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