The Vindication of Computer Simulations

  • Nicolas FillionEmail author
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 327)


The relatively recent increase in prominence of computer simulations in scientific inquiry gives us more reasons than ever before for asserting that mathematics is a wonderful tool. In fact, a practical knowledge (a ‘know-how’) of scientific computation has become essential for scientists working in all disciplines involving mathematics. Despite their incontestable success, it must be emphasized that the numerical methods subtending simulations provide at best approximate solutions and that they can also return very misleading results. Accordingly, epistemological sobriety demands that we clarify the circumstances under which simulations can be relied upon. With this in mind, this paper articulates a general perspective to better understand and compare the strengths and weaknesses of various error-analysis methods.


  1. Allison, D. B., Paultre, F., Maggio, C., Mezzitis, N., & Pi-Sunyer, F. X. (1995). The use of areas under curves in diabetes research. Diabetes Care, 18(2), 245–250.Google Scholar
  2. Batterman, R. W. (2002a). Asymptotics and the role of minimal models. British Journal for the Philosophy of Science, 53, 21–38.Google Scholar
  3. Batterman, R. W. (2002b). The devil in the details: Asymptotic reasoning in explanation, reduction, and emergence. Oxford: Oxford University Press.Google Scholar
  4. Batterman, R. W. (2009). Idealization and modeling. Synthese, 169(3), 427–446.CrossRefGoogle Scholar
  5. Bender, C., & Orszag, S. (1978). Advanced mathematical methods for scientists and engineers: Asymptotic methods and perturbation theory (Vol. 1). New York: Springer.Google Scholar
  6. Borwein, J., & Crandall, R. (2010). Closed forms: what they are and why we care. Notices of the American Mathematical Society, 60, 50–65.CrossRefGoogle Scholar
  7. Corless, R. M., & Fillion, N. (2013). A graduate introduction to numerical methods, from the viewpoint of backward error analysis (868pp.). New York: Springer.CrossRefGoogle Scholar
  8. Deuflhard, P., & Hohmann, A. (2003). Numerical analysis in modern scientific computing: An introduction (Vol. 43). New York: Springer.Google Scholar
  9. Feigl, H. (1950). De principiis non disputandum…? In Inquiries and provocations (pp. 237–268). Dordrecht: Springer. 1981.CrossRefGoogle Scholar
  10. Fillion, N. (2012). The reasonable effectiveness of mathematics in the natural sciences. PhD thesis, London: The University of Western Ontario.Google Scholar
  11. Fillion, N., & Bangu, S. (2015). Numerical methods, complexity, and epistemic hierarchies. Philosophy of Science, 82, 941–955.CrossRefGoogle Scholar
  12. Fillion, N., & Corless, R. M. (2014). On the epistemological analysis of modeling and computational error in the mathematical sciences. Synthese, 191, 1451–1467.CrossRefGoogle Scholar
  13. Galileo (1687). De motu. In I. Drabkin (Ed.), On motion and on mechanics. Madison: University of Wisconsin Press. 1960.Google Scholar
  14. Grcar, J. (2011). John von Neumann’s analysis of Gaussian elimination and the origins of modern numerical analysis. SIAM Review, 53(4), 607–682.CrossRefGoogle Scholar
  15. Hacking, I. (1992). The self-vindication of the laboratory sciences. In A. Pickering (Ed.), Science as practice and culture. Chicago: University of Chicago Press.Google Scholar
  16. Hamming, R. (1980). The unreasonable effectiveness of mathematics. The American Mathematical Monthly, 87(2), 81–90.CrossRefGoogle Scholar
  17. Higham, N. J. (2002). Accuracy and stability of numerical algorithms (2nd ed.). Philadelphia: SIAM.CrossRefGoogle Scholar
  18. Humphreys, P. (2004). Extending ourselves: Computational science, empiricism, and scientific method. New York: Oxford University Press.CrossRefGoogle Scholar
  19. Kadanoff, L. P. (2004). Excellence in computer simulation. Computing in Science & Engineering, 6(2), 57–67.Google Scholar
  20. Oberkampf, W., Trucano, T., & Hirsch, C. (2004). Verification, validation, and predictive capability in computational engineering and physics. Applied Mechanics Review, 57(5), 345–384.CrossRefGoogle Scholar
  21. Reichenbach (1949). The theory of probability: An inquiry into the logical and mathematical foundations of the calculus of probability. Berkeley: University of California Press Berkeley.Google Scholar
  22. Salmon, W. C. (1991). Hans Reichenbach’s vindication of induction. Erkenntnis, 35(1–3), 99–122.Google Scholar
  23. Tai, M. M. (1994). A mathematical model for the determination of total area under glucose tolerance and other metabolic curves. Diabetes Care, 17(2), 152–154.CrossRefGoogle Scholar
  24. Tal, E. (2011). How accurate is the standard second? Philosophy of Science, 78(5), 1082–1096.CrossRefGoogle Scholar
  25. Truesdell, C. (1980). Statistical mechanics and continuum mechanics. In An idiot’s fugitive essays on science (pp. 72–79). New York: Springer.Google Scholar
  26. Wilkinson, J. H. (1963). Rounding errors in algebraic processes (Prentice-Hall series in automatic computation). Englewood Cliffs: Prentice-Hall.Google Scholar
  27. Wilson, M. (2006). Wandering significance: An essay on conceptual behaviour. Oxford: Oxford University Press.CrossRefGoogle Scholar
  28. Winsberg, E. (2010). Science in the age of computer simulation. Chicago: University of Chicago Press.CrossRefGoogle Scholar
  29. Wolever, T. M., Jenkins, D. J., Jenkins, A. L., & Josse, R. G. (1991). The glycemic index: Methodology and clinical implications. The American Journal of Clinical Nutrition, 54(5), 846–854.Google Scholar

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of PhilosophySimon Fraser UniversityBurnabyCanada

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