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Models, measurement and computer simulation: the changing face of experimentation

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Abstract

The paper presents an argument for treating certain types of computer simulation as having the same epistemic status as experimental measurement. While this may seem a rather counterintuitive view it becomes less so when one looks carefully at the role that models play in experimental activity, particularly measurement. I begin by discussing how models function as “measuring instruments” and go on to examine the ways in which simulation can be said to constitute an experimental activity. By focussing on the connections between models and their various functions, simulation and experiment one can begin to see similarities in the practices associated with each type of activity. Establishing the connections between simulation and particular types of modelling strategies and highlighting the ways in which those strategies are essential features of experimentation allows us to clarify the contexts in which we can legitimately call computer simulation a form of experimental measurement.

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Notes

  1. For an excellent paper on modelling in climate science see Norton and Suppe (2001).

  2. A model can be based on some theoretical belief about the world that is suggested by the data or it can sometimes be understood as simply a statistical summary of a data set. Data assimilation is an example that extends beyond straightforward issues of description; here models are used to fill in gaps in observational data and to translate noisy observations into a collection of initial model-states. They function as tools for generating data.

  3. Consequently we need very sophisticated models in order to represent the apparatus in the appropriate way. Because the knowledge associated with the measurement comes via the model the apparatus and the model function, in many respects, as a single system.

  4. What is less clear is the connection between models, measurement and representation when we are dealing with statistical models. Statistics, in particular structural equation modelling, makes use of measurement models which specify the relationships among latent variables and determines how these variables will be measured. This is sometimes referred to as model specification and is probably the most important and difficult step in the process since if the model is incorrectly specified or the wrong measured variables are chosen to reflect the latent ones, there is little hope the model will give any kind of useful information. Here the model takes centre stage in defining the object of study and it is the model itself that is investigated. Again, the question of whether this kind of activity is best described as measurement or calculation will determine, at least to some extent, the kind of results we take the model to provide. Space prevents me from addressing issues related to this type of modelling in the paper. I mention it simply to highlight the pervasiveness of the connection between models and measurement.

  5. Despite this “paper” approach to theorizing Maxwell claimed that his field equations were deduced from experimental facts with the aid of general dynamical principles about matter in motion. This allowed him to treat the field variables as generalized mechanical variables that contained terms corresponding only to observables. Once a physical phenomenon can be completely described as a change in the configuration and motion of a material system the dynamical explanation is complete. Until that time, however, we must rely on mechanical images, analogies and models that furnished visual conceptions of the phenomena, conceptions whose sole function was heuristic. For more on Maxwell’s claims about deduction from phenomena see Morrison (1992).

  6. See Baltimore Lectures, 120, pp. 282–283.

  7. For a more extensive account see Morrison (2008).

  8. Kelvin complained that even the so-called measurement of c involved a purely electromagnetic procedure, the only use made of light was to see the instruments. c was determined by measuring the electromotive force used to charge a condenser of a known capacity which was then discharged through a galvanometer. This would give an electromagnetic measure of the quantity of electricity in the galvanometer.

  9. Even after the experimental proof of the existence of electromagnetic waves by Hertz in 1888, Kelvin remained critical of Maxwell’s theory and its postulation of the displacement current. For more on Kelvin’s views about measurement and models see Smith and Wise (1989).

  10. To that extent it is more than a little ironic that the empiricism that motivated Kelvin’s use of mechanical models evolved into a form of methodological and theoretical dogmatism that prevented him from understanding and accepting the fundamental components of the most successful theory of his time.

  11. Humphreys (1990) was one of the first to draw our attention to the importance of simulation in understanding features of mathematically oriented theorizing and their connection to mathematical models and modeling practices more generally. That discussion continues in his 2004. Hartmann (1995) has also emphasised several important features of simulation including their dynamical aspects. For a discussion of issues surrounding the materiality of simulations see excellent papers by Winsberg (2008) and Parker (2008) as well as Morgan (2003a, b). Hughes (1999) has an interesting discussion of computer simulation and the Ising model.

  12. The notion of experiment I am interested in here is one that goes beyond numerical experiment intended as a kind of mathematical number crunching.

  13. I take it that “object” here means apparatus whereas in computer simulation the object is the simulation run on the digital computer.

  14. For an extensive treatment of simulation using particle methods see Hockney and Eastwood (1994). A good deal of my discussion of this method borrows from their account. I introduce the notion of a “simulation system” as a way of isolating what I take to be the crucial features of the particle method.

  15. Other methods of discretization include finite difference approximations and finite element approximations.

  16. Unlike an experiment one is not directly manipulating a “material object” in a computer simulation, unless of course we think in terms of the materiality of the digital computer itself. Parker (2008) refers to computer simulation studies as material in this latter sense.

  17. There are issues here about the degree of departure between the discretized simulation model and the mathematical model, that is, whether the former is an accurate representation of the latter. To some extent these issues are practical problems resolved via calibration and testing and hence are not reasons for general scepticism regarding the representational capacity of the simulation model itself. .

  18. For more details see Hockney and Eastwood (1994, p. 3). As they point out, one advantage is that a number of particle attributes are conserved quantities so no need to update the system as the simulation evolves.

  19. The decision to use a particular method depends on a variety of factors including the size of the system, whether the forces are long range, non-zero interaction, smoothly varying etc.

  20. Provided of course that the other relevant calibrations on the machine have been performed.

  21. Winsberg (2003) has suggested a similar view in his claim that simulation, like experiment, has, to use Hacking’s phrase, a life of its own.

  22. This, of course, is just the sense in which models function as mediators between theory and material systems. I will have more to say about the specifics of this link below.

  23. Consequently we would be unable to capture many of the uses of computer simulation in experimental contexts, specifically astrophysics and cosmology.

  24. The use of the term ‘direct’ is important here. It is not that the target system is not being investigated in contexts where there is a strong reliance on models but rather there is no direct access to the target system making the model the immediate object of inquiry.

  25. This is a different issue than the kinds of considerations required for measurement by, for example, National Bureau of Standards where it is necessary to take into account variation in temperature, change in length due to atmospheric pressure etc. Those kinds of considerations are over and above the correction factors described above.

  26. It is important to note here that this is a different issue from what we typically call the “theory of the apparatus” which involves the theoretical knowledge required to build a machine that will function in the desired way. However, I should also point out that in designing machines like the LHC, computer simulations of particle paths provide crucial data for the alignment of magnets etc.

  27. Batitsky (1998) argues that even things like length measurements cannot be justified solely on the basis of our perceptual interactions with the world. Hence, the notion of fundamental measurement is essentially an empiricist’s myth.

  28. Sometimes this distinction is absorbed or collapses into the fundamental/derived distinction. Causey (1969) defines a derived measurement as one which has dimensions expressed in terms of previously given fundamental quantities. Fundamental measurements are those that those that can be made independently of the possibility of making any other measurements.

  29. I come back to this point below.

  30. The experiment did however measure the magnetic moment of the silver atoms.

  31. For a detailed discussion of these measurements see Morrison (2007).

  32. In the pendulum case we are interested in both precision and accuracy and hence concerned not only with the status of the physical pendulum as a measuring device (internal validity) but also with its ability to measure the true value of g (external validity). The correction factors applied to the idealized model are relevant for both. Hence, contrary to the distinction introduced by Winsberg, the modelling involved in experimental contexts relates to both internal and external validity and includes the physical system under investigation as well as the object being manipulated.

  33. A general epistemological issue that emerges from this discussion concerns the changing nature of both measurement and experiment. In the end it may be that the account of computer simulation I have argued for is one that is more appropriate to the natural rather than the social sciences. However, given the complex nature of measurement in the social sciences I am inclined to think that the two contexts may be remarkably similar. Justification of that intuition will have to wait for another time.

  34. Support of research by the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. I would also like to thank the participants of the Oberlin Colloquium, particularly Ron Giere and Wendy Parker for their comments and questions. Thanks also go to Eran Tal for many useful conversations, comments and challenges.

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Morrison, M. Models, measurement and computer simulation: the changing face of experimentation. Philos Stud 143, 33–57 (2009). https://doi.org/10.1007/s11098-008-9317-y

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