The original version of this story appeared in Quanta Magazine.
In 1974, five years before he wrote his Pulitzer Prize–winning book Gödel, Escher, Bach: An Eternal Golden Braid, Douglas Hofstadter was a graduate student in physics at the University of Oregon. When his doctoral adviser went on sabbatical to Regensburg, Germany, Hofstadter tagged along, hoping to practice his German. The pair joined a group of brilliant theoretical physicists who were agonizing over a particular problem in quantum theory. They wanted to determine the energy levels of an electron in a crystal grid placed near a magnet.
Hofstadter was the odd one out, unable to follow the others’ line of thought. In retrospect, he’s glad. “Part of my luck was that I couldn’t keep up with them,” he said. “They were proving theorems, but they had nothing to do with the essence of the situation.”
Hofstadter instead decided to test out a more down-to-earth approach. Rather than proving theorems, he was going to crunch some numbers using an HP 9820A desk calculator—a computerlike machine that weighed nearly 40 pounds and could be programmed to perform complex computations.
Hofstadter needed it to solve a particular formulation of the Schrödinger equation, which lies at the core of quantum mechanics. When fed certain information about an electron and its environment as inputs, the Schrödinger equation describes how the electron will behave. In particular, its solutions tell you the amount of energy the electron can have.
In the case that Hofstadter was interested in, the Schrödinger equation includes a variable called alpha, the product of the magnetic field’s strength and the area of one grid square. Alpha captures information about the forces acting on the electron.