The pair joined a group of brilliant theoretical physicists who were agonizing over a particular problem in quantum theory. “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.