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COMPUTING SCIENCE

The World in a Spin

Brian Hayes

Pierre Simon de Laplace had a plan for understanding everything. To this celestial mechanic, it looked simple: The particles of matter produce forces, and those forces in turn move the particles. So if we could just measure all the forces and motions at any one instant, we could calculate the entire history of the universe—past, present and future.

Two centuries of progress in the sciences have not fulfilled Laplace's vision; on the contrary, quantum mechanics, and lately chaos theory, have undermined faith in his program. But let's pretend. If we study a computational model of the universe rather than the real thing, we really can track all the forces and motions. The laws of physics can be kept as simple as we please, since we invent and enforce them. In this toy universe, we can banish all quantum uncertainties, and trace every last detail of every microscopic event. Yet even in such an open and transparent world, total knowledge is still elusive. Although we can follow the individual particles, we have trouble seeing how they act in the aggregate. For example, we may well fail to predict basic thermodynamic phenomena such as boiling and freezing. We could know the whereabouts of every molecule of water in an artificial ocean, but not know whether the stuff is solid or liquid or vapor.

The prototypical system for exploring issues of this kind is called the Ising model. It is a model of matter pared down to its barest essentials—just about the simplest imaginable system in which large numbers of particles might be expected to produce some kind of cooperative behavior. If Laplace's plan can be made to work anywhere, it should succeed here. But the Ising model has proved a difficult challenge, even when attacked with some heavy-duty mathematics and computer science. Indeed, the most important version of the model remains without an exact solution.




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