26/06/2024

Folha: 'Gödel and the birth of dictatorships'

Kurt Gödel – Reprodução

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

At the end of 1939, German submarines made crossing the Atlantic a dangerous adventure. Escaping conscription into the Reich, Kurt Gödel (1906–1978) left Vienna for Princeton in the opposite direction: accompanied by his wife, Adele, he crossed Asia on the Trans-Siberian Railway, the Pacific, and, again by train, North America.

At the Institute for Advanced Study in Princeton, he did some of his most important work, including proving the consistency of the Axiom of Choice and the Continuum Hypothesis, two statements that played a crucial role in 20th-century logic and mathematics.

Half a dozen years later, Gödel decided to apply for American citizenship. One of the first steps was to name his witnesses: his friends Albert Einstein (1879–1955) and Oskar Morgenstern (1902–1977), economist and co-founder of game theory , the most important area of application of mathematics to the social sciences. Fortunately for us, Morgenstern left a written account of the process.

Meticulous and obsessive, Gödel prepared for his naturalization hearing by studying absolutely everything about the history and culture of the United States , from the human settlement of the continent to the exact boundaries of Princeton's neighborhoods. It was no use his friends, who had already been naturalized, insisting that the judge wouldn't go into such minutiae: he continued studying more and more books and articles on any related topic.

Until one day, very excited, Gödel informed Morgenstern that he had discovered, with great regret, that the United States Constitution contains contradictions, and that he knew how to demonstrate how someone could become a dictator and install a fascist regime in the country, all " within the four lines of the Constitution "!

His colleague tried to persuade Gödel to drop the subject, saying that even if he were right—which Morgenstern doubted—"such things are very improbable." With what we know today, it's clear that he should have taken the matter much more seriously and, at the very least, recorded Gödel's demonstration for the benefit of future generations.

The naturalization judge knew Einstein and allowed the witnesses to participate in the hearing. Unfortunately, he began by asking where Gödel came from and what the regime of his country was. "From Austria, which was a republic and is now a dictatorship ," was the reply. "Very bad! But that couldn't happen here," the judge remarked. That was enough to launch Gödel into a long and enthusiastic explanation of his discovery.

To read the full text, visit the newspaper's website.