On 3 Mar 2010 David H. Bailey of Lawrence Berkeley National Lab gave a “distinguished seminar” at the University of Delaware entitled “Computing as the Third Mode of Scientific Discovery.” The full lecture is available here: Online presentation.

Abstract:

The latest state-of-the-art scientific computer systems have achieved over 1 “Pflop/s” (one million billion floating-point arithmetic operations per second). Scientists have capitalized on this computational power by developing a wide range of sophisticated programs that are becoming so effective that scientific computing is now widely regarded as the third mode of scientific discovery, after theory and experiment.

In other words, the computer has become a virtual laboratory, wherein “experiments” can be performed to explore phenomena that are too complicated, expensive or dangerous to explore by ordinary empirical experiment. Many examples of this methodology will be described, including studies in climate and environmental science, astrophysics, biology, engineering, and mathematics.

Among the examples of such computations, the author will describe some recent research wherein new formulas of mathematics have been discovered, using high-precision numerical computations on state-of-the-art computers. Perhaps the best-known such discovery is a new formula for the mathematical constant pi, which has the curious property that it permits one to calculate digits of pi beginning at an arbitrary starting position in the binary expansion.