In Search of Klingsor. Jorge Volpi
quickly realized, was going to be as agonizing as determining the quadrature of a circle.
Aside from Elizabeth’s new obsession with gowns, fabrics, veils, and laces, another idiosyncrasy came to light during this prewedding period: her ever-increasing jealousy. Marriage, to Elizabeth, was nothing less than complete and total surrender. Soon she began demanding more frequent visits from him. In addition to his usual Saturday and Sunday trips to New York, he now found himself traveling there several days a week, often to be with her for no more than a few hours. Unfortunately for Bacon, these trips offered no opportunity for increased intimacy. Bacon, then, was reduced to coming and going at Elizabeth’s behest, like a yo-yo in the hands of a child.
As a kind of punishment for his disobedience, Elizabeth began to demand, sometimes with shrill cries and other times with gentle caresses, a detailed report of his daily activities. “Where did you go?” “Why?” “With whom?” were the three basic questions, the tenets of a belief system she practiced with the fervent devotion of the recent convert. Any sudden observation, pointless comment, or unexpected turn of conversation would instantly become the motive for an interrogation that could last hours. She acted as though any activity that didn’t specifically focus on her represented a crime against their love. As far as Elizabeth was concerned, Bacon’s schedule of conferences, classes, and work assignments at the institute were little more than transparent alibis aimed at hiding his infidelity.
The most surprising thing of all was that Bacon responded to Elizabeth’s inventory of complaints with sweet nothings and apologies. Over and over again during those months he would ask himself exactly why he was subjecting himself to this military discipline which, in the end, was going to kill his spirit. The answer, alas, was simple: guilt. He knew that in spite of her temper tantrums, Elizabeth trusted him. And he also knew that her suspicions—though exaggerated at times—were not entirely unfounded. As he had explained to Professor Von Neumann, Bacon tried to maintain the relationship as it was by drawing Elizabeth’s attention to such banal topics as his oppressive job, so as to prevent her from inferring the real reason for his occasional absences. But gradually he learned that a man with a double life is a man condemned—not simply to lying but to inventing and defending half-lies, as if his world could be divided into two separate spheres, incompatible and complementary at the same time.
In late March of 1942, Von Neumann informed Bacon that Kurt Gödel, the eminent mathematics professor, would be coming to the institute in a few days to present one of his recent papers to a private audience. Unfortunately, this was to take place on the same day that Bacon had promised Elizabeth they would travel to Philadelphia. When Bacon told her, he explained the importance of the event and assured her they would make the trip the following month. Elizabeth, however, simply told him to go straight to hell. This wasn’t the first time she had threatened him—in fact, she was usually the one who would run back to him. But Bacon resolved not to give in this time. He was too determined to meet Gödel to let one of his fiancée’s idle threats get in the way. In fact, he thought, this might just be the perfect excuse to take a rest from her for a few weeks, to be alone and to think about his future.
“I’m sorry, Elizabeth,” he told her over the telephone, “but I have to be there.” He was suddenly aware that these final few days of freedom were nothing more than a brief prelude to a lifetime of indentured servitude, so he decided to take advantage of the time.
Professor Gödel was a short, taciturn man with the body of a flagpole; his general appearance called to mind an opossum or a field mouse, certainly not a genius of contemporary logic. Yet, it was true. He had become affiliated with the institute two years earlier, eight years after writing an article that overturned the foundations of modern mathematics.
In the course of over two millennia, mathematics had evolved in a disorderly fashion, like a tree with wild branches, twisting and wrapping around one another. Thanks to the discoveries of the Babylonians, the Egyptians, the Greeks, the Arabs, and the Indians, as well as the advances made in the modern West, mathematics had become something of a monster with a thousand heads, a discipline whose true nature nobody could even begin to understand. Mathematics was the most objective and evolved scientific instrument known to mankind, used daily by millions to resolve practical problems of everyday life. But amid all that infinite diversity, nobody knew for sure if mathematics might contain, somewhere within itself, a germ in decomposition, a fungus or a virus capable of refuting its own results.
The Greeks were the first to recognize this possibility in their discovery of the paradox. As Zeno and subsequent arithmetics and geometry scholars would prove, the strict application of logic occasionally produced impossibilities or contradictions that were not so easily resolved. The notion of the paradox went as far back as classical antiquity, in the dialogues of Achilles and the Tortoise, which refuted the notion of movement, or Epimenides’ paradox, which said a statement could be proven and refuted at the same time. Yet it wasn’t until the late Middle Ages that these irregularities began to multiply like malignant tumors. This heresy, which escaped the Pythagoreans as well as the fathers of the Church, proved that science indeed could be proven wrong, contrary to previous belief.
To put an end to this chaos, legions of scientific thinkers attempted to systematize mathematics and the laws that governed them. One of the first people to do so was Euclid. In his Elements, he attempted to derive all the rules of geometry from five basic axioms. Later on, philosophers and mathematicians like René Descartes, Emmanuel Kant, George Boole, Gottlob Frege, and Giuseppe Peano tried to do the very same thing in fields as far-flung as statistics and infinitesimal calculus, although their results were hardly conclusive. In the meantime, new paradoxes were emerging as well, such as those introduced by Georg Cantor in his set theory.
At the dawn of the twentieth century, the situation was more bewildering than ever. Conscious of Cantor’s theories and the aberrations they produced, the English mathematicians Bertrand Russell and Alfred North Whitehead joined forces in an effort to reduce the entire scope of mathematics to a few basic principles, just as Euclid had done two thousand years earlier. Together they devised something they called the type theory, which led to the publication, in 1919, of a monumental treatise entitled Principia Mathematica, which was based on an earlier tract by Russell. The purpose of the Principia Mathematica, which they worked on from 1903 to 1910, was to erase all the uncomfortable contradictions known to contemporary mathematics.
Unfortunately, the work was so vast and complex that in the end, nobody was truly convinced that all mathematical statements could be reduced to their theories without falling into contradiction at some point or another. Just a few years earlier, in 1900, a mathematician at the University of Göttingen named David Hilbert had presented a paper at the opening session of the International Conference of Mathematicians in Paris, which explained a theory that would thereafter be known as Hilbert’s Program. In this treatise he laid out a list of all the great unresolved mathematical problems, as a kind of blueprint for future mathematical research. One of these conundrums was the so-called axiom of completeness, which questioned whether the system later described in the Principia—or any axiomatic system, for that matter—was comprehensive, complete, and free of contradiction. Could any arithmetic proposition be derived through his postulates? Hilbert thought the answer was yes, as he said to his colleagues gathered together in Paris: “All mathematical problems are solvable, we all agree with that. After all, when we set out to solve a mathematical problem, one of the primary things that draws us in is that calling we hear inside: Here’s the problem, it needs a solution. And this can only be found through pure thinking, because in mathematics there is no such thing as ignorabimus.”
“Hilbert’s Program became the bible of mathematicians and logicians of the world,” Von Neumann explained to Bacon one day. “To solve even one of his equations would mean instant fame. Can’t you just picture it? Hundreds of young minds, in every corner of the world, banging their heads to solve one of the pieces of Hilbert’s great puzzle. Maybe, as a physicist, you can’t grasp the magnitude of the challenge, but everyone wanted to prove himself. Everyone wanted to show that he was the best of them all. And it wasn’t just a race against unknown rivals, either; it was a race against time. It was madness.”
“I’m supposing you had tried to solve one of Hilbert’s