Layers of Models in Computer Simulations

Abstract

I discuss here the definition of computer simulations, and more specifically the views of Humphreys, who considers that an object is simulated when a computer provides a solution to a computational model, which in turn represents the object of interest. I argue that Humphreys's concepts are not able to analyse fully successfully a case of contemporary simulation in physics, which is more complex than the examples considered so far in the philosophical literature. I therefore modify Humphreys's definition of simulation. I allow for several successive layers of computational models, and I discuss the relations that exist between these models, the computer, and the object under study. An aim of my proposal is to clarify the distinction between computational models and numerical methods, and to better understand the representational and the computational functions of models in simulations.

Acknowledgements

Many thanks to Anouk Barberousse, Paul Humphreys, Cyrille Imbert, Julie Jebeile, and two anonymous referees of this journal for critical comments or suggestions that helped to improve this paper. This work has been conducted mainly at the IHPST in Paris while I benefited from a doctoral grant from the University of Paris 1 and from the ANR Compuphys project (ANR-08-JCJC-0035-01).

Notes

[1] Cf., for instance, Hughes (1999), Winsberg (1999), Norton and Suppe (2001), and Humphreys (2004). Hartmann (1996) prefers to speak about ‘processes’.

[2] Humphreys's conception seems to be more general than that of others, for instance than Hartmann's: it ‘leave[s] room for simulations of static objects as well’ (Humphreys 2004, 108) and Monte-Carlo methods (Humphreys 2004, 106), which Hartmann (1996, 83, 87–88) excludes.

[3] I do not wish here to diminish the importance of discretization in simulations: a philosophical analysis of it can be found in Lenhard (2007).

[4] Textbook presentations of the quantum rotor can be found in Schulman (1981, §23.1), Zinn-Justin (2003, §5.6), Kleinert (2007, §6.1). Papers about an ITPISR simulation of the quantum rotor are, for instance, Bietenholz et al. (1997) and Boyer, Bietenholz, and Wuilloud (2007).

[5] Path integral was invented by Feynman in the 1940s. Historical elements of the later development can be found in Reed and Simon (1975, 115) and Montvay and Münster (1994, 2).

[6] Cf., for example, Schulman (1981, ch. 26), Zinn-Justin (2003, ch. 4), and Kleinert (2007, §6.2).

[7] The name ‘Monte-Carlo’ refers to the random character of the casino games. For the origin of the Monte-Carlo method, see Metropolis and Ulam (1949), Galison (1997, ch. 8). Cf. Humphreys (1994), Galison (1997, ch. 8), Beisbart and Norton (2012) for historical and philosophical analyses.

[8] Although the concept of ‘model’ has been much discussed in the literature, I use it in a wide and uncritical sense here. The vocabulary will be more specific in section 4.

[9] The paper is actually about a rotor in quantum field theory, but the point about the representation is the same.

[10] For quantum field theory, a table of correspondence similar to Table 1 can be found in Gupta (1998, 22).

[11] Cf. section 2.1. Arguments are made about the quantum rotor, but could easily be generalized for any ITPISR simulation.

[12] It seems very unlikely that Humphreys or anyone else would like to consider that applying an imaginary time transformation or a reinterpretation is a simulation in itself. If one insisted to say that it amounts to providing a solution to some equation, and thus fits Humphreys's definition, then would not multiplying by −1 just be a simulation as well?

[13] If the label ‘theory’ may be questioned, it is at least a radical reformulation of the quantum field theory, with a different number of space dimensions, for instance.

[14] Note that this proposal could have the following one as a particular case: the statistical CM would belong to the core simulation, and the lattice and quantum models would be added to get the full simulation.

[15] A classical reference on analogical models is Hesse (1963). Note that there exist also analogue simulations (e.g. Humphreys 2004, §4.5), in contrast to digital simulations run on computers about which I am only concerned here.

[16] One can also say that the first CM also represents B, but analogically and more indirectly (cf. section 4).

[17] The representational role of a candidate CM may depend on the context and on the use of the simulation by scientists.