By Yannick Grannec, author of The Goddess of Small Victories
Gödel let himself die of hunger fearing he would be poisoned; Turing committed suicide swallowing arsenic.
Both were scientists of the absolute; both were anti-conformist and tormented. Both were obscure geniuses: idols of their colleagues, and unknown to the general public. Both were precocious founders of logic, the mathematical language on which deductive reasoning is based. Their tragic destinies and their pioneering works speak to each other, and yet they never even met. But the cursor on your smart phone is in fact the combined souls of Alan Turing and Kurt Gödel that still quivers a century after they were born.
In the thirties, Kurt Gödel and Alan Turing posed to themselves the same question: “Can we find a universal procedure to prove that a mathematical theory is true or false?”
They each, in their own way, answered “no”: there exist some mathematical truths that cannot be proven. In order to work around this “incompleteness” statement, Turing connected formal logic to a mechanical model. He created the Turing Machine, which is a theoretical algorithm that suggests that a human brain functions just like a calculator. Therefore, a calculator can “imitate” the logic of human reasoning, but also address its limitations.
For Gödel, the human mind is more than a Turing Machine, more than a complex connection between choices. The uniqueness of mind and matter is, for Gödel, a mere cultural prejudice. Gödel devoted his life to prove, through philosophy and mathematics, that there is “something else.” Turing, meanwhile, applied his discoveries to the resolution of the messages coded by the Enigma machine, built by the Germans to encipher and decipher coded messages.
Gödel ends up a paranoid recluse, and Turing is forced into secrecy and is persecuted—a sordid and pathetic end for two brilliant men.
Paradoxically, because they hit some limits in their scientific approaches, Gödel and Turing opened a new era that appears to us today without limits: that of computer science and artificial intelligence. The language of today’s computers owe their origin to that very logic that our two geniuses had mishandled. The true/false dichotomy has become “1/0,” the binary code.
The irony of their asymptotic destinies is that they both lived in Princeton without ever crossing paths. However, in that incredible intellectual and scientific milieu, they both rubbed shoulders with two other giants of scientific history: Albert Einstein and John Von Neumann. In light of the urgency caused by the war and the hatred of Nazism, the combined discoveries of these two geniuses led to the creation of the type of artificial intelligence necessary for deciphering the secret codes of the enemy and the making of the atomic bomb.
There is no doubt that if they were to meet today, Gödel and Turing would debate the question of the nature of human thought and intelligence and their potential incarnations, for better or worse—somewhere between your smartphone and nuclear arms.
Yannick Grannec is a graphic designer, freelance art director, professor of fine arts, and enthusiast of mathematics. Her debut novel, The Goddess of Small Victories, a fictionalized account of the lives and marriage of Kurt and Adele Gödel, was published in 2015. She lives in Saint-Paul de Vence, France.