Jim Holt (best-selling author of Why Does the World Exist?) recounts the story behind Gödel's citizenship test and his problem with the U.S. Constitution that almost halted it all. An excerpt from his new book When Einstein Walked with Gödel: Excursions to the Edge of Thought.
Aristotle, the second-greatest logician of all time, was also an expert on political constitutions. Can the same be said for the greatest logician of all time, Kurt Gödel? Gödel had a genius for detecting the paradoxical in unexpected places. He looked into the axioms of mathematics and saw incompleteness. He looked into the equations of general relativity and saw “closed time- like loops.” And he looked into the Constitution of the United States and saw a logical loophole that could allow a dictator to take power. Or did he?
The scene was New Jersey, 1947. Sixteen years earlier, Gödel had stunned the intellectual world by proving that no logical system could ever capture all the truths of mathematics— a result that, along with Heisenberg’s uncertainty principle, was to become iconic of the limitations of human knowledge. He had left Austria for the United States when the Nazis took over, and for nearly a de cade he had been a member of the Institute for Advanced Study in Prince ton. It was time, he decided, to become an American citizen. Earlier that year, he had found a curious new solution to Einstein’s cosmological equations, one that made space-time rotate rather than expand. In the “Gödel universe,” it would be possible to journey in a big circle and arrive back at your starting point before you left.
But Gödel’s research into time travel was interrupted by his citizenship hearing, scheduled for December 5 in Trenton. His character witnesses were to be his close friends Albert Einstein and the game theory co-inventor Oskar Morgenstern, who also served that day as his chauffeur. Being a fastidious man, Gödel decided to make a close study of American political institutions in preparation for the exam. On the eve of the hearing, he called Morgenstern in a state of agitation. He had found a logical inconsistency in the Constitution, he said. Morgenstern was amused by this, but he realized that Gödel was dead serious. He urged him not to mention the matter to the judge, fearing it would jeopardize his citizenship bid.
On the short drive to Trenton the next day, Einstein and Morgenstern tried to distract Gödel with jokes. When they arrived at the court, the judge, Phillip Forman, was impressed by Gödel’s eminent witnesses, and he invited the trio into his chambers. After some small talk, he said to Gödel, “Up to now you have held German citizenship.” No, Gödel corrected, Austrian. “Anyhow,” continued the judge, “it was under an evil dictatorship. . . but fortunately that’s not possible in America.”
“On the contrary, I know how that can happen,” cried Gödel, and he began to explain how the Constitution might permit such a thing to occur. The judge, however, indicated that he was not interested, and Einstein and Morgenstern succeeded in quieting the examinee down. (This exchange was recounted in the 1998 book In the Light of Logic by the logician Solomon Feferman, who apparently got it indirectly from Morgenstern.)
A few months later, Gödel took his oath of citizenship. Writing to his mother back in Vienna, he commented that “one went home with the impression that American citizenship, in contrast to most others, really meant something.”
For those of us who have never read the Constitution all the way through, this anecdote cannot but be disturbing. What was the logical flaw that Gödel believed he had descried in the document? Could the Founding Fathers have inadvertently left open a legal door to fascism?
It should be remembered that while Gödel was supremely logical, he was also supremely paranoid and not a little naive. There was something sweetly Pnin-like about him. He believed in ghosts; had a morbid dread of refrigerator gases; pronounced the pink flamingo that his hoydenish wife placed outside his window furchtbar herzig (awfully charming); and was convinced, based on nose measurements he had made on a newspaper photograph, that General MacArthur had been replaced by an impostor. His paranoia, though, was decidedly tragic. “Certain forces” were at work in the world “directly submerging the good,” he believed.
So was the contradiction in the Constitution, or was it in Gödel’s head? I decided to consult a distinguished professor of constitutional law, Laurence Tribe. Besides teaching at Harvard Law School, Tribe had a knack for algebraic topology in his undergraduate days.
“It’s unlikely that Gödel could have found anything of the form p and not-p in the Constitution,” Tribe told me. “What might have bothered him, though, was Article V, which places almost no substantive constraints on how the Constitution can be amended. He could have interpreted this to mean that as long as an amendment is proposed and approved in the prescribed way, it automatically becomes part of the Constitution, even if it would eliminate the essential features of a republican form of government and obliterate virtually all the protections of human rights.”
Tribe continued, “But if I’m correct, Gödel’s concern rested on something of a non sequitur. The idea that any constitution could so firmly entrench a set of basic rights and principles as to make them invulnerable to orderly repudiation is unrealistic. Nations like India that purport to make certain basic principles unamendable have in no sense experienced greater fidelity to human rights or democracy than has the United States.”
A couple of other legal scholars I spoke to concurred with Tribe that Article V must have been what was vexing Gödel. But the mystery of whether he found something genuinely kinky in the Constitution remains a bit like the mystery of whether Fermat really had a “marvelous proof ” of his last theorem. How I wish I had been the judge at that citizenship hearing. Imagine being presented with the opportunity to lean forward, look this agitated genius in the eye, and say, “Surely you must be joking, Mr. Gödel.”