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Ancient and Modern Cities Obeyed Same Mathematical Rule


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(Science Advances) – A key property of modern cities is increasing returns to scale – the finding that many socioeconomic outputs increase more rapidly than their population size. Recent theoretical work proposes that this phenomenon is the result of general network effects typical of human social networks embedded in space and, thus, is not necessarily limited to modern settlements.

The underlying organizational ingredients of modern cities were present in ancient settlements in the Basin of Mexico.
(Credit: Gabriel Garcia for the Santa Fe Institute)

Many studies over the last few decades have demonstrated that average properties of contemporary urban settlements – from socioeconomic outputs to land area to the extent of infrastructure – vary systematically and predictably with population size. For example, measures of the physical extent of urban infrastructure increase more slowly than city population size, thus exhibiting economies of scale. On the other hand, various socioeconomic outputs increase faster than population size and thus exhibit increasing returns to scale.

Recent theory, building from comparative analyses of large data sets for many urban systems around the world, has proposed that these properties of modern cities take a simple mathematical form and emerge from a few general principles of human social organization. This view posits the primary role of cities in human societies as social reactors: Larger cities are environments where a larger number of social interactions per unit time can be supported and sustained. This generic dynamics, in turn, is the basis for expanding economic and political organization, such as the division and coordination of labour, the specialization of knowledge, and the development of (hierarchical) political and civic institutions.

Santa Fe Institute (SFI) Professor Luis Bettencourt researches urban dynamics as a lead investigator of SFI’s Cities, Scaling, and Sustainability research program. When he gave a talk in 2013 on urban scaling theory, Scott Ortman, now an assistant professor in the Department of Anthropology at CU Boulder and a former Institute Omidyar Fellow, noted that the trends Bettencourt described were not particular to modern times. Their discussion prompted a research project on the effects of city size through history.

To test their ideas, the team examined archaeological data from the Basin of Mexico (what is now Mexico City and nearby regions). In the 1960s – before Mexico City’s population exploded – surveyors examined all its ancient settlements, spanning 2000 years and four cultural eras in pre-contact Mesoamerica.

They examined the extent to which increasing returns are apparent in archaeological settlement data from the pre-Hispanic Basin of Mexico. They reviewed previous work on the quantitative relationship between population size and average settled area in this society and then present a general analysis of their patterns of monument construction and house sizes.

According to them, estimated scaling parameter values and residual statistics support the hypothesis that increasing returns to scale characterized various forms of socioeconomic production available in the archaeological record and are found to be consistent with key expectations from settlement scaling theory. As a consequence, these results provide evidence that the essential processes that lead to increasing returns in contemporary cities may have characterized human settlements throughout history, and demonstrate that increasing returns do not require modern forms of political or economic organization.

Whereas the expression of these activities is local and reflects history and culture, the larger cities in any urban system, on average, share common characteristics as they magnify social interaction opportunities and provide better matching complementarities, thereby increasing the productivity and scope of material resources and human labour. 

An important aspect of these ideas is that the theoretical derivation of scaling relations does not invoke specific characteristics of modern economies, industrialization, or global trade, but instead relies only on basic self-consistent characteristics of human social networks embedded in space. Consequently, these models are potentially applicable to ancient (and even non-urban) settlement systems and make a set of integrated and novel predictions for the structure and function of these systems that can be tested using archaeological evidence.

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