In Constructing Quarks (1984) Andrew Pickering discussed the early experiments on atomic parity violation performed at Oxford University and at the University of Washington and published in 1976 and 1977. The results disagreed with the predictions of the Weinberg-Salam (W-S) theory of unified electroweak interactions. Another experiment, performed at the Stanford Linear Accelerator Center in 1978, on the scattering of polarized electrons from deuterons confirmed the theory. Pickering regards the Oxford and Washington experiments as mutants, slain by the SLAC experiment.

By 1979 the W-S theory was regarded by the high-energy physics community as established, despite the fact that as Pickering recounts, “there had been no intrinsic change [emphasis in original] in the status of the Washington-Oxford experiments.” (Pickering 1984, p. 301).

A great deal of attention has been paid by philosophers to the use of computers in the modelling of human cognitive capacities and in the construction of intelligent artifacts. This emphasis has tended to obscure the fact that most of the high-level computing power in science is deployed in what appears to be a much less exciting activity: solving equations. This apparently mundane set of applications reflects the historical origins of modem computing, in the sense that most of the early computers in Britain and the U.S. were devices built to numerically attack mathematical problems that were hard, if not impossible, to solve non-numerically, especially in the areas of ballistics and fluid dynamics. The latter area was especially important for the development of atomic weapons at Los Alamos, and it is still true that a large portion of the supercomputing capacity of the United States is concentrated at weapons development laboratories such as Los Alamos and Lawrence Livermore.

The central claim of this paper is that computer simulation provides (though not exclusively) a qualitatively new and different methodology for the physical sciences, and that this methodology lies somewhere intermediate between traditional theoretical physical science and its empirical methods of experimentation and observation. In many cases it involves a new syntax which gradually replaces the old, and it involves theoretical model experimentation in a qualitatively new and interesting way. Scientific activity has thus reached a new milestone somewhat comparable to the milestones that started the empirical approach (Galileo) and the deterministic mathematical approach to dynamics (the old syntax of Newton and Laplace). Computer simulation is consequently of considerable philosophical interest. In view of further technical developments in the near future, computer experts suggest that we are at present only at the very beginning of this new era.

It’s uncontroversial that notions of idealization and approximation are central to understanding computer simulations and their rationale. So, for example, one common form of computer simulation is to abandon a realistic approach that is computationally non-tractable for a more idealized but computationally tractable approach. Many simulations of systems of interacting members can be understood this way. In such simulations, realistic descriptions of individual members are replaced with less realistic descriptions which have the virtue of making interactions computationally tractable. Such simulations can be supplemented with empirically determined correction factors which render the output produced by means of the idealizations more in accord, one hopes, with what the more realistic approach would have produced had it been computationally tractable. Another way to utilize computers is to replace an idealized but analytically tractable account of some phenomenon with a less idealized account which has no closed form or analytical solutions but where the computer can be used generate approximations to the desired solutions.

In a paper fifteen years ago about the meaning and the possibility of the beginning and end of time, our redoubtable session chair, John Earman, ended up like this:

These remarks are a kind of manifesto of an approach to philosophical questions about space and time dating from the late 1960’s.

Some of what is true about the world is thought, by some, to be true of necessity. Other truths about the world are merely contingently true, it is said. Next we get a familiar distinguishing of necessity into its various kinds. Anything whose contrary would contradict the laws of logic is logically necessary. Anything compatible with these laws is logically contingent. There are, of course, grave problems in finding a principled way of discriminating the logical truths from all the others. Some propositions are not logically necessary but are metaphysically necessary. For Kant, I suppose, the alleged facts that every event had a cause, and that in any change a substance remained unchanged would be such facts. So, I suppose, would be the necessary but synthetic truths of geometry and arithmetic. For more contemporary philosophers genuine identity statements, either singular or general, might have such a status.

This essay will survey various considerations that arise when a branch of physics requires formulation in terms of partial differential equations (or some facsimile thereof). My examples will derive almost exclusively from classical continuum (=smeared out matter) mechanics. Although the relevant formal facts are well known, it is difficult to find coherent discussions of how the underlying phenomena ought to be viewed. In this paper, I will give an introduction to some of the issues, although I will confess at the outset that I am not certain how these matters should be finally adjudicated. Certainly it would be helpful if philosophy paid more attention to the underlying issues.

Some of the points I will discuss bear upon some of Professor Sklar’s observations. Although my attention will be largely directed towards the status of boundary conditions (and related forms of singular surface), many of my examples can be adapted, mutatis mutandis, to initial conditions as well.