In This Article Computational Science

  • Introduction
  • Early Work
  • General Overviews
  • Models and Simulations
  • Equation-Based Simulations and Agent-Based Simulations
  • Large-Scale Simulations
  • Simulations and Experiments
  • Visualization and Representation
  • Computational Science and Emergence
  • Computational Science and Computer-Assisted Mathematics
  • Validation and Verification of Simulations
  • Quantum Computation, Digital Physics, and Monte Carlo Simulations
  • Philosophical Offshoots

Philosophy Computational Science
Paul Humphreys
  • LAST REVIEWED: 08 October 2015
  • LAST MODIFIED: 24 July 2012
  • DOI: 10.1093/obo/9780195396577-0100


Computational science is a recent addition to the stock of scientific methods. Many scientists and philosophers hold the view that it constitutes a third principal mode of scientific investigation that supplements the traditional methods of theory and experiment. Its most frequently discussed form is that of digital computer simulations, but data analysis, computer proofs and proof assistants in mathematics, computer-assisted scientific instruments, visualization techniques, and the study of emergent phenomena are all part of computational science. Modern computer simulations were introduced in the 1940s. Philosophers initially focused their attention on uses in artificial intelligence rather than in scientific computation more generally, with the result that most of the philosophical literature on the topic of computational science is of relatively recent origin. Because of this, what counts as the boundaries of this field and the topics within it are still evolving. Some of the features of computational science that make for distinctive philosophical issues are the dependence on the available technology of which theoretical methods can be effectively used, a lack of epistemic access by humans to the details of many evidential processes, the replacement in some cases of data drawn from material experiments by data generated from simulations, problems of validating and interpreting enormously complex models, claims that the universe is itself a computational device, and connections with artificial intelligence and the philosophy of mind. In addition, some of the sources clearly indicate that familiar philosophical issues, such as realism and empiricism, epistemological externalism and internalism, theory and experiment, take an interesting twist within this new area. The articles in this bibliography have been selected with an eye to illustrating the novel character of problems raised by computational science. They include some drawn from the social studies of science literature as well as a majority that appeared in squarely philosophical sources. Articles and books that are especially suitable for neophytes and those that require a technical background are identified as such. All other sources are accessible to those with a solid background in philosophy. Thanks to Anouk Barberousse, Mark Bedau, Cyrille Imbert, Tarja Knuuttila, Johannes Lenhard, Margaret Morrison, Wendy Parker, and Michael Stoeltzner for helpful suggestions in compiling this bibliography.

Early Work

After the first military applications were run on the ENIAC computer in the mid-1940s, unclassified scientific articles about computational science, including those that emphasized methodological issues, began to appear. Philosophical articles about simulating human cognition, as in Turing 1950 and Newell and Simon 1976, became the focus of much discussion. Humphreys 1991 and Rohrlich 1991 are perhaps the first English language philosophical papers explicitly focused on computer simulations outside artificial intelligence. Hartmann 1996 is another influential early article. Metropolis and Ulam 1949 is a good example of a self-consciously new scientific method that is put into historical perspective in Galison 1996.

  • Galison, Peter. “Computer Simulations and the Trading Zone.” In The Disunity of Science: Boundaries, Contexts, and Power. Edited by Peter Galison and David Stump, 118–157. Stanford, CA: Stanford University Press, 1996.

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    A historically oriented paper focused on the introduction of Monte Carlo methods as a novel technique. It emphasizes the importance of direct modeling of stochastic physical processes by those methods rather than by using differential equation models. It also has some important insights into the relations between pure and applied mathematics.

  • Hartmann, Stephan. “The World as a Process: Simulations in the Natural and Social Sciences.” In Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View. Edited by Rainer Hegselmann, Ulrich Mueller, and Klaus G. Troitzsch, 77–100. Dordrecht, The Netherlands: Kluwer, 1996.

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    Provides an influential characterization of simulations as the mimicking of one dynamical process by another.

  • Humphreys, Paul. “Computer Simulations.” In PSA 1990: Proceedings of the 1990 Philosophy of Science Association Biennial Meetings. 2 vols. Edited by Arthur Fine, Micky Forbes, and Linda Wessels, 497–506. East Lansing, MI: Philosophy of Science Association, 1991.

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    Discusses the limitations of analytically solvable models and argues that computer simulations are a sui generis method that have become the dominant approach in some sciences. Provides a working definition of computer simulations, later modified in Hartmann 1996.

  • Metropolis, Nicholas, and Stanislaw Ulam. “The Monte Carlo Method.” Journal of the American Statistical Association 44.247 (1949): 335–341.

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    A seminal work on the Monte Carlo method with a number of insightful methodological remarks. Some technical background required.

  • Newell, Allen, and Herbert Simon. “Computer Science as Empirical Inquiry: Symbols and Search.” Communications of the ACM 19 (1976): 113–126.

    DOI: 10.1145/360018.360022E-mail Citation »

    A highly influential essay that lays out the basis of classical artificial intelligence. Their main claim is that the successful operation of a physical symbol system provides necessary and sufficient conditions for intelligent action. Suitable for all levels.

  • Rohrlich, Fritz. “Computer Simulations in the Physical Sciences.” In PSA 1990: Proceedings of the 1990 Philosophy of Science Association Biennial Meetings. Edited by Arthur Fine, Micky Forbes, and Linda Wessels, 507–518. East Lansing, MI: Philosophy of Science Association, 1991.

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    Argues that computer simulations constitute a new methodology for the physical sciences. The article anticipates later discussions in drawing parallels between experiments and simulations, noting the role of non-integrable motions, and the differences between the syntax of cellular automata and differential equation models.

  • Turing, Alan. “Computing Machinery and Intelligence.” Mind 59 (1950): 433–460.

    DOI: 10.1093/mind/LIX.236.433E-mail Citation »

    A classic article, widely cited and very readable, that contains criteria for judging when a simulation has accurately imitated human verbal behavior. These criteria came to be known as the Turing Test.

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