In Search of Klingsor

“I can’t do that, either. I … I wouldn’t know how to explain it to you, Professor.” Bacon took a gulp of bourbon to fortify himself. “The other girl is very different. I don’t even know if I truly know her, much less love her. We barely even talk.”

“That’s a problem, that’s for sure … you’ve got a real problem on your hands,” Von Neumann mused. “Do you see how, once again, I was right? These are the issues that affect us all the time, even if we can’t admit it to ourselves. But don’t think that mathematics doesn’t come in handy at times like this.” The professor finished his drink and immediately poured himself another. Aside from his one sip, Bacon had barely touched his. “That’s why I’m so taken with game theory. Or did you just think it was some eccentricity of mine, passing the time with heads and tails and poker games? No, Bacon, what makes these games truly fascinating is that they mimic the behavior of men. And they serve, above all, to clarify the nature of three very similar issues: the economy, the war, and love. I’m not kidding. These three activities effectively represent all the battles we men wage against one another. In all three, there are always at least two wills in conflict. Each one attempts to take the greatest possible advantage of the other, at the least possible risk to himself.”

“Like in your war example.”

“Exactly, Bacon. Now, recently I have been more worried about the economic application of this theory, but your case would be a fine exercise to test. Let’s see. There are three players: you and your two girlfriends, whom we will call—in the interest of discretion—A and B. You will be C. Now you tell me what each person wants.”

Bacon’s hands grew clammy, as if he were preparing for confession. “The first one, the one you call A, is my fiancée. She wants us to get married. She’s always hinting at it and pressuring me—it’s all she thinks about. Girl B, on the other hand, only wants to be with me, but that, obviously, will be impossible if I agree to marry A.”

“Understood. And you, what do you want?”

“That’s the worst part of it. I don’t know. I think I’d like to keep things just as they are right now. I don’t want things to change.”

Von Neumann got up from his chair and began to pace around the room. He clapped his hands, as if he were applauding something, and then contemplated Bacon with a paternal, ever so slightly condescending look in his eyes.

“I’m afraid that you are trying to bet on inaction, perhaps the most dangerous thing you can do in a case like this. You can try, of course, but even the laws of physics would be against you on this one. In games, one always attempts to move ahead, to advance to new objectives, and slowly destroy the adversary. That’s how your two women are behaving. Both of them are trying to corner you, bit by bit, while you simply assume a defensive stance.” Von Neumann returned to his chair and rested his fat hand upon Bacon’s shoulder. “As your friend, I have to warn you that your strategy is doomed to fail. Sooner or later, one of them is going to wear you down. In fact, they don’t even realize it but they are actually competing with one another. You’re not a player in this, boy! You’re only the prize!”

“So what should I do, then?”

“Oh, dear Bacon. I’m only referring to game theory, not real life. Reason is one thing—as you so astutely observed in our last discussion—but human will is an entirely different animal. All I can say is that if I were in your shoes, there would only be one thing to do.”

“And are you going to tell me what that is, Professor?”

“I’m sorry, Bacon. I’m a mathematician, not a psychologist.” From somewhere deep beneath Von Neumann’s flushed countenance, an almost imperceptible, feline smile began to emerge across his lips.

Bacon knew that Einstein, ever since his Berlin days, loved to go on walks. Every day he would set out on the path between his house and the institute, and he particularly enjoyed chatting with a walking companion. The talks never lasted more than a few moments, but his companions treated them as if they were precious pearls of wisdom. Many illustrious physicists visited Princeton specifically to catch the professor on one of these walks, because it was during those moments that his mind was at its most relaxed and fertile.

One day Bacon decided to wait for Einstein outside of his office, cubicle 115 of Fuld Hall, hidden behind the staircase landing. He was scared, secretly embarrassed, like someone who chases after a movie star in the hopes of getting an autograph. That was the reason he was in Princeton, after all—to get to know men like Einstein, not to listen to Von Neumann’s eccentric psychology, and certainly not to put up with the indifference of his older colleagues.

Just like the journalists who had dedicated themselves to popularizing—or, rather, misinterpreting—Einstein’s theories, Bacon quickly learned the meaning of relativity. The seconds crawled by, agonizingly slowly; it was as if all the underground arteries connecting the universe were somehow, maddeningly, all blocked up. He had been waiting for about forty minutes now. Like a spy or a sentinel, or someone waiting for a miracle to happen, he maintained his vigil, waiting for the physicist to emerge from his office. Each time someone walked past him, Bacon waved hello timidly, and then raised his hand to his head as if to indicate that he had finally remembered the reason that had brought him there, and then walked in the opposite direction until he was certain the coast was clear. He felt like some kind of inept bodyguard, the anachronistic sentry of the Institute for Advanced Study.

Finally the door opened, and Einstein emerged, walking straight toward the exit. He wore a black suit and his hair, Bacon noticed, wasn’t nearly as white or as messy as it appeared in photographs. This was the moment he had been waiting for. But at the last minute Bacon faltered, and that one moment was all it took. Einstein scurried past him down the staircase. The great physicist hadn’t even noticed Bacon as he ran downstairs; he simply went on his way, indifferent to that dim shadow. By the time Bacon realized his mistake, it was too late. The professor was already out of the building. There was no way he could run and catch him by surprise; the idea was to make the encounter appear casual. If it seemed premeditated, Einstein would just get rid of him as quickly as possible. Bacon was furious at himself, but he was not about to give up so quickly. In an almost dreamlike state, Bacon began to follow Einstein—at a prudent distance, of course—digging deep into his coat pockets, leaving Fuld Hall behind.

Determined and giddy, Bacon was barely conscious of what he was doing, and of what an absurd endeavor it was. He was too focused on hiding behind the cars and ash trees that lined the streets to realize exactly what he was getting himself into. As Einstein advanced down the street, Bacon followed him. Finally, Einstein arrived at number 112 Mercer Street, where he lived with his secretary, Helen Dukas. Upon seeing Einstein disappear into his house, Bacon breathed a sigh of relief. Using his shirtsleeve, he wiped the perspiration from his forehead and headed back toward the institute.

The next day, Bacon was prepared to make up for his previous ineptitude. Today he would face Einstein for real, and if the circumstances allowed, he would confess his earlier conduct. It was said that the professor had a good sense of humor, and perhaps this would be the best way to break the ice with him. Just after noon, Bacon returned to his spot, like a soldier determined to fulfill his mission. Only moments after Bacon had reassumed his position at the stairwell, Einstein emerged from his office, once again at full speed. Bacon was unprepared for this surprise attack and, once again, the professor sped past him toward the exit, barely noticing Bacon.

His pursuit of the professor eventually evolved into yet another one of his daily routines, just like the calculations he executed for Professor Von Neumann, the phone calls he received from Elizabeth, and Vivien’s evening visits. Even if he were bold enough to confess it to anyone, who would believe him? That he was pursuing Einstein, like a spectrum, a wave that kept trying to move closer to the author of relativity? Out of the question. In the meantime, Bacon worked on his technique; as time went by he felt surer and surer of himself, certain that he was becoming nearly invisible…. Slowly, the walk toward 112 Mercer Street became as natural as afternoon tea, or the solution of a couple of matrices; he did it out of necessity, or like a bad habit. Einstein almost always walked home alone, although every so often someone would join him—old or young, famous or unknown, each occupied the spot that was supposed to belong to Bacon, the most devoted of his disciples.

Only once did Einstein notice him. A thick fog hung in the air that lay like a greasy film covering the faces of the passersby with an unbecoming, yellowish tint. The birds’ chirping rang through the air like a fire alarm signal sent out from one nest to the other. Suddenly, without any warning, Einstein turned on his heels and fixed his gaze squarely on Bacon, who was now frightened as a deer. It looked as though his sophomoric game was up. Bacon had lost.

“Do you work at the institute?” Einstein said upon recognizing him.

Perhaps this was the moment he had been waiting for, Bacon thought: the chance to initiate a friendship, albeit distant, with the man whose story he had followed more than any other, and to whom he felt connected by a profound, almost mysterious sense of awe and admiration.

“Yes, I do,” Bacon replied, breathlessly awaiting the professor’s next pronouncement, as if hanging on to the words of an oracle.

“It’s cold,” exclaimed Einstein, dazed.

That was all he said. Nothing more, no revelation, no prophecy. He didn’t even ask Bacon’s name. He bent his head slightly, as if to say good-bye, and continued on his way alone, absent, beneath the weak light whose structure intrigued him so. Now—finally!—Bacon could boast to the rest of the world that yes, he had received a dose of the genius’s wisdom, and he would treasure those marvelous words as if God himself had bellowed them: It’s cold. Bacon laughed to himself, still trembling, and waited for Einstein’s gray silhouette to recede, like the brilliant glow of the stars which he spoke of so eloquently. The next day, Bacon resumed his pursuit of the professor, but now with the serenity of a man who had completed his mission.

HYPOTHESIS IV:On Gödel’s Theory and Marriage (#ulink_955c5ab7-073b-51d0-979c-aac6cf35185b)

When her soul was tranquil, Elizabeth’s eyes were the color of olives. But Bacon could always be sure that the tranquillity would soon give way to thunder whenever they began to acquire a slightly coppery tone. At those times, all he could do was remain quiet and wait for the angry torrent of words to come pouring out of Elizabeth’s mouth, dying down to a trickle only after a few minutes. Her wrists were so slender that he could hold them between his thumb and pinky, and her neck was as strong and firm as a sunflower’s stem, but when she became incensed—a fairly frequent occurrence—her diminutive proportions grew exponentially, like those of a cobra in heat. All the innocence and courtesy she so carefully exhibited during social functions would evaporate, replaced by a torrent of fiery reproaches and menacing threats, a snit of such proportions that by the time it was over, she had nearly asphyxiated herself. Only then would she begin to feel remorseful, and as she allowed sweet tears to rain down on her cheeks, Bacon, moved by such a show of emotion, would have no other choice than to caress her delicate chin and run his fingers through her tousled hair, calming her down until she could muster enough strength for her next attack.

Elizabeth was the kind of woman who always looked as if she had just stepped out of the pages of a fashion magazine: Her dresses were fitted, her jewelry took the form of tiny insects, and her hats sprouted feathers the likes of which Bacon had seen only in the movies. Her violet eye shadow and colorful rouge only enhanced her childlike complexion, reminding Bacon of a little girl trying to be like her mother by stealing and applying globs of her makeup. Bacon was always touched by this curious spectacle; in that inharmonious combination of lust and innocence, vanity and naïveté, he saw evidence of the sensitivity his fiancée hid behind her haughty appearance.

Aside from Elizabeth’s undeniable beauty and artistic talents (she was a student at an art academy in New York), there was something else about her that appealed to Bacon’s mother: her aristocratic lineage. Elizabeth, she explained to her son, was the only daughter of a rich banker from Philadelphia whose greatest desire was to see his daughter happy. When he saw her for the first time at a French restaurant on Fifth Avenue, Bacon knew that she would play an important role in his life—though not for any of the qualities his mother had mentioned. It was the tiny adolescent figure, the cascade of curls that tumbled out from under her hat, and the way that, in spite of her well-cultivated manners, she couldn’t help twisting and untwisting her fingers in her lap. Bacon had always appreciated that rather aggressive quality found in many spoiled girls, for he sensed it was simply their way of masking their inability to solve the problems of day-to-day life. In short, he liked Elizabeth because she was the opposite of Vivien.

That afternoon, somewhere between the lobster and the chocolate cake, Elizabeth made a confession—that is, she recited the words she assumed a liberal scientist like Bacon would want to hear from a girl: She was a painter. She spoke eloquently of the importance of art and freedom, and explained that money, to her way of thinking, was simply one among many means to happiness. The significance of her declarations was largely lost on Bacon—the champagne they drank took care of that—and Elizabeth worked hard to soften her sharp, grating voice into something closer to sensual. Meanwhile, Bacon’s mind was mainly focused on discerning the shape of her breasts beneath the cherry-colored blouse and the fine European lingerie that (he was certain) lay beneath it. He never once lifted his gaze to meet her eyes, but Elizabeth continued on, undeterred, with her detailed lecture on the history of art, convinced that a promising young scientist like Bacon couldn’t help falling in love with a woman of such great intellect.

One day, Bacon grabbed her hand and attempted to kiss her in the middle of the street. Elizabeth, employing her family’s old husband-catching technique, slapped him hard on the cheek, hard enough to call the attention of several passersby. She then told him to behave like a gentleman, and asked him to please walk her home. Once again, the tactic proved highly effective: Dazzled by this flash of temper, Bacon asked when he could see her again. After considering the idea for a few moments, Elizabeth accepted. From then on, they averaged about two dates a week, generally on Saturday mornings and Sunday afternoons, although almost an entire month went by before she would allow Bacon’s lust-filled lips to settle upon her own tightly pursed pair.

In theory, Bacon despised Elizabeth’s games, and he continued sleeping with Vivien about three times a week, though without the slightest trace of any sort of courtship ritual. Yet he nevertheless remained enthusiastic about the progress of his relationship with Elizabeth, precisely because she refused to let him touch her. In one of nature’s absurd paradoxes, he would dream of Elizabeth’s tiny body while savoring the largesse of Vivien; he yearned for Vivien’s silence as he endured Elizabeth’s insufferable discourses.

Bacon knew that the laws of civilized society—inspired by the laws of classical mechanics—were inflexible. Sooner or later, his double life would have to end; he could have only one of them. And it would have to be Elizabeth. His mother, his friends, his professors, his fellow graduate students—none of them would forgive him if he abandoned the delightful young lady who they always assumed would become his wife for a cafeteria worker. Resigned to a fate that seemed beyond his control, Bacon went out and bought a ring with a tiny blue diamond and gave it to Elizabeth one windy evening in March of 1942, beneath the moonlight, as prescribed by the laws of romantic love.

They hadn’t settled on a wedding date, but from that day forward, Elizabeth did little more than visit bridal shops to study the endless array of available wedding dresses. Each time she saw her fiancé she would describe, with the very same patience she dedicated to her lectures on surrealism and the avant-garde, the complicated floral patterns of each model, since she found herself incapable of deciding on one single gown. The decision, Bacon 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 problems,” Bacon interjected, knowing in advance what the answer would be, but giving Von Neumann a chance to unleash his vanity like a hungry tiger.

“Well, of course I tried it, Bacon, we all tried it. In fact, we’re still trying. For months I became obsessed by the completeness axiom and the challenge it presented.” Von Neumann scratched his chin reflectively and lowered his voice a notch, as if he were narrating a great suspense novel. “Just as Professor Gödel did later on, though he had more success with it than I. At first, I thought I had found the correct approach. My intuition told me that the goal was not impossible to achieve, as I had previously thought. Have you ever had that feeling of your skin tingling, like when someone scratches their nails against a blackboard? It was incredible.”

“And so what happened?”