Minds and Machines (2006) 16:95–100 DOI 10.1007/s11023-005-9007-x


Springer 2006

Book Review Paul Humphreys, Extending Ourselves: Computational Science, Empiricism, and Scientific Method, Oxford and New York: Oxford University Press, 2004, viii+172, $47.50, ISBN 0-19-515870-9. Paul Humphreys presents a philosophical analysis of the computer’s impact on scientific methodology, the first monograph on these issues from a distinct philosophy of science view. If you like thrilling summaries of less than five words, it would be: Technology changes epistemology. One part of the book is devoted to the particular novelties of simulation and, more generally, computational methods that comprise a Ôrevolution’ in scientific methodology. Another part places that development into the broader context of the evolution of scientific empiricism – the quest to extend ourselves with the help of ever new instruments, this time the digital computer. The combination of fine-grained analysis and comprehensive story, of novelty and continuity, renders the book especially appealing. The author writes with admirable precision in content and style, combining a smooth and deliberate argumentation with concise and stimulating outlines. The subject of simulation comprises a multitude of facets, including different disciplinary approaches, spanning from computational science to history. Even within philosophy itself simulation has given rise to some controversies, for instance about the role and status of simulation ‘‘experiments’’. See, e.g., the stimulating contributions of Fox Keller (2003), Galison (1997), Morgan (2003), or Winsberg (2003). Not least, Humphreys himself, since (1991), has made several important contributions to that discussion. Hence, while the time seems ripe for a monograph, its first task is to organize the matter into a coherent approach, transforming a complex mixture of factors into a suggestive story. Humphreys offers a cogent one that summarizes and elaborates the viewpoint indicated by the title of the book. He treats simulation as a special case of computational science and embeds the new methods into a broader context of the dynamics of scientific empiricism: extending our human capabilities by instruments lies at the heart of the dynamics of science and in this respect, microscopes and computers function analogously: For just as observability is the region in which we, as humans, have extended ourselves in the realm of the senses, so computability is the region in which we have extended ourselves in the realm of mathematical

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representations. And not computability in principle, but computability in practice. (p. 50) The book is divided into three more or less equal-weighted parts, each one of about 50 pages. The first is concerned with scientific empiricism in general and prepares the ground for the mentioned analogy between instruments. It is very readable, discussing instrumentalism versus realism and the significance of properties rather than objects. In this part and throughout the book the author illustrates his arguments by well-selected examples, mainly from physics. The second part is devoted to computational science, while the third specializes in simulation. In the following I will be concerned with the computer and simulation-related parts that can be read independently from the first one. For Humphreys, the computer gains its basic significance as a new instrument that outperforms another tool for doing mathematics, the differential calculus. The comparison between these two particular tools provides the crux of the argument: Now we have the massive deployment of modeling and simulation on digital computers. This last development is one that is more important than the invention of the calculus in the 1660s, an event that remained unparalleled for almost 300 years, for computer modeling and simulation not only are applicable to a far broader range of applications than are the methods of calculus, but they have introduced a distinctively new, even revolutionary, set of methods into science. (p. 57) Humphreys emphasizes the technological character of the computer not as a solver of equations, but as requiring the implementation of algorithms that produce a feasible solution in reasonable time. He refers several times to the motto ‘‘in practice, not in principle’’, indicating that the traditional philosophy of science will have to adapt: the philosophical analysis of simulation methods cannot focus on in-principle questions, but has to investigate inpractice ones. Compared to the accounts of Galison or Fox Keller, Humphreys looks very much like a traditional philosopher, while his credo ‘‘Our slogans will be mathematics, not logic; computation, not representation; machines, not mentation’’ (p. 53) diverts him from traditional views in philosophy of science, constituting an original mixture of both traits. I discuss the resulting tension in the rest of this review. According to Humphreys, computer simulations as new scientific instruments enlarge the realm of tractability in mathematics. Thus his argumentation centers around solving equations. However, the task of ‘‘solving equations’’ implies certain restrictions on the new instrument. Fascinating and hotly debated issues like man-machine interfaces, or the discussion in artificial intelligence about machines simulating certain capacities of humans,

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or about the computer simulating a virtual reality, fall through the cracks. These topics would surely add some additional flavor to simulation and would, in my view, fit well with Humphreys’ own slogan. The question of whether computer simulation can imitate certain phenomena of nature or capabilities of humans seems to lie across the grain of mathematical equations. E.g., already in the late 1940s Norbert Wiener had reasoned about the interface between organic and mechanic systems as a kind of prosthesis – a conception that resonates directly with ‘‘extending ourselves’’. A closer look reveals, furthermore, that the concept of simulationas-imitation could also contribute to the author’s core theme, the problem of simulating mathematical equations, or solving them numerically. For Humphreys, the distinction between numerical solution and imitation of a dynamic is not essential: ‘‘Although numerical solutions are often not exact, this is not an essential feature of them – some numerical solutions give the same exact values as analytic solutions’’ (p. 65). While that is true, the interesting case is the other one, when numerical solutions are not exact, i.e. not a solution (in the strict sense) at all. Often they are not even an approximation to the solution—if one exists at all. What then makes simulations feasible or adequate? This question would belong clearly to the core subject of Humphreys’ approach. E.g., a system of finite difference equations that corresponds to a system of partial difference equations does not, in general, provide a solution to it. Admittedly, often the finite difference equations equal the partial difference equations in the limit. But that is an assertion that violates Humphreys’ own motto ‘‘in practice, not in principle’’. Hence the term ‘‘numerical solution’’ may be a misleading one, because in most numerical and simulation strategies, the imitation of behavior serves as the criterion of adequacy. What kind of instrument is simulation and how does it function? Again, a part of Humphreys’ slogan – ‘‘computation, not representation’’ – pinpoints an intriguing feature of simulations: they introduce a new twist to the debate about representation, indicated by catchwords like visualizations or virtual reality, the latter not included in the scope of the book. The author characterizes simulation as a subdomain of computational science. Namely, simulations are based on temporal processes of calculation (he gives credits to Stephan Hartmann). Humphreys states that simulations differ from abstract representations mainly in this respect. And he adds a second characteristic of simulation: ‘‘It is with the representation of the output that one of the key methodological features of simulations emerges’’ (p. 110). I agree that output representations take part of the load that abstract mathematical representations had to shoulder according to established method. How visualizations can be successful in substituting (at least partly) for mathematical derivations is indeed a tricky question. Maybe simulation will even challenge the pivotal role of mathematical equations, thus

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challenging also Humphreys’ principal idea taking simulations as instruments to solve equations. As was mentioned already, Humphreys intends to separate simulation from computational methods, i.e. to determine the special characteristics of simulation as an instrument. To achieve this he proposes a careful, though complicated, definition of simulation: System S provides a core simulation of an object or process B just in case S is a concrete computational device that produces, via a temporal process, solutions to a computational model that correctly represents B, either dynamically or statically. If in addition the computational model used by S correctly represents the structure of the real system R, then S provides a core simulation of system R with respect to B (p. 110). This definition avoids mention of the vague concept of imitation – at the cost, however, of including ‘‘correct representation’’. In general, one of the key problems in the philosophical debate on simulation is to adjust the concepts of representation and modeling. Humphreys follows a highly original strategy to treat that problem: he quite consciously takes as the units of analysis what he calls computational templates, not models or simulation models, because the latter are tailor-made for certain applications, and hence would be too specific for philosophical analysis. To give an example, Newton’s second law is a schema called ‘‘theoretical template’’ by Humphreys (p. 60). An appropriate specification of that template, making it computationally tractable, would transform it into a computational template. He relates templates to models like a part to the whole: The sextuple ÆTemplate, Construction Assumptions, Correction Set, Interpretation, Initial Justification, Output Representationæ then constitutes a computational model’’ (p. 103). Humphreys thus circumvents the debate about modeling and the mediating role of models that, for instance, Winsberg gives center stage. I suspect, however, that the construction of templates, whose nontriviality Humphreys mentions explicitly (p. 64), will lead back directly into a discussion wellknown in the context of models and modeling. The term ‘‘template’’ is well established in computational science and suggests that objects of that kind can travel easily across disciplinary boundaries. Humphreys claims that the sciences will be, and partly are, reorganized according to computational templates instead of theories. While the impact of technology on the social and disciplinary organization of science is surely an important one, open questions remain in regard to other characteristics. Should templates be conceived of as a new mathematical form, or do they replace mathematical representations? Humphreys stresses

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that one template can have very different uses in different contexts, but that is true for mathematical representations in general. Neither templates nor models are viewed as fixed objects. Humphreys envisions a process of mutual adjustment in the light of ongoing evaluation that lies behind his term ‘‘correction set’’. It is important, I think, that this account can cover those striking cases where the models or templates, like in cellular automata or neural networks, have little structure, while the adjustment of parameters can cause them to fit complex phenomena to a surprising degree. However, the term ‘‘correction set’’ suggests a rather clean procedure, while in real world cases the revision normally depends on a murky mixture of factors. Hence the concept of correction sets risks deviating from Humphreys’ motto ‘‘in practice, not in principle’’. Something like the negotiations in Galison’s ‘‘trading zone’’ would present a possible alternative. To conclude, I would like to mention a most intriguing issue related to simulation that is introduced briefly but substantially in Humphreys’ book, namely the relation between simulation and understanding (a notoriously vague, but important term). Humphreys describes how understanding and representation get calibrated in simulation and hence methodology and epistemology get linked: Increases in human understanding obviously are not always facilitated by propositional representations, and in some cases are precluded altogether. The form of the representation can profoundly affect our understanding of a problem, and because understanding is an epistemic concept, this is not at root a practical matter but an epistemological one (p. 114). Humphreys distinguishes understanding from predictive power and ascribes an ‘‘epistemic opacity’’ to simulation that inhibits understanding: This opacity can result in a loss of understanding because in most traditional static models our understanding is based upon the ability to decompose the process between model inputs and outputs into modular steps, each of which is methodologically acceptable both individually and in combination with the others (p. 148). I think it is a correct observation that simulation often is accompanied by epistemic opacity, but I think it is an open question whether simulation causes a loss in understanding or whether it makes opacity and understanding compatible in a new way. Due to the nearly ubiquitous use of simulation the answer to this question is of great significance for an analysis of current developments in science and technology. Again this amounts to a touchstone for Humphreys’ motto ‘‘in practice, not in principle’’ (that can’t be repeated too often): If philosophical priority lies with the practical success

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of science and technology, the degree of opacity compatible with understanding is an empirical question. A philosophical reconstruction, on the other hand, would introduce more normative measures of what can count as ‘‘understanding’’. Any answer will have to take into account the peculiarities of simulation as a technological instrument. I conclude by quoting the last sentence of the book summarizing Humphreys’ views on the implications of extending ourselves: ‘‘The philosophy of science, or at least that part of it which deals with epistemology, no longer belongs in the humanities’’ (p. 156). References Fox Keller, E. (2003), Models, Simulations, and ‘‘Simulation Experiments’’, in H. Radder, ed., The Philosophy of Scientific Experimentation, Pittsburgh: The University of Pittsburgh Press, pp. 198–215. Galison, P. (1997), Image and Logic: A Material Culture of Microphysics, Chicago and London: University of Chicago Press. Humphreys, P. (1991), Computer Simulations in A. Fine et al., ed., PSA 1990, The Philosophy of Science Association, pp. 497–506. Morgan, M. (2003), Experiments Without Material Intervention. Model Experiments, Virtual Experiments, and Virtually Experiments, in H. Radder, ed., The Philosophy of Scientific Experimentation, Pittsburgh: The University of Pittsburgh Press, pp. 216–235. Winsberg, E. (2003), Simulated Experiments: Methodology for a Virtual World, Philosophy of Science 70, pp. 105–125. JOHANNES LENHARD Institute for Science and Technology Research University of Bielefeld 33501 Bielefeld Germany E-mail: [email protected]