Alan Wilson (1939–): A Renaissance Man in Regional Science

Abstract

Sir Alan Geoffrey Wilson is no ordinary regional scientist. Some sixty years ago, he began his career as a mathematician and theoretical physicist analyzing bubble chamber events at the Rutherford Laboratory in Harwell, England. However, he soon realized that his ambition was to study and model people in cities rather than particles in gas chambers. His move to work with a transportation planning research group in Oxford in 1963 would mark the beginning of a long, productive, and impactful career in regional science. Yet, he did not entirely abandon physics: Thermodynamics ended up being a motivation and basis for many of his ideas and innovations, including his signature entropy-based spatial interaction framework. Over the years, Alan Wilson’s “sphere of interest” has remained relatively focused on cities and systems of cities, and, particularly, the modeling of spatial interaction, location activity, and urban evolution. In these areas, he has made significant theoretical and methodological contributions. He has drawn upon and impacted various disciplines and subdisciplines, including some outside the conventional walls of regional science. What is more, Sir Alan Wilson is not just a scientific giant. He has worn many badges in his lifetime: educator, administrator, philanthropist, planner, politician, businessman, and entrepreneur, and in all these roles, he has been highly successful. But, as argued by chapter author Laurie Schintler, Alan Wilson is even more than that: He is also an artist and a philosopher, making him a Renaissance man in regional science.

Alan Wilson

1 Overview

We build too many walls and not enough bridges.

—Sir Isaac Newton

Sir Alan Geoffrey Wilson is not an ordinary regional scientist. Some sixty years ago, he began his career as a mathematician and theoretical physicist analyzing bubble chamber events at the Rutherford Laboratory in Harwell, England. However, he soon realized that his ambition was to study and model people in cities rather than particles in gas chambers. His move to work with a transportation planning research group in Oxford in 1963 would mark the beginning of a long, productive, and impactful (and still very active!) career in regional science. Yet, he did not entirely abandon physics: Concepts, theories, and mathematics from physics would serve as a basis and motivation for many of his ideas and innovations, including his signature entropy-based, spatial interaction framework.

Over the years, Alan Wilson's “sphere of interest” has remained relatively focused on cities and systems of cities, and, particularly, the modeling of spatial interaction, location activity, and urban evolution. In these areas, he has made significant theoretical and methodological contributions, which are spotlighted in several articles and special issues (Gombrich and Oléron-Evans 2019; Clarke 2009, 2011; Waldorf et al. 2004; Johnston 2019). He has published countless papers, books, reports, and commentaries, drawing upon and impacting various disciplines and subdisciplines, including outside the conventional walls of regional science. However, Alan Wilson is not just a scientific giant. In his lifetime, he has worn many badges: educator, administrator, philanthropist, planner, politician, businessman, and entrepreneur, and in all these roles, he has been highly successful. But Alan Wilson is even more than that: He is also an artist and a philosopher.

Truly transformative scientific advancements and revelations are the product of two interrelated forces: “…curiosity, which drives one on toward discovery, and a love of play (gout de jeu) or sheer enjoyment of the game itself, which encourages inventive thought” (Le Lionnais 1969). These are the defining features of a creative genius—a scientific artist—and the essence of Alan Wilson. Wilson is engaged “with the world of ideas” (Grombrich and Oléron-Evans 2019), intellectually curious about everything from how cities evolve and morph over short and long periods to how concepts and methods from the natural sciences transfer and translate to a regional science context. His scholarly adventures often begin with an idea from another field, an analogy—or a mystery worth pursuing. Alan Wilson also has a love of play, i.e., a “genius for synthesis.” He has a creative capacity to harness and combine seemingly disparate approaches, principles, and perspectives and to “connect-the-dots” in novel and metaphoric ways. In the process, he builds on the “shoulders of giants,” exploiting the work of other Great Minds who have already begun to “pave the way” or who “planted a seed.” Moreover, he is continually taking stock of, synthesizing, and clarifying the state of knowledge—painting an ongoing portrait of the scientific landscape.

All of this is encapsulated in Wilson’s philosophy of science, which he follows himself and communicates to the regional science community regularly. For theory and model development, as well as planning and education—and problem-solving, more generally—the “Wilsonian” philosophy emphasizes a systems perspective and algorithmic and systematic approaches infused with creativity and imagination. To this end, inter- and cross-disciplinary ideas and viewpoints, along with cooperation and coordination between researchers, planners, policymakers, and even politicians, are imperative. According to Wilson, such bridges are crucial for engendering analytical frameworks and theoretical advancements that are unifying, universal, versatile, and, ultimately, transdisciplinary. In fact, as Wilson notes, to arrive at “a general paradigm, eclecticism and integration are the order of the day” (Wilson 1972).

This chapter provides an up-to-date tour d’horizon of Alan Wilson’s long list of contributions to science and society, highlighting his ingenuity for bringing together and bridging people, disciplines, concepts, and techniques systematically, deliberately, and creatively to solve a broad spectrum of problems.

2 Personal and Professional Journey

You have to make the rules, not follow them.

—Sir Isaac Newton

On the surface, Alan Wilson’s personal and professional trajectory appears to be a “random walk”—i.e., a path consisting of a succession of indiscriminate steps. However, his trajectory has been more like a thermodynamic system, characterized by critical junctures and transitions, with each phase bringing new opportunities, roles, focal points, experiences, and accomplishments that build on and leverage those of the prior stages. While Alan Wilson has faced enormous barriers and challenges throughout his life and career, he has been able to overcome them “simply by being smart enough to rise above them” (Kelly 2003). In doing so, he sets his own rules, intervening proactively to steer his course in desirable directions—to facilitate positive phase transitions—which has contributed to great successes and accolades and to a life and career that has been anything but conventional.

Alan Wilson was born in Bradford, Yorkshire, on January 8, 1939. His upbringing was relatively modest, but supportive. In his own words, “I was brought up in the poorest part of Bradford: Laisterdyke. My father was a wool-sorter at Whitehead’s. Both my parents had left school at 14 but were determined that I got a good education.” (Kelly 2003). When his family moved from Bradford to Darlington, Alan enrolled in the Queen Elizabeth Grammar School, which would be a pivotal initial condition in his career. According to Wilson, unlike Bradford, which had several schools, Darlington was a one-grammar-school town that sought to send a handful of students to Oxford or Cambridge (Kelly 2003). Alan Wilson was one of them; he was accepted to Cambridge at Corpus Christi, and off he went.

In 1960, Alan Wilson graduated from Cambridge with training in mathematics and theoretical physics. He then went on to join the Rutherford Laboratory, a laboratory involved in analyzing real-time particle physics experiments at CERN in Switzerland (Kelly 2003). Wilson’s duty was to carry out computer-based statistical analysis and testing, which, as he says, “was an unbelievable responsibility. If my bit didn’t work, a multimillion-pound experiment didn’t get analyzed” (Kelly 2003).

Yet, Alan Wilson aspired to pursue a more “social” and “useful” field while still being a mathematician (Wilson 2021). After “hawking” himself around Oxford to secure a research position that could enable him to transition from the physical sciences to the social sciences (Kelly 2003)—and a series of rejections along the way (Wilson 2021)—he took a different route, accepting an elected position as Labour Councillor in Oxford. As he notes about that job, it “was an important early experience for me, functioning in a political environment, convinced that it was possible to change things for the better” (Reisz 2017). Wilson then successfully landed a research-oriented appointment at the Institute of Economics and Statistics in Oxford to work with a transport group comprised of economists, marking another turning point in his professional journey, setting in motion his career in regional science. After two years in this role, he went on to serve as Head of the Mathematical Advisory Unit, Ministry of Transport (1966–1968). On being hired as a mathematician rather than a social scientist, Wilson remarked, “The civil service flew into a flap because he couldn't be admitted as an economic adviser because he wasn't officially an economist. They asked me what I was. I said a mathematician. So they made me a mathematical adviser…” (Kelly 2003). Wilson then served as Assistant Director of the Centre for Environmental Studies in London (1968–1970). In 1969, Alan Wilson founded the journal Environment and Planning A, serving as an editor until 1991, and since then, as Honorary Editor.

In this phase of his career, Alan Wilson’s passion for urban modeling and planning—and reputation as a regional scientist—began to blossom and take off. At the Institute of Economics and Statistics, he “was given the job of modeling person flows, such as the journey-to-work, in cities” (Wilson 2021), which was a valuable and inspirational experience for him. As he notes about the job, “The deal was that I did all their maths and computing, and they taught me economics along the way! I was lucky enough to solve a problem that was waiting to be solved—how to model transport flows in cities—and I was accepted as a social scientist” (Reisz 2017). Reflecting on what he had learned about the physics of gases, Wilson developed the idea of using entropy maximization to model trip distribution—i.e., the allocation of travelers between origins and destinations. The work took him only a couple of weeks, an effort well worth it, as it launched “his name internationally in a field he had only just entered” (Kelly 2003). At the Ministry of Transport, Alan Wilson had an opportunity to apply this framework in a real-world context, specifically to the United Kingdom. In his role at the Centre for Environmental Studies, he was given “the freedom to shift towards attempting to build a comprehensive urban model,” which, he has said, “ended up being a life’s work!” (Wilson 2021).

Alan Wilson’s professional journey then branched off in a different but related direction. In 1970, he was appointed Professor of Urban and Regional Geography at the University of Leeds, a quite impressive feat given that he did not have a geography degree or a Ph.D. While at Leeds, he was “one of a small number of academics with a genuinely international reputation.” He also served as Pro-Vice Chancellor (1989) and Vice Chancellor (1991–2004) at the university. In this administrative capacity, he was highly successful, increasing enrollment and research income in magnitudes or order (Grombrich and Oléron-Evans 2019). Wilson had essentially transformed the university from a “sleepy and underfunded” institution to a vibrant and prosperous epicenter of intellectual and scholastic activity (Riesz 2017).

In the late 1980s, Alan Wilson (with geographer Martin Clarke) founded the company Geographical Modeling and Planning (GMAP) Ltd., which used entropy-based modeling to advise retailers on where to locate their stores. It ended up being one of the most successful ventures to spin out of Leeds University. The company had “major blue-chip clients,” including “Ford, Exxon/Mobil, BP, Barclays, Sainsbury’s, Asda, Thomas Cook, and HBOS” and was “the largest geographical consultancy in the world” at the time (Clarke 2009).

In 2004, Alan Wilson once again altered his career trajectory, accepting the appointment of Director-General for Higher Education in the United Kingdom. Not only was he the first to serve in this post, but he broke the mold of a typical politician. As Kelly (2003) wrote soon after Wilson took the job, “In Wilson, the government will have an adviser who, for once, does not spring from that cadre of bureaucrats who have little working knowledge of poverty.” Alan Wilson played a “critical role in the government’s drive to promote inclusion and diversity in higher education” during his term. In this regard, he was highly successful. For instance, he was responsible for establishing the Office for Fair Access, which opened new avenues for underserved communities to access a college education. Wilson was also instrumental in cutting “red tape” in the UK government (Riesz 2017).

In 2006, Alan Wilson briefly returned to his alma mater, Cambridge, at Corpus Christi, after being elected Master of the school. One year later, he joined the spatial complexity powerhouse, the Centre for Advanced Spatial Analysis (CASA) at University College London (UCL), as Professor of Urban and Regional Systems. In this period, Wilson also served as Chair of the Arts and Humanities Research Council (2007–2013), Chair of the Home Office Science Advisory Council (2013–2015), and Chair of the Lead Expert Group for the Government Office for Science Foresight Project on The Future of Cities.

From 2016 to 2018, Alan Wilson served as founding CEO of the Alan Turing Institute. He was then appointed Executive Chair of the Ada Lovelace Institute, where he is now actively involved in leading research teams in big data, machine learning, and artificial intelligence (Gombrich and Oléron-Evans 2019). Emphasizing the importance of convening different people and perspectives to advance data science in a transformative, ethical, and inclusive way, Alan Wilson remarked after joining the Ada Lovelace Institute that:

A key component of the Institute’s mission is to convene diverse voices to create a shared understanding of ethical issues in data and AI, and my first priority as Chair will be to recruit a Board that reflects this diversity. We are seeking people from different sectors and disciplines to set the strategy and remit of the Ada Lovelace Institute and to actively participate in its work. The Board will connect academic fields such as philosophy, data science, and social science, with civil society and public deliberation, policy and regulation, and international perspectives.¹

In recognition of his impressive scholarly and professional achievements and successes, Alan Wilson has received numerous awards, medals, and honors. He is a Fellow of both the distinguished Royal Society and the British Academy and was awarded the Laureate d’Honneur by the International Geographical Union and the Prize in Regional Science by the European Regional Science Association (ERSA). In 2001, he was knighted by the Queen of England, approximately three centuries after the first scientist to be bestowed that honor, Sir Isaac Newton.

3 Research Trajectories, and Transitions

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

—Sir Isaac Newton

Like his professional journey, Alan Wilson’s research trajectory is characterized by well-defined transitions and phases that build on each other. In chronological order, these areas generally include the modeling and analysis of (1) bubble chamber events, (2) spatial interaction and location behavior using entropy maximization and mathematical optimization, (3) complex urban structure and dynamics using nonlinear dynamic equations, dynamic systems theory, and microsimulation, and (4) global networks and comprehensive urban systems using big data, machine learning, and other related analytical tools. Wilson has also written extensively about higher education, urban and regional planning, and science philosophy. The word cloud in Fig. 1 highlights the evolving and expanding universe of Alan Wilson’s areas of interest in greater detail.²

Fig. 1

Evolving and expanding universe of Alan Wilson’s research

3.1 Entropy Maximization, Spatial Interaction Modeling, and Location Analysis

If I have seen further than others, it is by standing upon the shoulders of giants.

—Sir Isaac Newton

The 1950s ushered in the era of large-scale urban transport and land-use modeling, particularly in the USA. In this context, the gravity model adapted from Newton’s law of gravitation, as well as the intervening opportunities model and “back-of-the-envelope” approaches (i.e., lookup tables and diversion curves), was en vogue, used as the primary vehicles for predicting the flows of people and goods within cities. Yet, there was no consensus on which theory or method was most appropriate, nor on specific questions about how to incorporate the effects of policies, appropriately calibrate the deterrence function to account for distance decay, and disaggregate the framework to account for the varying characteristics of trips and individuals (Williams 2019). Moreover, as Alan Wilson noted, there was a mathematical inconsistency in the gravity model. Specifically, it did not “conform to the method of bounds,” and it could “generate nonsense predictions,” such as more people traveling to a destination than realistically possible. Thus, the equations required “fudge factors” to get the right answers, corrections that he recognized from “the statistical mechanics of gases” (Kelly 2003). Wilson also had concerns about the gravity model lacking a behavioral foundation (Clarke 2009).

In the mid-1960s, Alan Wilson set out to develop an analytical framework that could address these issues and shortcomings (Clarke 2009). In doing so, Wilson was influenced by complexity scientist Warren Weaver. Weaver (1948) distinguished between three types of problems or systems: simple, disorganized complexity, and organized complexity, suggesting the appropriateness of methods for analyzing each type of system. Alan Wilson saw large numbers of people moving around in a city, such as via commuting activity, as interacting only weakly, constituting a system of disorganized complexity. Thus, according to Weaver (1948), statistical mechanics and probability theory were the most appropriate means for modeling such phenomena (Wilson 2021). Wilson was also inspired by economist and regional planner Gerald Carrothers, who provided a “germ of the idea,” but one that had not been acted upon (Wilson 1972). Carrothers (1956) wrote:

The behavior of molecules, individually, is not normally predictable, while in large numbers their behavior is predictable based on mathematical probability. Similarly, while it may not be possible to describe the action and reactions of the individual human in mathematical terms, it is quite conceivable that interactions of groups of people may be described in this way.

Another source of inspiration came from Edwin Thompson Jaynes and others (see, e.g., Jaynes 1957), who were applying entropy maximization to various problems outside of physics (Wilson 2021).

The stars aligned, and Alan Wilson had a “eureka” moment. He realized that the gravity model’s balancing constraints were analogous to partition functions from statistical mechanics. Using Boltzmann methods and maximizing an entropy function, Wilson formulated a spatial interaction framework that remarkably addressed all the concerns raised about the gravity model and other approaches being used for transportation and land use planning at the time (Williams 2019). Wilson had creatively applied the “laws that predict the average behavior of atoms to the average behavior of the population of cities” (Kelly 2003).

In 1967, Alan Wilson unveiled his entropy-based spatial interaction model (SIM) in “A Statistical Theory of Spatial Distribution Models” using trip distribution as an archetypal illustration (Wilson 1967). This paper, which has ended up being one of his most cited manuscripts, was published on a whim (without peer review) in Transportation Research to fill a gap in the journal’s first issue (Wilson 2021). A few years later, Wilson demonstrated that an entire family of spatial interaction models could be derived from entropy maximization through accounting principles and mere adjustments of the production and attraction constraints (Wilson 1971). The singly constrained model was significant for regional science in that it added a “locational dimension to the spatial interaction model” (Wilson 2010a, b).

Wilson’s early work on entropy maximization was summarized in the book Entropy in urban and regional modelling, which is recognized as a classic and trail-blazing book in regional science (Waldorf et al. 2004). As Gould (1972) wrote soon after its publication, “The book not only presents an extraordinarily valuable approach to solving relevant spatial and social problems at the very time we need every approach we can muster, but stands as one of the most imaginative and thought-provoking works in geographic literature.” In another monograph, Urban and Regional Models in Geography and Planning (1974), Alan Wilson gave a “much more complete account and organized the field’s technical apparatus.” In his review of the book, Michael Batty wrote: “Alan Wilson is an acknowledged master of the field and his individuality, brilliance and style are stamped on this book, like on all of his works. He is bringing to urban studies what people like Chomsky have brought to Linguistics and Rashevsky to mathematical biology and this book is worthy of his contribution” (Batty 1975).

Alan Wilson’s entropy maximization framework brought many innovations in urban and regional modeling, planning, and evaluation (Boyce and Williams 2015; Williams 2019; O’Kelly 2010). First, it improved spatial interaction and transportation models by introducing:

• 1. “balancing” factors related to the Lagrange multipliers in optimization, which translated to standard accessibility indices

• 2. a generalized cost function for characterizing spatial separation between origins and destinations (going beyond simple distance-based metrics) and that can capture travelers’ perceptions of impedance

• 3. a negative exponential function of generalized cost to capture friction decay

• 4. the capacity for disaggregation by types of activities and groups and different levels of spatial resolution.

Additionally, entropy maximization was found to be consistent with utility maximization, thus providing a behavioral foundation to the method (Wilson 1971; Reggiani et al. 2021). Moreover, as a statistical averaging or probability maximizing process, the method was consistent with Bayesian inference and, accordingly, could be used in situations where there is a paucity of information or data (Wilson 1970). Thus, Wilson’s entropy maximization framework provided a statistically grounded, theoretically based, and policy-sensitive method (Williams 2019), creating new and expanding opportunities for urban regional modeling and analysis.

Indeed, the work was revolutionary in both a practical and scientific sense. It catalyzed a paradigm shift in “theoretical and methodological perspectives on spatial flows in cities,” essentially replacing sole use of Newtonian principles for spatial interaction modeling, much like how Newton’s physics paradigm upended the view of the world developed by Aristotle thousands of years before him. Furthermore, similar to how Newton’s cosmological synthesis provided a universal and unifying exposition of the earth and the cosmos enabling others to stand on his shoulders (including regional scientists!), entropy maximization was an integrated and versatile foundational methodology upon which other creative individuals could build. As Wilson himself notes, entropy maximization “opened up a set of ideas that could be applied more widely … it was a high-level methodology that had applications in many disciplines” to address a spectrum of problems (Wilson 2010a). Entropy maximization was also germane to a “wide range of SI phenomena” and “person movements for different reasons—e.g., commuting, migration, goods movement, telephone calls, marriage selection, newspaper circulation, bank cheques, and spread of innovation,” and frankly, any system involving spatial interaction and location behavior (Wilson 1971).

As Morton O’Kelly wrote about Wilson’s book Entropy in urban and regional modelling: if it “was an initial stock offering, the original units would now have split many times and the original investors no doubt handsomely rewarded!” (O’Kelly 2010). In fact, many Great Minds (including Alan Wilson) have built on the method, contributing to various theoretical and methodological advances, including “extensions of the core model, links to mathematical programming, the relationship to economics, and the introduction of a dynamic spatial structure hypothesis” (Wilson 2010a). Moreover, Wilson’s entropy maximization framework has been applied in various domains, disciplines, and contexts, including geography, transport, urban studies, economics, business, migration, criminal justice, defense, security, international trade, education, archeology, history, economics, healthcare policy, and political science. It has even been referenced in the computational mechanics literature on modeling stress distributions in rocks (see, e.g., Mishnaevsky 1998).

Figures 2 and 3 provide visual perspectives of the “offspring” of Alan Wilson’s entropy maximization framework based on citations to his book Entropy in urban and regional modelling. Figure 2 highlights individuals who have referenced Wilson’s book, while Fig. 3 shows journals in which these individuals published. In each case, only the giant component—the largest connected subgraph—is shown. The colors (shown in the online version only) reflect communities of authors and journals, and the sizes of the nodes indicate the number of times an author or journal has referenced the book.

Fig. 2

Main offspring of Alan Wilson’s entropy maximization framework (Authors)

Fig. 3

Main offspring of Alan Wilson’s entropy maximization framework (Journals)

3.2 Evolutionary Dynamics of Complex Urban Systems

An object in motion tends to remain in motion along a straight line unless acted upon by an outside force.

—Sir Isaac Newton

In the late 1970s, Alan Wilson began to shift gears, reorienting his focus from fast dynamics in cities to longer-term urban evolution and the “spatial distribution of people and organizations and corresponding physical structures”—or slow dynamics (Clarke and Wilson 1983). At this juncture, he was also determined to develop a “kitbag of techniques” that “could be useful in real-world settings”—from business to planning (Clarke 2009). Part of his motivation to go off in this direction was to address a growing number of criticisms of large-scale urban modeling, including that such models were not practical or accessible (Clarke 2009). Additionally, accelerating improvements in computing capabilities made using microsimulation, cellular automata, network analysis, agent-based modeling—and computer-simulated solutions to large models—feasible, enabling a shift from simpler to more complex urban modeling.

Wilson’s first major contribution in this area (with urban planner Britton Harris) was to demonstrate how the exemplar problem of retail location could be embedded in a dynamic equilibrium framework (Harris and Wilson 1978). Once again, he was influenced by Weaver (1948). Specifically, Wilson saw retail competition as a problem of organized complexity, in which retail outlets are interacting strongly to compete for customers and revenue. Thus, the appropriate methodological foundations for modeling such phenomena were not in statistical mechanics but instead in applied nonlinear dynamics (and differential equations) (Harris and Wilson 1978), tools that Sir Isaac Newton had developed and used centuries before Wilson to characterize spatial dynamics in our universe. Wilson also saw an analogy with the prey-predatory problem, particularly that “species competing for resources were similar” to retailers’ rivalry and competitive behavior, thus making Lotka-Volterra (L-V) equations a suitable basis for model formulation. This work was significant in that it demonstrated that “nonlinearities and interdependencies can lead to bifurcation properties in system development” and, consequently, “the possibility for multiple equilibria” in urban models. It also marked the beginnings of “a method for modelling the evolution of cities, using the urban analogue of the equivalent issue in developmental biology” (Wilson 2018).

Wilson (with geographer Martin Clarke) then moved on to modeling cities in disequilibrium, recognizing that “systems of organized complexity tend to be out of equilibrium because the interacting subsystems each have different rates of change” (Clarke and Wilson 1981; Harris and Wilson 1978). This work’s analytical and mathematical underpinnings were in dynamic systems theory and catastrophe theory, as summarized in his book Catastrophe theory and bifurcation: applications to urban and regional systems (Wilson 1981). Beginning again with retail location as an archetypal example, Wilson demonstrated how complex interdependencies between urban subsystems introduce “new bifurcation properties, which can lead to transitions at critical values of new parameters from stable solutions to periodic solutions” (Wilson 1981; Clarke and Wilson 1983, 1985). Thus, slight parameter changes could “flip systems from one state to another,” leading to profoundly different urban dynamics and structures (Clarke 2009). During this phase of his research, Wilson also showed how a dynamic systems approach could be integrated with other methods such as spatial interaction modeling and microsimulation to model interrelated urban subsystems, including agriculture, industrial location, retailing, residential location, housing (Clarke and Wilson 1985).

Later, Wilson re-connected with statistical mechanics and thermodynamics. He realized that Boltzmann’s methods could be applied to a broader range of systems and disciplines than what was recognized at the time (Wilson 2008). He demonstrated how Boltzmann techniques and Lotka and Volterra (BLV) equations could be integrated to model spatial interaction and structural evolution, providing a richer modeling framework than that based on scale-free networks (Wilson 2009). Additionally, recognizing that the “use of Ising models in physics represented a kind of locational structure problem” with dynamics in the form of phase transitions, Wilson developed a set of analytical frameworks for modeling discontinuous change and related dynamics in urban systems (Wilson 2009). These models, along with visualization techniques, provided planners with the tools for assessing how to “avoid undesirable phase transitions” or how to “invest bring about desirable ones” (Wilson and Dearden 2011).

Alan Wilson was instrumental in bringing microsimulation—including in a Geographic Information System (GIS) context—to regional science. According to Wilson, analytical methods are not appropriate for modeling certain kinds of systems, particularly those for which “there is a lot of heterogeneity amongst components”—e.g., in healthcare systems involving patients with different characteristics and needs. In such situations, systems should ideally be modeled from the bottom up.

4 The “Wilsonian” Philosophy

We are certainly not to relinquish the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple and always consonant to itself.

—Sir Isaac Newton

As highlighted, Alan Wilson has an affinity and flair for solving complex problems. His philosophy of science, which he began to nurture and articulate in the early stages of his career (Wilson 1968, 1969a, b, 1972) and continues to follow religiously, is essentially a grand roadmap for problem-solving. In Knowledge power: Interdisciplinary education for a complex world, he summarizes key aspects of this philosophy, referred to here as the Wilsonian philosophy. In essence, it is a framework—or “intellectual toolkit”—for engendering the capabilities—or “knowledge power”—to address complicated and seemingly intractable problems within and across systems, disciplines, and domains—from research to education to planning and beyond (Wilson 2010b). In this regard, super-concepts that transcend disciplinary boundaries are crucial for developing the breadth and depth of knowledge necessary for tackling complex problems, as are generalized frameworks and models for addressing generic issues—i.e., super-problems.

The Wilsonian philosophy exploits concepts and theoretical principles from complexity as a strategy for handling difficulty and complexity. Thus, to address problems, a dynamic, systems approach is in order, precisely one that encompasses the following³:

• 1. Systematic and algorithmic approaches, coupled and integrated with abstraction, artistry, and inquisitiveness (coding, computation, creativity, curiosity)

• 2. Diversity of methods, perspectives, and strategies along with sensing mechanisms to promote desirable phase transitions and avoid negative ones (control, consciousness)

• 3. Sharing of knowledge across and between different groups (i.e., policymakers, planners, politicians, researchers, administrators, business persons, educators, and citizens), fields and disciplines, and even humans and machines! (communication, coordination, collaboration)

• 4. Lifelong learning to facilitate knowledge accumulation, pattern recognition, and situational awareness (cognition, classification, culture).

Alan Wilson stresses the importance of abstract thinking, including analytical and symbolic reasoning, along with systematic and algorithmic approaches, for framing issues and understanding problems and systems through model-building, testing, analysis, and evaluation. As a scientific method, he favors hypothetico-deductive reasoning, which uses theory and abstraction to develop mathematical models that can be used for systematic testing to draw inferences about a specific example. In particular, Wilson believes that the “the essence of scientific activity is the making of hypotheses or theories and the testing of predictions of these against empirical information and observations” (Wilson 1972), in contrast to the Newtonian inductive approach, which draws broad generalizations through statistical testing on specific examples or observations. As he points out, it is impossible to “derive general truths from facts,” as Newton’s method seems to imply. Theories only represent “the best approximation to truth at any time” and are, therefore, always subject to change and the possibility of being invalidated altogether (Wilson 1972).

In fact, Alan Wilson can be credited for bringing the hypothetico-deductive approach to regional science, particularly at the height of the quantitative geographic revolution. At the time, he argued that geographers were placing far too much emphasis on inductive reasoning and empirically driven, statistically based research. Thus, they were disusing “imagination, invention, deduction, and the various other mental faculties that contribute to the attainment of a well-tested explanation.” Quoting Davis and Johnson (1909), Wilson remarks, it is like “walking on one foot, or looking with one eye, to exclude from geography the ‘theoretical’ half of the brainpower, upon which other sciences call as well as the ‘practical’” (Wilson 1972). At the same time, he does not advocate for the complete dismissal of the inductive approach; both types of reasoning are essential elements of the toolkit to be used appropriately (Wilson 2010b).

Wilson’s “process of invention” provides a recipe for developing universal analytical frameworks that can be modified to address and study particular problems at hand. The process begins with a “good idea”—an analogy from another field or discipline, which he notes requires “exercises of creative imagination of the highest order,” although he recognizes that ingenuity is not easily or automatically manufactured. (As he points out, we do not even yet fully understand how such processes work and transpire in the human mind!). The next step is to engage model builders from another field or discipline and apply the model to a new context. The last stage is to modify models through disaggregation and shifts in scale or level of resolution, where the nature of the problem under consideration dictates an appropriate lens—e.g., modeling a household or a neighborhood or sector versus an entire transportation and land system in a city.

While indeed the use of analogies and metaphors in the regional sciences has a long tradition (e.g., Newtonian laws of gravitation for modeling spatial interaction), Alan Wilson can be credited for popularizing and expanding their utilization for urban modeling and planning (Sui 2010). Wilson believes that analogies are not only essential for developing novel ideas and solutions, but they also provide a critical link to urban systems modeling. Here, he distinguishes between direct and formal analogies, where the former applies to systems with common physical characteristics and the latter to situations where “there are similarities of form, but not of physical characteristics.” Formal analogies are the basis of systems science, thus providing the foundations and motivation for dynamic systems approaches in urban planning (Clarke and Wilson 1985).

However, as Wilson emphasizes, it is critical to exercise caution when transferring concepts, methods, and theoretical principles from the natural sciences to the social sciences. In regional science, analogies must be framed in relevant geographic and spatial economic theory and offer new interpretations of existing theories of cities and regions (Wilson 1969a, b). Moreover, models borrowed from other fields must be tailored to the particular problem being modeled or analyzed which. At the end of the day, the analogy must be tossed out, and one should arrive at concepts that cut across disciplinary boundaries—i.e., “super-concepts.” According to Wilson, entropy is one of those super-concepts. Specifically, entropy maximization is not a “strict” analogy from physics but rather a higher-level model and conceptual frame of reference that can be applied broadly across disparate disciplines and contexts (Wilson 2021).⁴

The Wilsonian philosophy emphasizes the vital role that technology (especially the computer) plays in understanding and solving complex problems across different domains. In this regard, it is imperative to always be on the frontier of new computing capacities and capabilities, to assess and exploit what can be done with the state of technology at any point in time. Modeling large, complex systems requires using computers for simulation purposes and solving the equations, as opposed to simpler systems, which are handled analytically in algebraic or other terms (Wilson 2010a, b). However, Wilson does not view computers as mere calculating machines; computers also provide a powerful mode of communication and artistry. For example, with the advent of Geographic Information Systems (GIS) in the 1970s, he immediately saw the potential of computerized mapping to visualize the inputs and outputs of analysis and modeling, ultimately making them more palatable and compelling to end-users. Moreover, according to Wilson, computer-based visualization is also a way to “see” cities and regions in ways not possible with the raw data alone. As he remarks, “A colour map is worth a thousand lines of code!” In all these ways, “there is a critical interaction between computer power and mind power”—i.e., human–machine synergy, is a dimension of knowledge power (Wilson 2010b).

One of the primary tasks of the planner is to anticipate and control the trajectory of a system of interest—e.g., a city or institute of higher education. Yet, this poses an array of challenges, especially for systems of organized complexity, which are subject to path-dependent processes, nonlinearities, and phase transitions, artifacts that are difficult to predict. Additional challenges relate to the fact that the same events do not recur over time in social and economic systems, unlike natural systems where similar events are repeated, making their future paths easier to anticipate.

As maintained by Alan Wilson, modeling and visualization are essential tools for understanding and managing these complexities and ultimately steering the course of a system in a desirable direction. In particular, models enable one to conduct “what if” forecasting scenarios to assess how different interventions might impact the structure and dynamics of a system. Through sensitivity analysis, it is possible to assess the spectrum of possible outcomes given different parameter settings and initial conditions and generate what Wilson refers to as “possibility cones,” an idea inspired by hurricane prediction cones. For urban planning, the “DNA” of a city can be used “to explore and visualize the possibilities of transition given the structural starting point,” which, as Wilson notes, is a sort of “genetic medicine’ approach” (Wilson 2009). This tactic is beneficial in that it limits the “space of development possibilities by focusing on a set of starting conditions.”

According to Wilson, cyberneticist and psychologist Ross Ashby’s Law of Requisite Variety, which specifies that the controlling system “must have at least as much variety as the system it is trying to control in order to be effective,” provides additional insight on how to manage complex systems (Wilson 2010b). In this regard, a maximum diversity of approaches—integrating “the best of the ideas from this variety”—is imperative, especially for ensuring that “a variety of attacks on problems is possible” (Wilson 1968). Further, inspired by the work of neuroscientists Karl Friston and Klaus Stephan, Wilson envisages the planning system as a human brain. He argues that planners can intervene in an urban system to promote desirable outcomes, similar to how the brain minimizes free energy to avoid phase transitions (Wilson 2009; Deardon and Wilson 2011). Combining this idea with Ashby's Law, he concludes, “If the brain is replaced by ‘urban planning system’ and its environment by ‘the city,’” then “the planning system has to model the city in order to have a chance of success”—i.e., modeling is key to effectively controlling a complex, urban system (Wilson 2009). Moreover, as Wilson observes, Ashby’s Law of Requisite Variety and Friston’s free energy model are two sides of the same coin: They both come down to entropy maximization!

Finally, the Wilsonian philosophy stresses the importance of coordination, collaboration, and communication between all partners in the “knowledge space” (i.e., scientists, educators, administrators, planners, policymakers, politicians) (Wilson 2010b). Each entity has unique knowledge to bear, and thus through the exchange of knowledge, the knowledge power of each entity can be maximized. Planners must have a solid understanding of policy to articulate objectives and decide what the planning process should ultimately achieve (Wilson 1968). Planners and policymakers should be cognizant of the political process, as it dictates what plans are eventually implemented (Wilson 1968). In this respect, performance indicators are helpful; they provide a way for communicating effectively with politicians to argue for the best alternatives (Wilson 1968). There should also be a two-way exchange between researchers and planners, both of whom have an action focus. Research is necessary for stimulating innovations in modeling, and planning provides a real-world laboratory for testing and evaluating models (Wilson 1968). Lastly, educators play a crucial role in the entire system, especially in shaping the minds of future regional scientists and practitioners by providing them with the skills and tools, along with the creative capacities necessary for solving complicated problems through knowledge power (Wilson 1968, 2010b).

5 Concluding Remarks

In one person he combined the experimenter, the theorist, the mechanist—and, not the least, the artist in exposition.

—Albert Einstein writing about Newton

Alan Wilson is a gravitational force in regional science. He is a great attractor, bringing together ideas and people to advance our knowledge of cities and regions and enhance our ability to analyze, model, and predict such systems, not unlike how Sir Isaac Newton integrated and unified the body of knowledge at his time, revolutionizing our understanding of the celestial and terrestrial worlds and our capacity to model such phenomena mathematically. However, contrary to Newton, who quipped, “I can calculate the motion of heavenly bodies, but not the madness of people,” Alan Wilson has expanded our ability to model “people in motion,” especially in an urban and regional context.

Indeed, Alan Wilson is a person of many talents, including those of an artistic and creative nature. He is a polymath with breadth and depth of knowledge and insight across and within a spectrum of disciplines, domains, and contexts. He has an insatiable curiosity about cities and regions—how they work, how they can be modeled, and how they can be disrupted in ways that advance societal interests. He also exhibits determination and perseverance in all of his endeavors. These are the traits common to all Renaissance Men in history (Elfmar and Griffiths 2012)—from Aristotle to Sir Isaac Newton to Ada Lovelace to Albert Einstein to Alan Turing. Accordingly, Alan Wilson is aptly referred to as a Renaissance Man in Regional Science.