All those folds and fissures make life difficult for a neuroscientist: they bury two thirds of the brain's surface, or cortex, where most of the information processing takes place. With so much of the brain hidden, researchers have a hard time seeing exactly which parts of the cortex are doing what and how they are related to one another. "People want to see what's in the folds," says Monica K. Hurdal, a computer scientist at Florida State University, who has created a computer program to flat-map the brain. Conventional imaging techniques usually display cross sections of the brain, making it difficult to view the entire surface. For example, an MRI scan might show areas that look to be adjacent but are, if they have a deep fold between them, actually far apart.

"Converting a sphere into a plane is not so difficult," Hurdal explains, "but it does require that certain compromises be made." The Mercator projection of the earth, for instance, preserves shapes and angles at the expense of areas, so that the polar regions look far too large in relation to the equatorial ones. The mathematical basis for the Mercator projection is an 1851 law of geometry known as the Riemann mapping theorem (although the 16th-century cartographer himself wasn't aware of it, of course). It says that a three-dimensional curved surface can be flattened while preserving the angular information, thereby yielding a so-called conformal map.

   
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