Brain atlases like these, averaged together from scans of 20 right-handed men, show how and where brains vary in shape. The biggest differences (in pink) cluster in the temporo-parietal lobe, the seat of language, logic, and other traits unique to humans.
At first glance, it’s tough to distinguish between an image of an average brain of normal shape and one of an average brain of schizophrenic shape. But when Bookstein compares the normals with the schizophrenics using a thin-plate spline, the difference is obvious. In the schizophrenics, a little triangular area in the back of the corpus callosum, the central conduit for all communications between the two sides of the brain’s cortex, seems swollen—as if nature had grabbed some landmark points and pushed them apart to create a caricature. Because the shape of the corpus callosum barely varies in healthy people, even this modest swelling turns out to be statistically significant.

“I really did want to see if I could somehow offer help to people who come down with schizophrenia,” Bookstein says, pointing to the swollen corpus callosum. “To the extent that this pattern is correct, it would permit me to figure out who’s going to get it before [they have their first psychotic breaks].” If doctors knew which patients showed signs of developing schizophrenia, they might try prescribing medications in advance. At the very least, the patients could be counseled to avoid alcohol and addictive drugs, which can complicate the disease.


Bookstein’s work on schizophrenia is still a step ahead of mainstream thinking. Then again, his mind has always moved a little bit faster than others. “I was a bit of a prodigy,” he notes matter-of-factly. At the age of 11, he taught himself algebra from library books. At 14, he won a statewide mathematics competition and, at 15, he entered the University of Michigan. He sailed through college in three years and went to graduate school for mathematics at Harvard.

Thanks to such atlases, brain surgeons like Arthur Toga and Andrew Cannestra (below left) can now remove tumors they wouldn’t have dared touch before.
It seemed as if he were prepared to take off into the mathematical stratosphere. But at Harvard, the self-taught math whiz suddenly found he couldn’t just improvise his own solutions anymore. “I lasted about four weeks and realized that this just wasn’t going to work,” Bookstein says. “I was going to be a lousy mathematician.” He switched to sociology, but things didn’t go much better there. All of his ideas for research were either too ambitious or too off-the-wall. With a laugh, he recalls what his dissertation committee thought when he submitted a proposal to use the mathematics of general relativity to measure social change: “We don’t know what this is. We know it’s not sociology. Please find something else to do with your life.”

After a couple years of working various jobs, Bookstein heard about a program at Michigan for oddball scholars with bright ideas. Out of 200 applicants, he was one of seven chosen for the program. Back in Ann Arbor, they still remembered the wunderkind from eight years before. When Bookstein returned there in 1974, he came with a characteristically grand scheme in mind—to work out a mathematically correct theory of shape.

These days, talking with Bookstein can still be an intense experience, though he says he has lightened up since he began running a bed-and-breakfast with his wife, Edith. “When he gives a lecture, the rate of information transmittal is very high,” says Leslie Marcus, a paleontologist at the American Museum of Natural History and a self-described “facilitator” for the new morphometrics. “It’s like having a fire hose put in your mouth.” Indeed, Bookstein talks quickly—in perfectly composed paragraphs, as if quoting from a book—and types even faster. Watching him navigate around a three-dimensional brain image on his computer workstation is enough to induce vertigo.
Morphometrics may be new to doctors, but paleontologists have used it for almost two decades. In 1996, statistician Christopher Small, of the University of Waterloo in Ontario, showed how the evolution of the human skull can be recreated by moving around just three landmarks on a single line (left). Now Bookstein and Horst Seidler of the University of Vienna have added a dramatic twist to the same idea. In a paper published last month, they and their colleauges used morphometrics and ct scans to compare the insides of human and proto human skulls. The top picture to the right is of an Australopithecus skull 2.5 million years old. The skulls below it belong to a 600,000-year-old Homo heidelbergensis, a 300,000-year-old proto-Neanderthal, and a modern human, respectively. Though the Australopithecus brain case is noticeably smaller, those below it are nearly identical to one another. Our high foreheads may make us seem smarter than our ancestors, but the truth is that our frontal lobes haven’t grown or changed shape in 600,000 years—our sinuses have simply shrunken. Even half a million years ago, Bookstein and Seidler conclude, humans probably had the raw ability to play poker or plan battles—they just hadn’t developed the culture yet.

That intimidating style, and the devilish math behind morphometrics, may account for why physicians have been slow to adopt his techniques. “What’s the holdup of using shape measurement? It’s a harder concept,” says David Kennedy, a neuroscientist at the Harvard Medical School Center for Morphometric Analysis. “If I say that the volume of the hippocampus is 13 cubic centimeters, we all know what I mean. If I talk about spherical harmonics or a thin-plate spline, clinicians don’t have a grasp of what is biologically meaningful about that.”

The field of schizophrenia research is booming these days, thanks to the window on the brain provided by magnetic resonance imaging (mri). But it doesn’t occur to many researchers that they need a whole new theory of shape to interpret what those mri scans are telling them. Most researchers, like Kennedy, still prefer studying volumes. “To be honest, volumetric measures have done pretty well,” says Paul Thompson, a neuroscientist at the University of California at Los Angeles. Among other things, researchers have found that the hippocampus is usually smaller in schizophrenics, whereas some of the ventricles (four cavities at the center of the brain that are filled with cerebrospinal fluid) are larger.