Coupling planning models with models of spontaneous order

When the E&P stable was organised, ‘B’ took design and planning research with a computational emphasis. The underlying research motivations included designers looking for more science, engineers looking for social science, and social scientists enjoying the mixed company afforded by the quantitative social science revolution. In this heterogeneous field there was little anchoring orthodoxy in terms of philosophy of science, and the journey that followed is probably best seen as a period of discipline-building through epistemological innovation, methodological invention and trial-and-error. The lack of orthodoxy meant that few approaches were ever written off as errors, however, and while B has always been regarded as hard to get into, it has offered a liberal welcome to a great diversity of scholars. The journal’s new sub-title, ‘urban science’, perhaps signals arrival at some stage of maturity after 50 years of experimentation.

A discipline needs its specific ontology, and some work published in B over the decades has been in pursuit of appropriate entities to study: neighbourhood definitions, shape-grammatical objects, functional cities and regions, landscape patches, axial lines, pixelated social surfaces, demand and supply zones, networks, stocks and flows, central places, urban fields, externalities, tax districts, rent gaps, transit-oriented-development, city systems and so on. Disciplines mature by advancement of deductive logic that defines an ontology offering helpful abstractions of complexity. This has been a crucial contribution of the journal. A discipline also advances by inductive inference that builds theory about ontological abstractions, and redefines ontology to better reflect measurable and actionable qualities. The journal’s contribution in this respect has been to imagine, borrow, implement, test and refine techniques, methodologies, algorithms, heuristics, logical and empirical models, simulations, visualisations and decision-making tools. The journal is a treasure trove of inventions in pursuit of a more ordered and verifiable scientific urban planning.

Many if not most of the methods published have been motivated by an interest in prediction. In this sense, the journal maps a journey that is policy, engineering and design motivated and strongly normative. The journal’s positivist science ethic has arguably been secondary to its normative concerns and in this sense, its rebranding as an urban science journal is significant. In the 1970s, B helped urbanists navigate from cybernetic mechanistic optimisation to behavioural theory and stochastic models, but the motivation remained largely predictive. The predictive models became more ‘realistic’ with the behavioural turn, embodying explicit explanation (and becoming more explainable), requiring more data and computational power. The result was not necessarily better prediction, however.

To illustrate, consider five modelling paradigms familiar to B’s readers: spatial-interaction, agent-based models (ABM), discrete-choice, general equilibrium and cellular automata (CA). In extremis, these, respectively, gave us: (i) zonal models of flows (trips, expenditure etc) disaggregated to an overwhelming number of representative sub-groups each requiring calibrated friction and attraction parameters; (ii) ABM digital twins with as many agents as the real population – an urban version of Carroll’s 1:1 map of the world (that does not do ‘nearly as good as the real thing’); (iii) a fictional neo-classical utility-maximising machine of representative shoppers with assumed multi-parameter preference functions interacting with their environment and each other to optimise movement; (iv) closed-system deductive models of urban economies solved analytically for optimal price; and (v) CA growth models beyond the wildest dreams of early development-potential mappers, driven by behavioural cell-conversion heuristics and multiple weighted GIS and remote sensing (RS) layers.

In their own ways, models published in B sought to capture ever more detailed behaviour in pursuit of more accurate prediction. Many can be thought of as explanatory models motivated by the idea of decision-support. The problem is that taken to operational level, such models tend to need hundreds if not thousands of parameters. Urban models rich in explainable behaviour are generally too complex to understand when used predictively. Behaviourally enriched simulations articulate sophisticated theories of the city and help visualise what-if analysis. They may have predictive power, but the paradox of overfitting – the more detail in a model the less predictive it is because of external validity problems – is linked to a deeper paradox of planning. The city is self-organising. Planners and designers make their plans but the shape of cities is determined by a multitude of autonomous steps.

Academic planning has yet to adequately theorise the relationship between spontaneous and planned urban-spatial order. Jane Jacobs wrote doctrine not theory. Likewise, the urban modelling community has been slow to come to a parsimonious linkage of these two fundamental kinds of order governing human cooperation over the ages. The urban science embraced in B’s new name offers fresh perspectives on this difficult question.

Urban allometry (aka urban scaling) is a biological idea, which brings scientific urban planning back to its roots (pioneer planning scholar Patrick Geddes was a biology professor). Urban allometry is an analogy – borrowed from evolutionary biology. But if cities are super-organisms or eusocial colonies then perhaps it is more than an analogy. Judged by the coverage in Nature and similar journals, science at the start of the 21st century is willing to view cities as a biological phenomenon. Some social physics models historically favoured in B are clearly analogical borrowings. Humans are not actually attracted by gravitational force between cities in proportion to collective physical mass. But in urban scaling, evolutionary biology may well have a serious claim on the study of spontaneous order in human society.

Urban allometric scaling regresses urban performance (log Y), for example, log GDP, on city population size (log N). These are single parameter models, with the exponent β capturing how a single agglomeration economy moves with urban complexity β ∼ δ log Y/δ log N (absolute change). Put another way, they capture the elasticity of an externality with respect to complexity: ε_Y ∼ ((δ log Y)/Y)/((δ log N)/N). When β < 1 the allometric relationship measures an economy of scale from human clustering, for example, when Y measures total road length. A β > 1 is capturing returns to scale of an externality (positive externalities such as income, or negative externalities like crime). It is reasonable to ask if single parameter models are a backward step in explanatory theory, compared to elaborate urban dynamics of the past half-century. The response is epistemologically challenging.

The reductionism is not driven by predictive parsimony. The scientific motivation comes from the biological interest in the city as an aggregate whole. Surprisingly perhaps, urban scaling science is a new harbinger of holism. N appears in the model not so much as a numerical count of people, but as a surrogate measure of the manifold interconnectedness of those people. Beta captures an observable output from unobservable complexity proxied by population size. In this sense, urban scaling models are explanatory, not predictive. They ‘explain’ (narrate mathematically via a statistical model) the remarkable regularity with which collective output moves with the size-related complexity of human-human, human-capital, human-technology and human-environment interactions. They are models of spontaneous social-spatial order.

How to link them to the kind of predictive models published in B and designed to test outcomes of alternative designs, plans, policies, technologies, and futures? The idea that crime, innovation and GDP tend to rise at a regular 15% above per capita is depressingly deterministic for a scholarly community wedded to the idea of what-if prediction for better social outcomes. Does the full-circle journey back to biology remove the agency that has so motivated urban social, engineering and design science?

Well, perhaps yes in the sense of confirming that many kinds of urban dynamics are beyond human control. Capitulation to this reality is long overdue. The good news, however, is that by better understanding the bounds of controllable dynamics, we can better discern the limits of planning. For example, while local public expenditure may deterministically scale with city size (revealing a ‘law’ of collective action directed towards local public goods) (Webster, 2024), residuals around the curve reveal something important about scope for intervention. We may not be able to change the shape of a scaling curve but we may be able to help individual cities perform better against the size-adjusted mean (shift along the residual distribution). Urban policy makers and planners have traditionally relied on performance comparisons that use per capita measures. Urban allometric models provide performance targets, norms and comparisons adjusted for the performance-producing capacity of human clusters. Smaller cities do not generally reach the per capita performance of larger cities because they do not have the same kind of interactive complexity within. So we need to compare cities on population (complexity)-adjusted performance. We can, for example, rank cities by their standardised residuals around the population-adjusted GDP curve. Doing this for Europe for 2021 data reveals that eight of the 10 best performing cities are German. Cambridge is 5th, Aberdeen 8th and London 32nd (Wundrak, 2021).

Modelling the residuals of single parameter urban performance curves is a productive agenda for explicitly coupling models of spontaneous order with models of planned order. The city with the highest positive normalised residual around a population-adjusted model of Chinese urban GDP is Karamay, a little known city in the far north-west of China. Like Aberdeen, it is an oil-production city (the name means ‘black oil’ in the Uyghur language). Its unusual performance for its size is due in large part to government policy. Given its inhospitable natural (arid) environment, it is also highly likely that urban design has played a part in its relative economic success.

Deterministic urban performance laws set bounds for realistic performance targets for individual cities. Patterns of residuals around them can reveal policy and planning-relevant information about how individual cities have out- or under-performed the mean and how long that has taken and by which route. Urban science ‘laws’ of spontaneous urban order can also help reduce the number of parameters in intervention-oriented predictive models. Laws of electromagnetism are vast reductions of sub-atomic complexity, but they work well-enough as reduced-form explanations to be able to predict outcomes of engineering problems.