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THINKING OUTSIDE THE BOX: KNOWLEDGE POWER. Alan Wilson Centre for Advanced Spatial Analysis University College London. Two objectives for the seminar. To make some general observations about generating good ideas as a researcher – and in particular, ‘thinking outside the box’

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## THINKING OUTSIDE THE BOX: KNOWLEDGE POWER

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**THINKING OUTSIDE THE BOX: KNOWLEDGE POWER**Alan Wilson Centre for Advanced Spatial Analysis University College London**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**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**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**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.)**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**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**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**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**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**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**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**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.**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’.**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.)**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.**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.**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.**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’.**Yij**Xi Zj Figure 3**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)**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.**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.**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.**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.**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.**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!**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??**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**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.**[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.**[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.**[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.**[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.**[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.**[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.**[21] Tomlin, J.A. (2003) A new paradigm for ranking pages on**the World Wide Web, WWW2003, May 20-24, 2003, Budapest, Hungary.

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