1.A Pirenne Hypothesis (Batten, pp. 117-120)
Batten discusses the "enduring controversy" regarding the transition of Europe from classical antiquity to medieval civilization. According to Batten, popular views attribute the revival of medieval towns in Middle Europe during the tenth and eleventh centuries to internal events, such as technological change, or the transfer of political authority from feudal lords to communities.
In contrast, the Belgian historian Henri Pirenne (1862-1935) hypothesized in a famous work (Pirenne, 1925), still much cited today, that the revival was due more to an external event: namely, "the impact of Islamic forces in the seventh and eight centuries (which) destroyed the commercial unity of the Mediterranean, thereby ending the Roman world in economic terms and ushering in a strikingly different civilization."
Batten (pp. 118-120) stresses three aspects regarding Pirenne's hypothesis:
1.B Mees Analysis (Batten, pp. 120-125)
Alistair Mees (Professor of Applied Mathematics, University of Western Australia) developed a qualitative nonlinear dynamic model in Mees (1975) illustrating how trading opportunities and employment dynamics might affect the relative size of urban and rural populations.
Batten argues (pp. 122-123) that the Mees model can be used to illustrate the Pirenne hypothesis. Mees posits the existence of two main economic groupings, farmers producing food and city merchants producing silk (say). Mees reasons that locally stable mixed population equilibria are more likely for weakly interconnected economies with isolated self-sufficient communities that have to provide for all of their own needs. But Mees also shows how mixed population equilibria can be destabilized by the opening up of new long-distance trading opportunities.
Following Batten, let f denote the percentage of the current population consisting of farmers, and let c denote the percentage of the current population consisting of city merchants. Consider, first, the case of a relatively isolated region in which farmers and city merchants must depend solely on each other for their needs. In this case, Mees reasoned that a mixed population of farmers and merchants would emerge rather than a specialized population consisting entirely of farmers or entirely of merchants.
This postulated system can be illustrated by means of the following phase portrait, where df/dt denotes the rate of change in f and dc/dt denotes the rate of change in c. Note that df/dt goes from negative to positive values as one ascends the left-vertical axis whereas dc/dt goes from negative to positive values as one descends the right-vertical axis.
f=100% df/dt c=0% /|\ | Positive | - - | Values | - - | Negative of df/dt | | Values | - - | of dc/dt 0 |____________________________________________| |Ec Em - - | Ef | - | Negative | - - | Positive Values | | Values of df/dt | | of dc/dt |___________________________________________\|/ f=0% dc/dt c=100%
Each point along the line between Ec and Ef corresponds to a particular population mix (f,c), which constitutes the state vector for the Mees dynamical system.
At point Ec=(0%,100%) the population (f,c) is specialized, consisting entirely of city merchants. At point Ef=(100%,0%) the population (f,c) is also specialized, consisting entirely of farmers. In contrast, at point Em=(fm,cm) the population (f,c) consists of a nontrivial mix of farmers and city merchants.
The three points Ec, Em, and Ef are all equilibrium points for the Mees dynamical system, in the classical sense that the system is at rest at each of these points. This is true because df/dt and dc/dt are both zero at each of these points, implying that the system state vector (f,c) is not changing.
The specialized population equilibria Ec and Ef are both unstable. That is, starting at either of these specialized population points, any sufficiently small perturbation in the population precipates a movement away from the specialized population point and towards the mixed population point Em.
For example, suppose the economy starts at Ec with f=0% and c=100%. Suppose a perturbation occurs that causes a slight increase in f (hence a slight decrease in c). This movement in the state vector (f,c) to the right of Ec results in a positive sign for df/dt and a negative sign for dc/dt, hence f continues to increase and c continues to decrease. This results in a further movement of (f,c) to the right. This rightward movement in (f,c) only ceases when the system converges to Em, where once again the state vector comes to rest. A similar analysis shows why any sufficiently small perturbation away from Ef also results in the convergence of the system to Em.
In contrast, Em = (fm,cm) is locally stable. Starting at Em, an analysis analogous to the preceding arguments shows that any perturbation in (fm,cm) either in the direction of Ec=(0%,100%) (fewer farmers, more city merchants) or in the direction of Ef=(100%,0%) (more farmers, fewer city merchants) that still leaves the population mixed to some degree will result in an eventual return to Em.
Thus, Em is the unique attractor for the Mees dynamical system as modelled above. Its basin of attraction is the whole range of state vectors (f,c) lying strictly between Ec=(0,100%) and Ef=(100%,0%).
How might Em be destabilized by the introduction of increased opportunities for long-distance trading?
These increased trading opportunities might increase the relative attractiveness (profitability) of being a city merchant, resulting in a flattening out of the shape of the "phase curve" between Ec and Em and a leftward movement in Em along the horizontal axis in the direction of Ec.
The leftward movement of Em -- hence of (f,c) -- implies that city merchants are becoming a larger portion of the mixed population in the locally stable equilibrium Em.
f=100% df/dt c=0% /|\ | Positive | | Values | | Negative of df/dt | - - | Values | - - | of dc/dt 0 |____________________________________________| |Ec Em - - | Ef | - - | Negative | - - | Positive Values | | Values of df/dt | | of dc/dt |___________________________________________\|/ f=0% dc/dt c=100%
If this process continues, eventually the phase curve could completely drop below the horizontal axis, implying the disappearance altogether of the mixed equilibrium point Em; see the diagram below.
In this case the only locally stable equilibrium point would be Ec, where the community consists entirely of city merchants who obtain all their food through trade with other regions.
f=100% df/dt c=0% /|\ | Positive | | Values | | Negative of df/dt | | Values | | of dc/dt 0 |____________________________________________| |Ec - | Ef | - - | Negative | - - | Positive Values | - - | Values of df/dt | | of dc/dt |___________________________________________\|/ f=0% dc/dt c=100%
Suppose the extent of long-distance trading opportunities in the Mees dynamical system can be increased from 0 by increasing a parameter q starting at q=0.
Suppose, also, that the phase curve first drops completely below the horizontal line connecting Ec to Ef when q=q*, implying that the equilibrium Em is lost when the value of q hits q=q*.
The Mees dynamical system thus experiences a bifurcation at q=q*, since its set of equilibria changes abruptly from {Ec,Em,Ef} to {Ec,Ef} at q=q*.
Batten discusses how groups of merchants might come to form a crude mental model of a simple economic network (three linked cities) through the trial-and-error construction of a set of condition-action rules for profitable trade. Batten claims (p. 133) that this form of learning by circulating "contributed to the emergence of a new urban hierarchy in Europe." He relates his intuitive discussion to empirical data on the growth of cities in Europe from 1000 A.D. to 1400 A.D. (Table 4.2).
Batten then discusses how city growth in Europe during the eleventh and twelfth centuries exhibited the properties of an autocatalytic network, with the emergence of ever more nodes and links growing outward from previously established nodes and links. Two main commercial networks first emerged, one in the north on the shores of the Baltic and North Seas, and the other in the south on the shores of the Mediterranean and Adriatic Seas. Subsequently, traders operating in these two networks came into increasing contact with each other through a Middle European bridge: namely, the establishment of trading fairs, in particular the famous French fairs at Champagne in the twelfth and thirteenth centuries that attracted merchants from the whole of Europe.
Batten stresses (p. 136) that the Champagne fairs were important not only as a major market for international trade but also as the center of an embryonic foreign exchange market in which different currencies could be bought and sold at relative prices determined by supply and demand. Batten concludes (p. 137): "More than any other single activity, the fairs did most to bring about an end to the economic isolation that the West had suffered during the Middle Ages."
Nevertheless, the fairs did not evolve into manufacturing centers or cities. Rather, they eventually disappeared. Batten highlights four main factors contributing to this disappearance:
Batten (p. 137) identifies the final factor, improved payment systems, as being "perhaps the most influential in the long run" in promoting the development of a more fully connected European commercial trading network.