The Nature of Scientific Proof in the Age of Simulations
Is numerical mimicry a third way of establishing truth?
In a series of lunchtime conversations with astrophysicist Piet Hut of the Institute for Advanced Study in Princeton, I discovered that we were both concerned about the implications of these ever-expanding simulations. Computational astrophysics has adopted some of the terminology and jargon traditionally associated with the experimental sciences. Simulations may legitimately be regarded as numerical experiments, along with the assumptions, caveats, and limitations associated with any traditional, laboratory-based experiment. Simulated results are often described as being empirical, a term usually reserved for natural phenomena rather than numerical mimicries of nature. Simulated data are referred to as data sets, seemingly placing them on an equal footing with observed natural phenomena.
The Millennium Simulation Project, designed and executed by the Max Planck Institute for Astrophysics in Munich, Germany, provides a pioneering example of such an approach. It is a massive simulation of a universe in a box, elucidating the very fabric of the cosmos. The data sets generated by these simulations are so widely used that entire workshops are organized around them. Mimicry has supplanted astronomical data.
It is not far-fetched to say that all theoretical studies of nature are approximations. There is no single equation that describes all physical phenomena in the universe—and even if we could write one down in principle, solving it would be prohibitive, if not downright impossible. The equations we study as theorists are merely approximations of nature. Schrödinger’s equation describes the quantum world in the absence of gravity. The Navier-Stokes equation is a macroscopic description of fluids. Newton’s equation describes gravity accurately under terrestrial conditions, superseded only by Einstein’s equations under less familiar conditions.
To understand the orbital motion of exoplanets around distant stars, it is mostly sufficient to consider only Newtonian gravity. To understand the appearance of these exoplanets’ atmospheres requires approximating them as fluids and understanding the macrosopic manifestations of the quantum mechanical properties of the individual molecules: their absorption and scattering properties. Each of these governing equations is based on a law of nature—the conservation of mass, energy, or momentum, or some other generalized, more abstract quantity such as potential vorticity. One selects the appropriate governing equation of nature and solves it in the relevant physical regimes, thus creating a model that captures a limited set of salient properties of a physical system. The term itself is widely abused—a “model” that is not based on a law of nature has little right to be called one.