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The Nature of Scientific Proof in the Age of Simulations

Is numerical mimicry a third way of establishing truth?

Kevin Heng

2014-05PerspectiveFp175.jpgClick to Enlarge ImageEmpiricism lies at the heart of the scientific method. It seeks to understand the world through experiment and experience. This cycle of formulating and testing falsifiable hypotheses has amalgamated with a modern form of rationalism—the use of reasoning, mathematics, and logic to understand nature. These schools of thought are couched in centuries of history and, until recently, remained largely distinct. Proponents of empiricism include the 18th-century Scottish philosopher David Hume, who believed in a subjective, sensory-based perception of the world. Rationalism is the belief that the use of reasoning alone is sufficient to understand the natural world, without any recourse to experiment. Its roots may be traced to the Greek philosophers Aristotle, Plato, and Pythagoras; its more modern proponents include Kant, Leibniz, and Descartes.

A clear example of both practices at work is in the field of astronomy and astrophysics. Astronomers discover, catalog, and attempt to make sense of the night sky using powerful telescopes. Astrophysicists mull over theoretical ideas, form hypotheses, make predictions for what one expects to observe, and attempt to discover organizing principles unifying astronomical phenomena. Frequently, researchers are practitioners of both subdisciplines.

Problems in astrophysics—and physics, in general—may often be rendered tractable by concentrating on the characteristic length, time, or velocity scales of interest. When trying to understand water as a fluid, it is useful to treat it as a continuous medium rather than as an enormous collection of molecules, because it makes it vastly easier to visualize (and compute) its macroscopic behavior. Although the Earth is evolving on geological time scales, its global climate is essentially invariant from one day to the next—hence the difficulty in explaining the urgency of climate change to the public. The planets of the Solar System do not orbit a static Sun, as it performs a ponderous wobble about its center of mass due to their collective gravitational tug, but it is often sufficient to visualize it as being so. Milankovitch cycles cause the eccentricity and obliquity of the Earth’s orbit to evolve over hundreds of thousands of years, but they are essentially constant over a human lifetime.

This separation of scales strips a problem down to its bare essence, allowing one to gain insight into the salient physics at the scale of interest.

Multiscale problems, on the other hand, do not lend themselves to such simplification. Small disturbances in a system might show up as big effects across myriad sizes and time scales. Structures on very large scales “talk” to features on very small scales and vice versa. For example, a grand challenge in astrophysics is understanding planet formation—being able to predict the diversity of exoplanets forming around a star, starting from a primordial cloud of gas and dust. Planet formation is an inherently multiscale problem: Uncertainties on microscopic scales, such as how turbulence and the seed particles of dust grains are created, hinder our ability to predict the outcome on celestial scales. Many real-life problems in biology, chemistry, physics, and the atmospheric and climate sciences are multiscale as well.

By necessity, a third, modern way of testing and establishing scientific truth—in addition to theory and experiment—is via simulations, the use of (often large) computers to mimic nature. It is a synthetic universe in a computer. One states an equation (or several) describing the physical system being studied, programs it into a computer, and marches the system forward in space and time. If all of the relevant physical laws are faithfully captured, then one ends up with an emulation—a perfect, The Matrix–like replication of the physical world in virtual reality.

In astronomy and astrophysics, this third way has come into its own, largely due to the unique status of astronomy as an experimental science. Unlike other, laboratory-based disciplines, astronomers may not exert full control over their experiments—one simply cannot rearrange objects in the sky. Astronomical phenomena often encode information about a subpopulation of a class of objects at a very specific moment in their evolution. To understand the entire population of a class of objects across cosmic time requires large computer simulations of their formation and evolution. Examples of different classes of objects include exoplanets, stars, black holes, galaxies, and even clusters of galaxies. The hope is that these simulations lead to big-picture understanding that unifies seemingly unrelated astronomical phenomena.

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