THINKING OUTSIDE THE BOX: KNOWLEDGE POWER

1. THINKING OUTSIDE THE BOX: KNOWLEDGE POWER Alan Wilson Centre for Advanced Spatial Analysis University College London

2. Two objectives for the seminar • To make some general observations about generating good ideas as a researcher – and in particular, ‘thinking outside the box’ • To offer some specific examples from personal experience • Invite everyone to transpose the general argument into their experience

3. KNOWLEDGE POWER • where does knowledge power come from? • academic disciplines • combinations of disciplines - interdisciplinary work – often inhibited by the social coalitions, especially in the sciences • practical experience

4. the power derives from: • concepts and theories • superconcepts that transcend disciplines • capabilities – for handling difficulty and complexity • systems thinking – beyond reductionism • capabilities for handling complexity • problem-solving, issue-resolving capabilities • analysis, design and policy capabilities

5. intuitively this suggests that we need depth and breadth • THINKING OUTSIDE THE BOX involves some kind of ‘breadth’ • are there superconcepts which can help us with the development of knowledge power? • how can we assemble an intellectual toolkit that gives us knowledge power? (A very individual thing of course.)

6. BUILDING AN INTELLECTUAL TOOLKIT • one personal view • think of authors who have particularly influenced you and who become part of your toolkit • learn to identify superconcepts and generic problems • know something about most disciplines? • examples from my own experience follow

7. Weaver’s classification of problems • Weaver (of Shannon and Weaver) was Science VP of the Rockefeller foundation in the 50s; he wanted to think through where the Foundation should be investing; in a very perceptive way he argued that there were three kinds of problem: • simple • of disorganised complexity • of organised complexity • and that the biggest challenges for science would be the third ...and how right he was – so locate your problem on that spectrum – a super concept perspective

8. Newton’s Law of Gravity – Weaver - 1 Yij = KXiZj/cij2 • “simple” because essentially a two-body problem • was used in transport modelling in the 1950s

9. Boltzmann’s entropy – Weaver - 2 S = klogW • mostly seen as the basis of the second law of thermodynamics – essentially statistical physics – works for gases because of statistical averaging • transport modelling in cities: in the 50s: being treated as a Newtonian system • shift to a Boltzmann perspective – and the averaging works brilliantly. the models work • achieved through (a) a change of perspective, Weaver-style-disorganised systems and (b) taking a concept – entropy – from an entirely different discipline

10. Boltzmann with Lotka and Volterra – Weaver - 3 • NB: the power of combination here • Physics: • classical gases - Boltzmann • lattices – generalised modelling methods • Geography • transport flows (Boltzmann) • the evolution of cities – and a shift now to complex systems (B and L-V) • Boltzmann fast dynamics combines with Lotka-Volterra slow dynamics

11. Biology and epidemiology • L-V and virus populations • Ecology • dealing with space: L-V with B-flows added • Economics • consumer and retailer behaviour (B) • retail structure and dynamics (L-V) • evolutionary and complex economics • the physical chemistry of mixtures

12. what are the common features? • retailers competing for customers • viruses competing for targets and resources • species competing for resources • industries (e.g.) competing for both resources and markets • chemicals competing for energy

13. A CURRENT EXAMPLE: NETWORK ANALYSIS • There has been an explosion of interest in the study of the evolution of spatial structures, particularly of so-called scale free networks (SFNs)[1]. Using the ideas above, we can show that the BLV methodology is under-used by researchers in this area and facilitates further development.

14. We need to bring together the concepts of equilibrium statistical mechanics to model flows (Boltzmann) and hypotheses to represent dynamics, building on Lotka and Volterra, together with a more general representation of networks. Given these historical associations, the integrated models can be characterised as ‘BLVN models’.

15. The SFN literature appears to be based almost wholly on a topological approach that characterises networks as a single set of nodes and a corresponding set of edges. The measure of spatial structure is the distribution of N(k), the number of nodes connected to others by k edges. (A measure of clustering of nodes is also sometimes used.)

16. Figure 1

17. The more general characterisation used in urban science employs three sets of nodes: • a set {i} that can represent the origins of some activity • a set {j} that can represent destinations • and an underlying network with nodes {h} and edges {e} that carry the interactions or flows between origins and destinations.

18. Figure 2

19. Prominence is then given to the modelling of real networks in space. The deployment of BLVN methods in urban and regional geography is well established[2] and it has recently been shown that they can be extended into ecology[3]. This perspective and the associated models have been largely neglected by scientists from other disciplines working in network analysis.

20. To fix ideas, consider the origin nodes to be centroids of zones which are residential areas of a city, the destination nodes to be retail centres, and the network to be an urban transport system – a mixture of roads and separate public transport links. There is then, potentially, an interaction, {Yij}, between each origin zone, {Xi}, and each destination zone, {Zj}, measured, for example, as either a flow of people or a flow of money spent in retail centres.

21. For simplicity, consider the flows of people. These flows are then carried on the underlying network. The flow from i to j will be carried on one or more routes of the network – subsets of {h} and {e}. One measure of the significance of a retail centre is then the sum of the flows into it, and this is potentially much more sensitive than a count of ‘edges’.

22. Yij Xi Zj Figure 3

23. It can be shown[6] that by maximising an entropy term – the Boltzmann part of the argument – S = klogW - subject to suitable constraints, Yij = AiXiZjαexp(-βcij) (1) where Ai = 1/ΣkZkαexp(-βcik) (2) We can now calculate the total inflow into each j: Dj = ΣiYij (3)

24. A key point is that modelling flow totals into nodes gives a much richer picture of spatial structure - and this in turn is a broader notion than ‘network’ structure.

25. We now consider the {Zj} changing on the basis of a ‘slow dynamics’ hypothesis. The flows into j have been attracted by a pulling power, Zjα. We can now hypothesise that if Dj > Zj, then Zj should grow, and vice versa[7]: ΔZj = ε(Dj – Zj)Zj (4) • for a suitable parameter, ε. These equations are recognisably related to the Lotka and Volterra equations, albeit in this case, with the ‘populations’ being spatially distributed but a single species.

26. The key variable which is used in SFN analysis is the number of edges at each node and p(k) is taken as the probability that a node has k-edges connected to it. • It is found empirically that this distribution often takes the form of a power law, p(k) = k-γ, for some parameter γ. The ‘network’, in this case, can be considered to be equivalent to either our {i} or {j} sets. • For definiteness consider the {j} set. Then if we measured Zj by the number of edges – which might be flows above some threshold – at j, then the size distribution of the Zj, say P(Z), would be equivalent to the p(k) distribution.

27. However, the ‘flows’ form the basis of a much richer concept and there is a method for then articulating network structure[4][5]. The dynamic model that represents the evolution of centres, the {Zj}, can be seen as a network generator and as the basis for SFN modelling. • The BLVN formulation can offer explanations for the spatial structure and the size distribution (and this is typically not the case in the SFN analysis); and, potentially, the basis of a power law. • There is a wide range of application that embraces many scale-free networks but locating them within a richer methodology.

28. There are many possible applications. These are wide-ranging in all aspects of urban and regional analysis[10] and there are examples in demography[11], economics[12][13] and ecology[14]. • There is huge potential in all areas of the scale-free networks’ enterprise: epidemiology[15], chemistry[16], physics[17], biology[18], geomorphology[19] and the world-wide web[20][21]. There is a tremendous programme of further exploration to be implemented.

29. CONCLUDING COMMENTS • while most of you are properly and fully rooted in your own disciplines and tool kits, I am arguing that you could find it fruitful to explore concepts and problems elsewhere • there is a continual tension between breadth and depth. If you are doing research, then depth is the key; if you want to expand your capability to be original, then a touch of breadth is a good thing! • that is what the knowledge power idea is about!

30. Super concepts • I have a list of around 60......some more ‘super’ than others • system, system representation, location, interaction, accounts, scales, hierarchy, information, flight simulators, conservation principles, optimisation, pattern recognition, networks, entropy, equilibrium, critical points, initial conditions, path dependence, emergence, microsimulation • What would your own examples be??

31. Final comment: Weinberg on research – “Be ambitious”! • “No one knows everything, and you don’t have to”. Jump in, sink or swim.....pick up what you need as you go along • “While you are swimming and not sinking, aim for rough water....go for the messes”. • “...forgive yourself for wasting time”. Supervisors may not like this, but it’s saying that if you’re being ambitious, you’ll have to explore territory which sometimes turns out to be unfruitful • but your growing intellectual toolkit will help you to navigate

32. References. • [1] Newman, M., Barabasi, A-L, Watts, D. J. (2006) (eds.) The structure and dynamics of networks, Princeton University Press, Princeton, N. J. • [2] Wilson, A. G. (2000) Complex spatial systems, Addison-Wesley-Longman, Harlow. • [3] Wilson, A. G. (2006) Ecological and urban systems models: some explorations of similarities in the context of complexity theory, Environment and Planning, A, pp. 633-646. • [4] Nystuen, J. D. and Dacey, M. F. (1961) A graph theory interpretation of nodal regions, Papers, Regional Science Association, 7, pp. 29-42.

33. [5] Rihll, T. E. and Wilson, A. G. (1987) Spatial interaction and structural models in historical analysis: some possibilities and an example, Histoire et Mesure II-1, 5-32. • [6] Wilson, A. G. (1970) Entropy in urban and regional modelling, Pion, London. • [7] Harris, B. and Wilson, A. G. (1978) Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models, Environment and Planning, A, 10, 371-88.

34. [8] Wilson, A. G. and Oulton, M. J. The corner shop to supermarket transition in retailing: the beginnings of empirical evidence, Environment and Planning, A, 15, pp 265-74, 1983. • [9] Clarke, M. and Wilson, A. G. (1985) The dynamics of urban spatial structure: the progress of a research programme, Transactions, Institute of British Geographers, NS 10, 427-451. • [10] Birkin, M., Clarke, G. P., Clarke, M. and Wilson, A. G. (1996) Intelligent GIS: location decisions and strategic planning, Geoinformation International, Cambridge.

35. [11] Rees, P. H. and Wilson, A. G. (1977) Spatial population analysis, Edward Arnold, London. • [12] Roy, J. R. and Hewings, G. J. D. (2005) Regional input-output with endogenous internal and external network flows, Discussion paper REAL 05-T-9, Regional Economics Applications Laboratory, University of Illinois, Urbana.

36. [13] Rosser, J. B. Jr. (1991) From catastrophe to chaos: a general theory of economic discontinuities, Kluwer Academic Publishers, Boston. • [14] Smith, C. H. (1983) A system of world mammal faunal regions. I. Logical and statistical derivation of the regions, Journal of Biogeography, 10, pp. 455-466. • [15] Moreno, Y. and Vazquez, A. (2003) Disease spreading in structured scale-free networks, European Physical Journal, B, 31, pp. 265-271.

37. [16] Gray, P. and Scott, S. (1990) Chemical oscillations and instabilities, Oxford University Press, Oxford. • [17] Thurner, S. (2005) Nonextensive statistical mechanics and complex scale-free networks, Europhysics News, November/December. • [18] Albert, R. (2005) Scale-free networks in cell biology, Journal of Cell Science, 118, pp. 4947-4957.

38. [19] Rinaldo, A. Banavar, J. R., Colizza, V. and Maritan, A. (2004) On network form and function, Physica, A, 340, pp. 749-755. • [20] Pastor-Satorras, R. and Vespigniani, A. (2004) Evolution and structure of the internet: a statistical physics approach, Cambridge University Press, Cambridge.

39. [21] Tomlin, J.A. (2003) A new paradigm for ranking pages on the World Wide Web, WWW2003, May 20-24, 2003, Budapest, Hungary.