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Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"The World in a Spin," by Brian Hayes. American Scientist, September-October 2000, pages 384-388.

Two hundred years ago, celestial mechanic Pierre Simon de Laplace had a plan for understanding everything: if we could just measure all the forces and particle motions at any one instant, we could calculate the entire history of the universe--past, present, and future. Unfortunately for Laplace, such an idea has lost favor in light of new advances such as chaos theory.

Nevertheless, we can still study a computational model of the universe, rather than the real thing, and be able to track the forces and motions. We define the laws of physics in this toy universe, making them as simple as we want, and we will be able to trace every last detail of every event.

The prototypical system for exploring such a universe is called the Ising model. Wilhelm Lenz invented it in 1920 as a simplified version of a ferromagnet, and Ernst Ising studied it in his doctoral dissertation a few years later. The elements of the model are called spins, which can be thought of as arrows pointing up or down; the spins are then arranged on a grid. Although the model appears simple on the surface, a careful study of spin interactions is highly complex. Thus we can use the Ising model to shed light on the workings of the real universe.

--- Benjamin Stein