In Search of Klingsor

“Exactly! It was a kind of miracle. My proof followed a complicated, perfect line of reasoning. I was convinced that with one of Hilbert’s problems on my CV, I would become famous.”

“So why didn’t it happen that way, Professor?”

“My good friend Bacon,” said Von Neumann, his thick, dry lips breaking into a smile, “it was a great stroke of luck for the world of mathematics that I did not dream a thing that night!”

When Gödel finally solved the problem in 1931, he was still a young, unknown mathematician. His paper, entitled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems, 1,” was like a bucket of cold water soaking the optimism of Hilbert’s ideas. In his article, Gödel showed that the Principia Mathematica allowed for the existence of propositions that were true yet unprovable—that is, “undecidable.” He then went even further by proving that this phenomenon would hold true in any axiomatic system, in all existing or future fields of mathematics. Against what all the experts had predicted, Gödel had proved beyond a doubt that mathematics were incomplete.

With shockingly simple reasoning, Gödel refuted the romantic notion that mathematics could fully interpret the world, free of the contradictions inherent in philosophical inquiry. His paper was so successful that he didn’t have to write the follow-up chapter he had originally planned. His explosive mission was over. The most astonishing aspect of Gödel’s achievement, however, was its simplicity. Reformulating Epimenides’ ancient paradox—of course, the bedrock of all mathematical paradoxes—he had hit upon the theorem which proved his hypothesis. It said:

To every w-consistent recursive class k of formulae there correspond recursive class-signs r such that neither v Gen r nor Neg (v Gen r) belongs to Flg(k) (where v is the free variable of r)

An approximate translation of this might be: “All consistent axiomatic formulations of number theory include undecidable propositions.” In simpler terms, Gödel said the following: “The system of Principia Mathematica offers no proof for this statement of number theory.” A possible expansion of the same: “This proposition of number theory has no proof within number theory,” which might also be stated in the following manner: “This logical proposition is unprovable by the very laws of logic.” The statement could even be extended to the realm of psychology: “It is impossible for me to prove this idea I have about myself.”

To recapitulate, Gödel stated that in any system—scientific, linguistic, mental—there will always exist statements that are true but unprovable. No matter how hard one tries, no matter how perfect a system one creates, there will nevertheless exist unprovable holes and voids, paradoxical arguments that behave like termites and devour the things that seem most solid. Gödel did for mathematics exactly what Einstein’s relativity theory, Bohr’s quantum theory, and the discoveries of their collective disciples did when they proved that physics was no longer an exact science—that is, an amalgam of absolutes. Nobody was safe in a world that was suddenly dominated by uncertainty. Thanks to Gödel, truth became more slippery and elusive than it had ever been before.

Vivien’s body stretched out again across Bacon’s bedsheets like a sinewy brown stain. She had arrived at his apartment just after dusk. Her long, bare arms were now lost in the darkness of the night, coated with a kind of dew from the persistent rain that fell outside. Only three days had passed since Bacon’s acrimonious telephone conversation with Elizabeth. As he began to kiss Vivien’s earlobes, he remembered that he had considered leaving her, too. But the moment she had arrived at his house, he knew that he would be unable to resist the temptation of possessing her once again.

As if freed from a prison sentence, for the first time in a very long time Bacon was overcome by the desire to be tender with his lover. Suddenly she seemed fragile and innocent, not pained and mysterious, and he wanted to make up for his many months of betrayal. Perhaps he was simply projecting the love he wanted for himself, but instead of watching her with cold eyes, he now decided to undress her, bit by bit, as if preparing a little girl for her bath. Then he kissed her on the lips slowly and tenderly (an indulgence he normally avoided) and stroked her curly black hair. And then, finally, he made love to her with the kind of tenderness usually reserved for love affairs with virgins. The only aspect of his routine that remained unchanged was the stubborn silence he maintained while penetrating her body.

“Do you love her?”

Nestled amid the sheets, Vivien looked like a drowning woman trying to defend herself against an enormous wave crashing down upon her. Bacon was lying on her back, and as he stretched himself on top of her body, he wondered if he had become the wave she was struggling against.

“No, well, I don’t know,” Bacon stammered.

“Are you going to marry her?”

“Yes.”

“Why, if you don’t love her?”

“Don’t ask me those questions. That’s just the way it has to be, I suppose. There are things a person has to do: get married, have children, die. Listen, from the beginning you knew. I never led you on, Vivien.”

“You don’t even remember my name. How could you possibly lead me on?” Vivien moved away from Bacon and got up from the bed. She didn’t seem angry, or even disappointed. She began gathering up her clothes, strewn across the floor.

Bacon looked at her as if he were staring at an ancient armoire that had suddenly sprung open, emptying bundles of photographs and lost memories onto the floor.

“Can I ask you something?” he finally said to her, haltingly, not even rising from the bed. “Just this once, Vivien, don’t go. Stay with me tonight. It’s raining. And I want to see your face in the morning.”

The next day, Bacon woke up very early, doubly vexed: by the unfamiliar presence of Vivien, and by the conference that Professor Gödel was to give that morning. For a few seconds he remained still, contemplating Vivien’s body as she continued sleeping peacefully. In the early morning light, she seemed lovelier than ever to him. Without making a noise, Bacon arose from the bed and got ready for the day. As he showered, he couldn’t shake the strange feeling of peace that he felt upon opening his eyes and finding Vivien at his side. He told himself he had to forget about her, but her perfume clung stubbornly to his skin. Much as he tried, he could not rub out her scent with soap and water.

During the past few days, Bacon had begun to read up on Gödel’s life, as if he were planning to discuss the man’s biography at some later date. All the professors at the institute seemed to admire and respect him, even if they often dropped hints indicating that his personality was as difficult as his theorems. But he was one of Einstein’s close friends.

Gödel had first come to the institute as a visiting professor in 1933, while still a professor at the University of Vienna. His lectures at that time (obviously) focused on the incompleteness of mathematics, and he tended to inspire intense (verging on obsessive) interest among those who came to hear him speak on the topic. Very few men of science, with the possible exception of Einstein, could boast of such an attentive audience. Oswald Veblen, who organized the event, was delighted by the enthusiastic turnout. And though Gödel used the very weakest voice to expound upon the fundamental theories of logic, the students devoured his sentences, as if deciphering them was an additional privilege that would grant them greater and deeper access to their master’s incredible conclusions.

Everything had gone according to schedule until one morning, when Gödel announced to Veblen that he had to return to Europe immediately. He would not be able to finish his lecture series. Unable to invent an excuse, he simply said that he felt a pressing need to return home, that he was terribly sorry but he couldn’t do a thing about it. After apologizing to the other professors at the institute, Gödel returned to Europe. Later on, in the fall of 1934, it was discovered that upon his return he had checked into the West-end Sanitarium, on the outskirts of Vienna, for psychiatric treatment, the victim of a profound clinical depression.

A year after this panic attack, Gödel reestablished ties with the academic community in Princeton and embarked upon another series of conferences. In 1939, shortly after Hitler had annexed Austria to the Third Reich, Gödel lost his position at the University of Vienna. To make matters worse, he was soon called into active duty by the Austrian authorities, despite his fragile state of health. In January of 1940, he and his new wife, Adèle Nimbursky, decided to leave for the United States. It was, however, the strangest sort of odyssey. Instead of traveling across the Atlantic, which they felt was too dangerous, Gödel and his wife set out for Russia, where they boarded the Trans-Siberian Railway headed for Japan. At Yokohama they set sail for San Francisco, where they arrived on March 4, 1940. A few days later, Einstein welcomed them to Princeton.

Bacon arrived at the institute and sat down in one of the last rows of the auditorium to await Gödel’s arrival, feeling the same anticipation he often felt before Vivien’s visits. He watched the mathematician enter and it seemed to him that the thirty-six-year-old professor looked more like a priest or a rabbi than a mathematician. His nose looked like the tiny protuberance on a turkey’s beak. His little eyes, shielded by thick, dark glasses, didn’t seem to radiate any particular intelligence. Nevertheless, Bacon and the others present were convinced that the skinny, bedraggled soul before them was a prodigy, a melancholy genius whose talent clearly came at the expense of his own mental health.

One of the unexpected revelations of Gödel’s theorem was the confirmation of the idea that genius and insanity are inextricably linked. If all mathematical systems contain statements that are true yet unprovable, couldn’t the same be true for the realm of the human mind? Just like mathematics, the mind is incapable of protecting itself in the face of chaos and confusion. It is impossible to discern one’s own sanity or insanity because there exists no such external mark of reference outside one’s own brain to prove the truth definitively. The insane person can judge himself only through the logic of the insane, and the genius, through the logic of genius.

On this occasion, Gödel gave a speech that was nothing more than a compulsive variation on the original theme he had sketched out during his previous lecture series at Princeton. He read his speech in an erratic, weak voice, offering little in the way of professorial showmanship, and the examples he provided were skimpy, pale sketches of his brilliant metaphors. In short, he was the polar opposite of Von Neumann, whose explications overflowed with wit and cleverness. Gödel’s reflections were somber and serious, as gray and boring as his personality. At the end of the lecture, Bacon went up to him, along with some other members of the institute, and, as planned, Von Neumann made all the introductions.

“Kurt,” he said, “you won’t believe me when I tell you this young man’s name.”

Gödel made a gesture indicating he wasn’t especially interested. Bacon tried extending his hand, but the professor did not even seem to notice the gesture.

“Francis Bacon. Can you believe that?” Von Neumann laughed. “Nothing less than Francis Bacon. Only this one, as opposed to the original, is a physicist.”

“I don’t believe in the natural sciences,” Gödel responded, in a tone that wasn’t trying to be condescending, but simply rational.

“But don’t you find it amusing, Kurt?”

Gödel’s eyes rested on Bacon’s for a moment, but rather than scrutinize him, Gödel was trying to understand this strange joke his American friends were making. Finally, Von Neumann took him by the arm, as if he were a stone sphinx on loan from a foreign art museum, and the others hurriedly dispersed. Only Bacon stood where he was, in the middle of the corridor, nonplussed by the mathematician’s listlessness.

When Bacon returned home that evening, Vivien was there. He was the one who had needed her so badly the night before, and now it was her turn to expose her weakness, against both her better judgment and their mutual agreement never to do such a thing. Just as she had done so many times before, Vivien was sprawled out on the bed, though this time dressed in a violet-colored blouse and black skirt, waiting for him with the serenity of a woman waiting for her executioner to arrive.

“What are you doing here?” was all he dared to ask. He let his briefcase fall to the floor with the subtlety of an anvil.

“I knew you wouldn’t like it.”

Bacon moved closer to Vivien, as cautious as a panther waiting to pounce on a deer. She didn’t even have time to sit up. Unable to hold back, Bacon began to kiss her bare feet, her legs, and, finally, after peeling off her clothes like the skin on a piece of tropical fruit, his lips found their way to her belly and then her breasts. He was certain that this was a mistake (even worse: this was the second time he had made the same mistake), but he didn’t care. He melted into Vivien’s warm skin, and would have happily stayed there for at least another night. After a few hours, however, it was Vivien who put an end to it all.

“I have to go now,” she said, still lying in his arms.

“Why?”

“It’s getting late.”

“So what? You can stay if you want.”

Vivien knew as well as he did that it wasn’t true, that they were deceiving one another, but there is nothing more false than an unwanted truth. It was better to imagine that the future was nothing more than one among many possibilities, a potential reality as nonexistent as the past. Just as adamant as Bacon had been in deciding not to see Elizabeth for the duration of Gödel’s lecture series, he was determined to savor this time with Vivien, like the derelict who squeezes his last orange down to the very last drop of juice.

For several weeks, Elizabeth had been unable to sleep more than a few hours at a time. For her, the inclement nights had turned into a kind of prolonged torture in which images of her fiancé passed before her eyes like a movie reel. She envisioned him involved in all sorts of terrible activities, most of them incompatible with marriage. She began to lose her appetite, and soon realized that if she carried on like this, she would end up a skinny, desperate woman. The first few days of their separation, she wanted to teach him a lesson, and resisted the temptation to track him down. She was too sure of herself to doubt, even for a moment, that he would swallow his pride and come back to her. Once he realized how pigheaded he was being, Francis would begin to woo her in earnest, and then she would lay down the law once and for all, and spell out the conditions which would govern their future together. Her present hardships and deprivation were worth it; they were the guarantee of a glorious future that lay ahead.

They had never been apart for such a long period. And with each passing day it became more and more difficult. It was a kind of race, and the winner would simply be the one whose willpower and tenacity held out longer (later on, Bacon would liken it to the race between Achilles and the Tortoise, his fate being that of the Tortoise). Fully aware that this challenge would determine the course of the rest of her adult life, Elizabeth decided she was prepared to go the distance. Whenever a bout of anxiety would weaken her resolve and tempt her to call him, she consoled herself with the reminder that he was surely suffering the very same anguish as a result of their separation.

A nightmare was what finally broke her will. In it, she fell victim to a horrible sickness, and instead of lamenting her death, Bacon went out and celebrated it! Elizabeth woke up in tears, convinced that her dream was a sign that her strategy was failing. What if he didn’t come after her? If he never really loved her in the first place? For the first time in her life she regretted her intransigence and hot temper; perhaps she had demanded too much of him. She loved him. She loved him more than before, more than she ever had. She thought of how stupid she had been. Why wait and become embittered by this separation? Why had she tested their love at all, when all she wanted was to have him by her side? Pride and vanity had no right to keep them apart! But there was still a chance to make amends for her mistake.

The morning after her nightmare, Elizabeth decided it was time to make peace with Bacon. By the time she arrived at Bacon’s house, it was eleven in the morning—he would be at the institute, naturally. She could barely move as she struggled beneath the packages piled high in her arms. From a distance, her slow, teetering walk evoked that of a robot in a science fiction movie. In her arms she carried wine and cheese, fruit, balloons, and even an adorable model train. In spite of the fact that she had never before set foot in Bacon’s apartment (she preferred him either to visit her at her home or to meet her at cafeterias and restaurants), from the beginning of their relationship she had insisted that he give her a key. Now she was ready to use that little device to surprise him, to delight him, and to convince him that the time had come for their reconciliation.

The lecture hall was filled to capacity. Bacon was certain, however, that only a small fraction of the audience would be able to understand the true significance of the words that fell from Kurt Gödel’s lips with such surprising ease. Veblen and Von Neumann were sitting in the first row, watching as Gödel shuffled around with the grace of a hippopotamus, scrawling formulas onto the blackboard like a caveman making stick drawings of a buffalo on a cave wall. The mathematician looked frightened, and he made every effort not to look directly at his audience, losing himself in the infinity point above the back wall of the room. That day, Gödel had turned his attention, and that of his audience, to the problem known as the continuum hypothesis, sketched out by the mathematician Georg Cantor in his set theory.

“Cantor’s continuum hypothesis,” he said softly, as if he were the only one in the auditorium, “can be reduced to this simple question: How many points are there in a straight line on a Euclidean plane?” Gödel waited for a moment, as if to allow the question to seep into his mind before tossing it back out like a giant marble. “Obviously, this question is only possible when we extend the concept of the word number to infinite sets.”

All of a sudden, Gödel stopped cold in his tracks, unable to comprehend why someone would interrupt his lecture. A heavy wooden door opened and then slammed shut, producing a resounding thud that destroyed the otherworldly mood that had settled over Gödel’s audience. Veblen and the other professors rose from their seats, while all eyes focused on the woman who had suddenly burst into the lecture hall.

“Where are you?” she screamed, unfazed by the strangers witnessing the scene. Every last bit of Elizabeth’s beauty had evaporated and what was left was a cold scowl as she scanned the rows for the face of her double-crossing fiancé. “You lied to me! Admit it!”

Seated in the back row, Bacon made out the silhouette of Elizabeth. He didn’t know what to do, whether to stand up and try to calm her down, or try to hide from her wrath altogether. Elizabeth, meanwhile, remained utterly indifferent to the suddenly uncomfortable atmosphere in the auditorium. Gödel was horrified.

Veblen quickly admonished her: “For goodness’ sake, miss, I don’t know who you are or whom you are looking for, but this is a university lecture. I must ask you to leave immediately, so the professor may continue his presentation.”

Elizabeth did not hear a word. She was too busy searching for her terrorized victim.

“Don’t try to hide!” she screamed. “Did you think I wouldn’t find out? That you could keep seeing that whore? How stupid do you think I am?”

“Elizabeth, please,” begged Bacon. Painfully aware of his audience, he tried his best to placate his fiancée. “We’ll fix all this later.”

“Later? Forget about later! I’m not going anywhere until you start explaining!” And she began to advance toward him, her face stained with tears that were as hot as the anger Bacon was beginning to feel.

“Mr. Bacon,” said Veblen pointedly, gesturing toward the exit. “Would you please explain to this young lady that we are in the middle of a very important lecture? Do you understand?”

By this time, Elizabeth was face-to-face with her fiancé. When he took her by the arm and tried to direct her toward the back of the lecture hall, she responded with a resonant slap across the face. The entire audience—with the exception of Gödel—breathed a prolonged oh! at the sound made by her hand, like that of a flyswatter slamming against a windowpane. Unable to endure any more humiliation, without even thinking, Bacon responded in kind. His blow was much less powerful but, due to an unfortunate matter of acoustics, much louder.

“This is unacceptable, Bacon!” Veblen exploded, though next to him Von Neumann let out an amused chuckle. “I will ask you again to please leave this room so we can go on.”

Elizabeth, stung by the slap, was not aware of what was happening around her. She had single-handedly caused a most disastrous scene which now felt more like a hazy, chaotic nightmare. The only thing she wanted was to embrace Bacon and fall into a long, deep sleep by his side. At the front of the lecture hall, Gödel watched the scene unfold in a state of complete and utter shock.

“You let her into your house,” Elizabeth sobbed as Bacon guided her toward the exit amid the stares of his colleagues. “You had that whore in your house.”

The last thing Bacon was able to see before leaving the auditorium was the furious face of Professor Veblen, which wordlessly told him that his currently favorable position and his no less brilliant future at the institute were both ruined. As he supported the exhausted body of his fiancée (now his ex-fiancée, he told himself), Bacon could scarcely begin to fathom the manifold consequences of the scene. Suddenly the three stable elements of his life—Elizabeth, the institute, and, yes, even Vivien—had crashed into each other like runaway trains. What would Von Neumann think of this, the unforeseeable outcome of his romantic games? Bacon led Elizabeth to a nearby room and sat her down in a chair. He remained there for a while, not touching or hugging her. He waited for a few minutes more. When she came to, she insulted him again and then, still trembling, got up and left the institute alone.

Meanwhile, back in the auditorium Professor Gödel made the announcement that he would be unable to continue with his lecture, and then he began to cry uncontrollably until Von Neumann walked up to the lectern to console him.

HYPOTHESIS V: On Bacons Departure for Germany

When Bacon returned to the institute a few days later, he went straight to Frank Aydelotte’s office. Aydelotte, the institute’s director and Flexner’s successor, had been looking everywhere for Bacon. Bacon had no idea what fate this meeting would hold for him, though he was reasonably certain it was nothing positive. He figured it to be somewhere between a strong reprimand and unequivocal expulsion. To make matters worse, he had another of his terrible migraines. He felt as if a knife were lodged in his skull, splitting his cranium in two: One side was healthy and resilient while the other was trembling with the frenetic, uncontrollable energy of a piston charging at full blast. These headaches were always precipitated by nerves or a great shock, and they came on with lightning force, like a shooting star in the night sky. As soon as he saw the lights twinkling, followed by the ominous symptoms of vertigo and nausea, Bacon knew that the pain wasn’t far off. It was useless to try and resist it. He had tried household remedies like tea (which only made him more jittery), or ice cubes on his neck (which only made him feel like a filet of sole on display at a fish market), or the useless, bizarre massages of his earlobes or pinky finger. They never provided even a moment’s relief. And then the inevitable pain would come. Just as inevitable as the merciless tongue-lashing that he was about to receive from Aydelotte.