Πέμπτη 4 Σεπτεμβρίου 2025

‘Ten Martini’ Proof Uses Number Theory to Explain Quantum Fractals

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.

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