Intelligence in Scientific Computing

Combining numerical techniques with ideas from symbolic computation and with methods incorporating knowledge of science and mathematics leads to a new category of intelligent computational tools for scientists and engineers. These tools autonomously prepare simulation experiments from high-level specifications of physical models. For computationally intensive experiments, they automatically design special-purpose numerical engines optimized to perform the necessary computations. They actively monitor numerical and physical experiments. They interpret experimental data and formulate numerical results in qualitative terms. They enable their human users to control computational experiments in terms of high-level behavioral descriptions.

Swimming in Space-Time

Cyclic changes in the shape of a quasi-rigid body on a curved manifold can lead to net translation and/or rotation of the body in the manifold. Presuming space-time is a curved manifold as portrayed by general relativity, translation in space can be accomplished simply by cyclic changes in the shape of a body, without any thrust or external forces.

The Role of Programming in the Formulation of Ideas

Classical mechanics is deceptively simple. It is surprisingly easy to get the right answer with fallacious reasoning or without real understanding. To address this problem we use computational techniques to communicate a deeper understanding of Classical Mechanics. Computational algorithms are used to express the methods used in the analysis of dynamical phenomena. Expressing the methods in a computer language forces them to be unambiguous and computationally effective. The task of formulating a method as a computer-executable program and debugging that program is a powerful exercise in the learning process. Also, once formalized procedurally, a mathematical idea becomes a tool that can be used directly to compute results.