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Book Summary: The Upright Thinkers

Author: Leonard Mlodinow

Substory: Struggles To Know: No Personal Struggles But A Cooperative Venture

When I was a graduate student, the problem I chose for my Ph.D. dissertation was the challenge of developing a new method for finding approximate solutions to the unsolvable quantum equations that describe the behavior of hydrogen atoms in the strong magnetic field outside neutron stars—the densest and tiniest stars known to exist in the universe. I have no idea why I chose that problem, and apparently neither did my thesis adviser, who quickly lost interest in it. I then spent an entire year developing various new approximation techniques that, one after another, proved no better at solving my problem than did existing methods, and hence not worthy of earning me a degree. Then one day I was talking to a postdoctoral researcher across the hall from my office. He was working on a novel approach to understanding the behavior of elementary particles called quarks, which come in three “colors.” (The term, when applied to quarks, has nothing to do with the everyday definition of “color.”) The idea was to imagine (mathematically) a world in which there are an infinite number of colors, rather than three. As we talked about the quarks, which had no relation at all to the work I was doing, a new idea was born: What if I solved my problem by pretending that we lived not in a three-dimensional world, but in a world of infinite dimensions?

If that sounds like a strange, off-the-wall idea, it was. But as we churned through the math, we found that, oddly, though I could not solve my problem as it arose in the real world, I could if I rephrased it in infinite dimensions. Once I had the solution, “all” I had to do to graduate was figure out how the answer should be modified to account for the fact that we actually live in three-dimensional space.

This method proved powerful—I could now do calculations on the back of an envelope and achieve results that were more accurate than those from the complex computer calculations others were using. After a year of fruitless effort, I ended up doing the bulk of what would become my Ph.D. dissertation on the “large N expansion” in just a few weeks, and over the following year that postdoc and I turned out a series of papers applying the idea to other situations and atoms. Eventually a Nobel Prize–winning chemist named Dudley Herschbach read about our method in a journal with the exciting name Physics Today. He renamed the technique “dimensional scaling” and started to apply it in his own field. Within a decade there was even an academic conference entirely devoted to it. I tell this story not because it shows that one can choose a lousy problem, waste a year on dead ends, and still come away with an interesting discovery, but rather to illustrate that the human struggle to know and to innovate is not a series of isolated personal struggles but a cooperative venture, a social activity that requires for its success that humans live in settlements that offer minds a plentitude of other minds with which to interact.