On Prospective Studies and Computer Modelling
Human beings have always been interested in, or worried about, the future of their societies. Sometimes they imagined ideal societies, like Plato in his Republic or Thomas More in Utopia. At other times, some wrote from a frightened and pessimistic point of view, like Huxley in Brave New World, Zamyatin in We, or Orwell in 1984. Marx displayed optimism towards an ideal future society, though in less detail than the aforementioned pessimistic visions (see Ollman, 1977 for an overview of his scattered remarks on a communist future). Following impressive technological advancement, especially from World War II on, even traditionally conservative sectors began to imagine possible future societies in which no one were to be poor and that this could be achieved on the basis of science and technology rather than through disruptive social upheavals. The science-fiction writers of the 1950s described future societies with a similar confidence in technology. Yet, technology alone could not abolish poverty and inequalities, and current societies do not resemble those imagined by science fiction. So far, at least, there are no flying cars. On the other hand, science fiction vastly underestimated the rise of information and communications technology.
Given the increasing pervasiveness and impact of computers and related technologies on the modern world, it is not surprising that mathematical models made soon use of computers to study national, regional or global societies and their futures (1). Yet, Latin America’s achievements in this regard are not widely known outside the region. In the 1960s, mathematical models were prepared under the influence of Oscar Varsavsky. They pursued theoretical goals such as a mathematical model for More’s Utopia (see Domingo and Varsavsky, 1967) while also following a “normative” approach, as may be seen in Varsavsky and Calcagno (1971) and the references therein. Those models had no influence outside Latin America, but they enabled the creation of a regional network (a valuable structure of contacts, unusual in Latin America, where, in general, scientists used to work only with colleagues in developed countries).
As is well known, the first prospective model that had a global impact was the World3 model, popularized in Meadows et al (1972). Although its approach was controversial, both technically and ideologically, the model was extremely important and very valuable because it enabled a worldwide discussion of its methodology and the formulation of several significant questions. World3 was followed by several different models, including an Argentine one that contested it, the Latin American World Model, which proposed a “normative” strategy to arrive in a feasible way at egalitarian societies (Herrera, Scolnik et al, 1976) (2).
Clearly, mathematical models are a powerful tool for prospective studies, be they national, regional or global. Castro and Jacovkis (2015) present a historic retrospective of this class of models and how they changed their objects of study. To a certain extent, all computer models of complex systems are powerful tools for this sort of research, much of which is prepared by think tanks or universities (or institutions related to universities). This is particularly true for models of climate change that show future scenarios, according to which the absence of urgent countermeasures would yield catastrophic consequences.
When do mathematical models become powerful tools for prospective studies? How and under what conditions can they become useful? It is necessary to explicate what are the underlying hypotheses, premises and assumptions (which are often implicitly ideological), the choice of variables and the relationships among them (i.e., their structure), and the estimates of their values (in lieu of actual measures or computations).
Any model, independent of its design or of the ideology of its modelers, is useful when one knows its assumptions. Any hidden assumptions are dangerous. A mathematical model may be technologically outstanding, may reflect as precisely as possible complex political, social, economic, cultural relationships, but it is inevitably based on premises and assumptions that should be (and sometimes are not) clearly stated. Hypotheses, assumptions, initial data, parameters and relationships must be explained and justified so that they can be reasonably changed according to a competing explanation or justification (sometimes referred to as the underlying “theory”). In addition, the model’s boundary conditions require precise definition (i.e., variables that influence the simulation over time and represent either feasible actions of agents capable to affect the results or out-of-control external variables). Finally, the model must allow the introduction of random (unpredictable) variables, and its likely reaction to those random inputs (its sensitivity to them) must be estimated.
If prospective mathematical models had existed in January 1914, could any of them have predicted that the following August Europe would be immersed in a horrific war? It is plausible that the lack of “risky” hypotheses relates to a lack of imagination on the part of the modelers, and not to a technical flaw. This deserves to be investigated further. A lack of boldness can impede the formulation of scenarios that may seem too utopic or dystopic but could become an unexpected reality.
To provide another example: As fracking technology became economically competitive in the 1990s, how long did it take for the geopolitical effects of fracking in the United States to register in simulation models? In another vein, how much criticism can a 1980s mathematical model face for predicting United States oil self-sufficiency (3). It is crucial to understand the prejudices or certainties that are built into a mathematical model. Conversely, uncertainties tend to be extremely useful for the preparation and discussion of mathematical models. If one does not dare to think in alternatives that seem impossible, one does not include them in the model.
A third example: For many years, most people (and modelers) thought that it was impossible that a communist country could return to capitalism. None of the most important mathematical models included that contingency among its feasible alternatives; but without mathematical models, Amalrik (1970), Todd (1976) and Carrère d’Encausse (1978) did forecast the fall of communism (although not necessarily the dynamics of the fall: what they had observed—and what modelers had missed— was that the system was rotten).
A model, through successive numerical experiments under different hypotheses, will not offer us a determined and deterministic future. It will offer us scenarios of different possible configurations in the future, each of them with different causal justification. This will permit, on the one hand, to see the feasibility of certain policies under different circumstances and, on the other hand, when the results obtained do not agree with what one expects, to analyze carefully the mathematical relationships and the hypotheses employed, in order to see whether it is necessary to slightly (or not so slightly) correct those relationships, data or hypotheses or to modify the model, globally or partially.
With this approach, a mathematical model is a powerful tool for analyzing future scenarios, feasibility of policies (independently of whether or not we like them) and plausible consequences. Moreover, the necessary interdisciplinary interaction between the developers preparing the model and those who will use it will enrich it even more. That is, in fact, its main strength: the very process of formulation, development, data analysis and interpretation of results can be discussed under several competing hypotheses, thus permitting a better comprehension of the system in its current state, and of future scenarios, under diverse circumstances (4). Just one word of advice: Do not expect the model to predict the future.
(1) It is worth remembering that even an analogue computer, the fascinating hydraulic macroeconomics computer MONIAC that used water, was built by Bill Phillips in 1949 in London.
(2) Currently an Argentinean group, headed by Rodrigo Castro and Hugo Scolnik (who was the deputy director of the Latin American World Model), with governmental support, has recovered and is adapting this model to a state-of-the-art mathematical modeling language, so that new experiments will be easily formulated and performed with updated data and novel hypotheses.
(3) Of course, discussions continue to exist about the likelihood of US energy independence, but that alternative has clearly been put on the table.
(4) In a sense, a similar approach is taken by Collins and Pinch (1998) when they discuss the usefulness of the “seven wise men” British econometric model. Besides, as they write (Collins and Pinch (1998: 152)), “[s]ocial science has its own methods and not all of these are quantitative by any means.”
Amalrik, Andrei, Will the Soviet Union Survive Until 1984?, New York: Harper & Row, 1970.
Carrère d’Encausse, Helène, L’empire éclaté, Paris: Flammarion, 1978.
Castro, Rodrigo and Jacovkis, Pablo M. (2015), Computer-based global models: from early experiences to complex systems, Journal of Artificial Societies and Social Simulation 18 (1) 13 <https://jasss.soc.surrey.ac.uk/18/1/13.html>.
Collins, Harry and Pinch, Trevor, The Golem at large: what you should know about technology, Cambridge, UK: Cambridge University Press, 1998.
Domingo, Carlos and Varsavsky, Oscar (1967), Un modelo matemático de la Utopía de Moro, Desarrollo Económico 7 (26): 3-36. Also in Varsavsky and Calcagno (1971), pp. 164-190.
Herrera, Amílcar O, Scolnik, Hugo D. et al, Catastrophe or new society? A Latin American World Model, Ottawa: International Development Research Center, 1976. Second edition: ¿Catástrofe o nueva Sociedad? Modelo Mundial Latinoamericano 30 años después, Buenos Aires: International Development Research Center – Instituto Internacional de Medio Ambiente y Desarrollo, 2004.
Meadows, Donella H., Meadows, Dennis L, Randers, Jorgen and Behrens II, William W., The limits to growth, New York: Universe Books, 1972. There were two updates: Donella H. Meadows, Dennis Meadows and Jorgen Randers, Beyond the limits, White River Junction, VT: Chelsea Green Publishing, 1992; and Donella H. Meadows, Jorgen Randers and Dennis L. Meadows, Limits to growth: the 30-year update, White River Junction, VT: Chelsea Green Publishing and London: Earthcan, 2004.
Ollman, Bertell (1977), Marx’s vision of communism: a reconstruction, Critique: Journal of Socialist Theory 8 (1): 4-41.
Todd, Emmanuel, La chute finale, Paris: Laffont, 1976.
Varsavsky, Oscar and Calcagno, Alfredo E. (eds.), América Latina: modelos matemáticos, Santiago de Chile: Editorial Universitaria, 1971.
Pablo Miguel Jacovkis specializes in interdisciplinary computational mathematical models. As a private consultant since 1970 he prepared models on fluvial hydraulics, hydrodynamics, hydrology, water resources, meteorology and geology. He has published many scientific and technical papers and supervised several Ph.D. and M.S. students in Computer Science, Mathematics, Engineering, Physics and Chemistry. At the University of Buenos Aires (UBA) he was Director of the Department of Mathematics at the School of Engineering and Director of the Institute of Applied Mathematics, Academic Secretary and Dean of the School of Sciences. He was President of the National Council for Scientific and Technological Research. Currently he is Secretary for Research and Development of the National University of Tres de Febrero and Professor Emeritus at UBA.
Banner Image: Stylized rendering of PDP-7 computer, which was first introduced in 1964. Graphic based on a photo of taken by Tore Sinding Bekkedal around 2005 and made available under Creative Commons license ShareAlike 1.0 Generic (CC SA 1.0) (Editor, 2018).Add to favorite