Introducing… Alan Wilson

Mathematical modelling in history and archaeology:

a personal journey

I started my research life as a mathematician, employed in elementary particle physics, but transferred after three years into the social science and for a number of decades, I have worked on mathematical and computer models of cities – more broadly on geographical systems. I have worked with economists and planners but in formal terms, established myself in Geography. I developed models of flows of all kinds – journeys to work, energy and materials flows for example – and the location of activities – where people live and work and so on. My ambition has always been to build a comprehensive (‘general’) urban model which incorporated all the interdependencies, and in some sense represented the ‘science’ of cities. This is highly relevant to public services and has commercial applications – for example in optimising networks of retail outlets and the models have been extensively tested in these contexts. So how did all this translate into history?

In 1985, I was a Professor of Geography in Leeds and a PhD student in History came to see me and said that someone had told her that I had some models that could help her. She had point data for identified settlements in Greece in the Ninth Century BC but nothing on their sizes. We adapted my retail model and estimated sizes – in effect from the topology of the points. Out popped Athens, Thebes, Corinth and so on. There was one surprise: a settlement estimated as large which had never been investigated. If I had the courage of my convictions, we should have immediately sent archaeologists to it. We published two papers (Rhill and Wilson 1987-A, B). I put it out of my mind. Then in the 90s, some American archaeologists picked it up and started applying the model and (in a limited way) the idea spread. I moved to UCL in 2007 and Andy Bevan, in the Archaeology Department somehow noticed that the Wilson in the Centre for Advanced Spatial Analysis (CASA) was the same Wilson as in ‘Rhill and Wilson’. We reproduced the 1987 work (with difficulty) and then extended it to Crete (Bevan and Wilson, 2013). This was taken up by Mark Altaweel and Karen Radner and applied in what in now Iraq (Davies et al, 2014). At the time I had an EPSRC project which included a security dimension – spatial interaction as ‘threat’ (Davies et al, 2013, Baudains et al, 2016, Baudains and Wilson, 2016, Guo et al, 2018) – and another venture was to use this model to ’predict’ the summer ‘tour’ of the Assyrian Emperor with his army round peripheral states Baudains et al, 2015).

I worked on a different history project with Joel Dearden: modelling the evolution of US cities in the Nineteenth Century with particular respect to the impact of railways and the emergence of Chicago (Wilson and Dearden, 2011). It is a refinement of this work which we will seek to apply to UK cities in the Industrial Revolution in LWM. This is a minor part of the LWM project but it should be interesting and offers the basis for linking the micro scale – the main focus of the project – to the macro (meso) scale.

My other connection to the humanities was a different one: I was Chair of the AHRC Council for six years from 2007. I want to take one point from that experience. We claimed that we were ‘world class’ and I continually asked what that meant. One of the best answers was that a project was world class if it was ‘transformative’ in the discipline. This is an ambition for LWM, not just for History but for the digital humanities. But what could this mean? I once sat next to a very distinguished historian at a dinner and set about explaining modelling in history. She listened patiently and then looked me in the eye and said: ‘But what are your findings?’! I was asked a similar question recently: ‘What do the models tell you that we don’t already know from the data?’ My response to this second question now gives me a better answer to the first than I managed at the time. First, models are very good at estimating ‘missing data’ – the size of settlements in the Greek example illustrates this. Secondly, the evolution of a system of cities – and of their internal activities and structures – are derived from a range of interdependent factors. It is these interdependencies that can be captured in mathematical models – up to a point of course! (I used multi-regional input-output modelling as an example in my response to the question – Levy et al 2016 – territory already very tentatively explored by economic historians.) There is now a long history of over five decades of this science being developed (and well tested) in a contemporary context. Modelling (and much else in LWM) can be transformative for History. It is worth being ambitious!!

References.

Baudains, P., Davies, T. P., Fry, H. M. and Wilson, A. (2016) From Colonel Blotto to Field Marshall Blotto, in Wilson, A. (ed.) Geo-mathematical modelling, Wiley, Chichester, pp. 283 – 292.

Baudains, P. and Wilson, A. (2016) Conflict modelling: spatial interaction as threat, in Wilson, A. (ed.) Global dynamics, Wiley, Chichester, pp. 145 – 158

Baudains, P; Zamazalová, S; Altaweel, M; Wilson, A. G., 2015. Modeling Strategic Decisions in the Formation of the Early Neo-Assyrian Empire. Cliodynamics: The Journal of Quantitative History and Cultural Evolution, 6(1), 1-23.
Bevan, A. and Wilson, A. G., 2013. Models of settlement hierarchy based on partial evidence. Journal of Archaeological Science, 40 (5), pp. 2415-2427. http://dx.doi.org/10.1016/j.jas.2012.12.025

Davies, T., Fry, H., Wilson, A. G., and Bishop, S.R., 2013 A mathematical model of the London riots and their policing. Nature Scientific Reports 3, 1303. doi:10.1038/srep01303

Levy, R. G., Oleron Evans, T., and Wilson, A. (2016) A global inter-country economic model based on linked input-output tables, in Wilson, A. (ed.) Global dynamics, Wiley, Chichester, pp. 51 – 72.

Davies, T., Fry, H., Wilson, A., Palmisano, A., Altaweel, M. and Radner, K. 2014. Application of an Entropy Maximizing and Dynamics Model for Understanding Settlement Structure: The Khabur Triangle in the Middle Bronze and Iron Ages.  Journal of Archaeological Science doi:10.1016/j.jas.2013.12.014.

Guo, W., Gleditsch, K. and Wilson, A., 2018 Retool AI to forecast and limit wars, Nature, 562, 331-333

Rihll, T.E. and Wilson, A.G., 1987-A. Spatial interaction and structural models in historical analysis:  some possibilities and an example.  Histoire et Mesure II-1, pp. 5-32. In: Working Paper 481, University of Leeds: School of Geography.

Rihill, T. and Wilson. A.G., 1987-B. Model-based approaches to the analysis of regional settlement structures: the case of ancient Greece. In: P. Denley and D. Hopkin, eds. 1987.  History and Computing. Manchester: Manchester University Press, pp. 10-20.

Wilson, A. G. and Dearden, J., 2011. Tracking the evolution of regional DNA: the case of Chicago. In: M. Clarke and J.C.H. Stillwell, eds. Understanding population trends and processes. Berlin: Springer,  pp. 209-222.