Science in the Age of Computer Simulation
DOI: 10.1063/PT.3.1221
About 20 years ago, while I was taking a midday stroll with colleagues, my mind wandered to a “large” molecular dynamics simulation I was working on. (That simulation could easily run on my laptop today.) After making some progress on a couple of problems that had been troubling me, I attempted to reenter my companions’ conversation by uttering, “But why should the iteration x (i + 1) = (a*x (i) + b) mod p have anything to do with the physics of aggregate formation?” My evident non sequitur was greeted with strange looks and “Huh? What are you talking about?” The publication of Eric Winsberg’s Science in the Age of Computer Simulation is too late to rescue that old conversation, but its existence will help to validate interest in philosophical questions about computational simulation.
Winsberg adopts the methods of philosophy of science to pose questions about how computational simulations relate to physical reality. His goal is not to answer all such questions but rather to frame some of them and suggest paths for investigation. He does not try to explain why, for example, the generation of random numbers can tell us something about particulate aggregation; his intent is to locate the question on the landscape of philosophical inquiry.
Philosophical investigation of how mathematics relates to physical reality has had a long history. At first glance, computer simulations may seem to consist merely of mechanical implementations of mathematical models. However, one of Winsberg’s main points is that the methods and approaches used in simulation are more than just numerical evaluations of formulas implied by mathematical analysis of a theory. Here I wish he had said something about the formal meaning of “implications” of a mathematical formulation. The claim that statement A implies statement B does not mean that B is somehow contained in A. In fact, it means that A is contained in B. Therefore, mathematical deduction locates a theory in the universe of mathematical truths, but it does not reveal the theory’s content.
In contrast, computational simulation produces knowledge different from that obtainable via deductions from theory; mathematical theory guides but does not determine how numerical models are constructed. Computational formulations are often amalgams of several theories, and they include various manifestly unphysical tricks—for example, adding artificial viscosity. Such techniques, however, generate epistemological questions about the relation between results of a simulation and the physical reality.
The distinction between facts obtained via deduction and those obtained via computation is treated well in Winsberg’s book. Chapter 4 discusses the difference between real and computational experiments. A particularly nice example given is the use of physical experiments as a kind of analogue computation—for example, using Bose–Einstein condensates to study the behavior of black holes. Chapter 5 discusses so-called multiscale computations, which rely on unphysical computational tricks to meld two or more incompatible theories, such as molecular dynamics and computational fluid dynamics (CFD).
Parts of the book seem to indicate a lack in the author’s background in applied mathematics and computational science. One example is the discussion of “exact” solutions of a differential equation. Winsberg appears to believe that numerically evaluating the closed-form solutions to the equation provides the best results. However, it’s well known that for some functions, including the Airy functions and the Hankel functions, approximating the differential equation is more numerically precise than evaluating the closed-form function directly. In general, closed-form solutions won’t give more insight than will the differential equation itself. In a similar vein, the author appears to expect too much from CFD. The reader may be led to believe that computational tricks are introduced because the partial differential equations cannot be indefinitely discretized. But, of course, CFD is itself an approximation. The Navier–Stokes equations are a versatile and powerful method for modeling fluids; but fluids are, in reality, ensembles of particles.
In spite of those quibbles, Science in the Age of Computer Simulation is an interesting and valuable book. I hope that it will stimulate more discussion and investigation of philosophical questions engendered by the enormous role that computational simulation plays in science.
More about the Authors
Francis Sullivan. Institute for Defense Analyses Bowie, Maryland.
