137: Jung, Pauli, and the Pursuit of a Scientific Obsession Part 13

Lucas numbers are like Fibonacci numbers but begin with 2: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, and so on. Like the Fibonacci series, the Lucas series also produces the Golden Ratio.

Fibonacci and Lucas numbers pop up all over the place, from how rabbits reproduce to the shape of mollusk sh.e.l.ls, to leaf arrangements that sometimes spiral at angles derivable from the Golden Ratio.

Because all these numbers are related, any formula for 137 in terms of the Golden Ratio can be rewritten in terms of Fibonacci and Lucas numbers, though whether this is anything more than merely abstruse relationships between certain numbers is not clear.

If one tries hard enough, 137 can be deduced from devilishly complicated combinations of "magic numbers" such as 22 (the first 22 human chromosomes are numbered), 23 (the number of chromosomes from each parent), 28 (the length of a woman's menstrual cycle), 46 (the number of pairs of chromosomes a person has), 64 (the number of possible values for the 20 amino acids in DNA), and 92 (the number of naturally occurring elements in the periodic table).

Sadly, all these are pure coincidences with no scientific basis. And still 137 continues to tantalize. In fact 137 has become something of a cult. According to one Web site, "The Fine Structure Constant holds a special place among cult numbers. Unlike its more mundane cousins, 17 and 666, the Fine Structure Constant seduces otherwise sane engineers and scientists into seeking mystical truths and developing farfetched theories."

Enrico Fermi with his incorrect equation for the fine structure constant.

Even Heisenberg had a go, fired by Eddington's number speculations. In a letter to Bohr in 1935 he reported "playing around" with the fine structure constant, which he expressed as . He was quick to add, "but the other research on it is more serious," referring to his and Pauli's attempts to derive it from quantum electrodynamics.

Many years later, Enrico Fermi, the physicist who christened Pauli's newfound weakly interacting particle the neutrino, was asked to pose for a photograph. He took his place in front of a blackboard on which he had written the fine structure constant-but incorrectly. Instead of he put . ( is shorthand for Planck's constant h divided by 2: h/2.) It was an excellent joke-and a joke comprehensible only to scientists. However, the joke backfired when the photograph was used for a stamp to commemorate him after his death. So he is caught forever standing next to this iconic equation-incorrectly written.

Surprisingly, 137 also crops up in an entirely different context. In the 1950s, Pauli developed a close friendship with Gershom Scholem, a prominent scholar of Jewish mysticism. When his former a.s.sistant Victor Weisskopf went to Jerusalem, Pauli urged him to meet Scholem, though he gave no hint of his own interests in Jewish mysticism. Scholem asked Weisskopf what the deep unsolved problems of physics were. Weisskopf replied, "Well, there's this number, 137."

Scholem's eyes lit up. "Did you know that 137 is the number a.s.sociated with the Kabbalah?" he asked.

In ancient Hebrew, numbers were written with letters, and each letter of the Hebrew alphabet has a number a.s.sociated with it. Adepts of the philosophical system known as the Gematria add the numbers in Hebrew words and thus find hidden meanings in them. The word Kabbalah is written in Hebrew: is 5, is 30, is 2, and is 100. The four letters add up to...137!

It is an extraordinary link between mysticism and physics. Two key words in the Kabbalah are "wisdom," which has a numerical value of 73, and "prophesy" (64): 73 + 64 = 137. G.o.d himself is One-1-which can also be written 10 (1 + 0 = 10). Take 10's const.i.tuent prime numbers, 3 and 7, and add the original 1: together they can be written 137.

In the bible the key phrase "The G.o.d of Truth" (Isaiah 65) adds up to 137. So does "The Surrounding Brightness" (Ezekiel 1) , and the Hebrew word for "crucifix", .

It turns out that, according to the Gematria, the number content of the letters in the Hebrew word for 137 add up to 1664. This happens to be the numerical value for a portion of the well-known pa.s.sage from Revelations 13:18: "Here is wisdom. Let him that hath understanding count the number of the beast." The rest of the pa.s.sage reads: "for the number is that of man; and his number is six hundred and sixty-six."

Homing in on the yet more arcane, a group of numerologists noticed that the number 82943 appeared at key places in Aztec and Roman texts and went on to argue that it was a key to a "new universal consciousness." Their confidence in this a.s.sertion was bolstered when they discovered they could relate it to the fine structure constant and the number of the beast-666-as follows: And more way out still, 137 is the foundation stone of a fiendishly complex "biblical mathematics" referred to by followers of "The Bible Wheel" as a "Holographic Generating Set." It is based on three geometric forms: a cube, A, divided into 27 subcubes; a hexagon, B, divided into 37 subhexagons; and a star of David, C, divided into 73 circles Of course 27 + 37 + 73 = 137. From this "generating set" with its Pythagorean-geometric aura, aficionados of the Bible Wheel claim to be able to generate biblical pa.s.sages and probe mystical numbers by multiplying A, B, and C in various ways.

Thus 137 continues to fire the imagination of everyone from scientists and mystics to occultists and people from the far-flung edges of society.

The last challenge.

With World War II behind them, Heisenberg and Pauli resumed their scientific correspondence. But the days of their collaboration and the frequent exchange of letters seemed to have ended. After all, they had been on opposite sides in the war. And Heisenberg's reputation was colored by the fact that he had remained in Germany and had ended up in charge of the German atomic bomb project. Most of his postwar colleagues, of course, had been involved in the Manhattan Project. Even Heisenberg's brilliance was not enough to overcome this stain.

Then in 1957 Heisenberg wrote to Pauli that he had the germ of a theory that could explain the ma.s.ses of elementary particles as well as most of the symmetries. In a preliminary test he was almost able to deduce the fine structure constant from his new theory. In his calculations it came to 1/250, which is not very far away from 1/137, in the same way as 1/3 is not far from 1/4, even though 3 is far from 4. This was extraordinary, given that Heisenberg's theory was still in its formative stages. Pauli immediately took up Heisenberg's suggestion to join him in his project.

"Never before or afterward have I seen [Pauli] so excited about physics," Heisenberg later recalled. It seemed as if the old days had come back. The two giants of quantum physics were working together once again.

"The picture keeps shifting all the time. Everything in flux. Nothing for publication yet but it's all bound to turn out magnificently," Pauli wrote exuberantly to Heisenberg at the start of 1958. "This is powerful stuff.... The cat is out of the bag and has shown its claws: division of symmetry reduction. I have gone out to meet it with my antisymmetry-I gave it fair play-whereupon it made its quietus.... A very happy New Year. Let us march forward toward it. It's a long way to Tipperary, it's a long way to go."

Heisenberg was equally excited. For him the theory was to be the culmination of his life's work. Over the years he had become entranced by the power of mathematics to probe and understand the physical world. And he knew how to use it. "A wonderful combination of profound intuition and formal virtuosity inspired Heisenberg to conceptions of striking brilliance," a colleague wrote. He had used his formidable insight and daring to apply mathematics to make his startling discoveries in quantum mechanics. These included the uncertainty principle; the first steps toward understanding the force that holds the nucleus together; and his attempts to produce a coherent theory of electrons and light, known as quantum electrodynamics.

The theory he was working on with Pauli was exactly what he was looking for. "The last few weeks have been full of excitement for me," he wrote to his wife's sister Edith in January 1958: I have attempted an as yet-unknown-ascent to the fundamental peak of atomic theory with great efforts during the last five years. And now, with the peak directly ahead of me, the whole terrain of interrelationships in atomic theory is suddenly and clearly spread out before my eyes. That these interrelationships display, in all their mathematical abstraction, an incredible degree of simplicity, is a gift we can only accept humbly. Not even Plato could have believed them to be so beautiful. For these interrelationships cannot have been invented; they have been there since the creation of the world.

Perhaps he also saw it as his chance to vindicate himself, to put behind him the fact that he had been the leader of the German atomic bomb project.

Together Pauli and Heisenberg wrote a joint paper that Pauli planned to lecture on during his forthcoming visit to the United States that January. Before leaving he wrote to Aniela Jaffe. He had been entirely engrossed in work with Heisenberg on a "new physical-mathematical theory of the smallest particles," he said.

The pace of their work was so overwhelming that often letters were not fast enough. The phone line between Zurich and Munich, where Heisenberg was based, was continually buzzing. For Pauli their research was so fundamental that he saw Jungian significance in it. Although he and Heisenberg were very different, he wrote to Jaffe, they were "gripped by the same archetype"-by reflection symmetry, in the fullest sense of the CPT reflection. "Director Spiegler! [Reflector] dictates to me what I should write and calculate," he declared.

He hoped that the "new year will see a beautiful theory that will light up the world." He had even had a dream about it: Pauli enters a room and finds a boy and a girl there. He calls out, "Franca, here are two children!" He had seen Heisenberg just three days earlier and interpreted the children as the new ideas which he was confident would emerge from their work. From the fact that there were two children, he drew an a.n.a.logy to his "mirror complex."

The work could be taken as a realization of the unconscious and "more specifically: a realization of the 'Self' (in the Jungian sense)." It was what Pauli had sought for years-physics and the psychology of the unconscious as mirror images, a scenario that had been destroyed by the violation of mirror symmetry (parity violation), but restored by CPT symmetry, Pauli's 1955 discovery about which he was still exultant.

On February 1, 1958, the lecture theater at the physics department at Columbia University was packed with over three hundred people. They were eager to see the great Pauli who was about to lecture on a theory formulated by the two giants of quantum theory. Niels Bohr, J. Robert Oppenheimer, T. D. Lee, and C. N. Yang, who had proposed the overthrow of parity, and C. S. Wu, the physicist who had performed the crucial experiment to prove it, all attended. The air was electric. But the distinguished audience had nothing but criticism for the new theory, though offered in a friendly manner. A key point in the theory was how newly discovered elementary particles decayed, how they transformed themselves into other particles. As Pauli was scribbling the equations on the blackboard, Abraham Pais, an eminent physicist and friend of Pauli's, raised his hand and objected, "But Professor Pauli, this particle does not decay like that." Pauli stopped midflow. There was a long silence. Then Pauli muttered, "I must get in touch with my friends in Gottingen about that," by which he meant Heisenberg. At this point, T. D. Lee remembers, you "could almost feel the silence." Others too pointed out loopholes in his mathematical proofs. Pauli continued his lecture but it was clear that the pa.s.sion had gone.

At one point Bohr and Pauli chased each other around a long table at the front of the room. Whenever Bohr ended up at the front he declared, "It is not crazy enough." Each time Pauli appeared he replied, "It is crazy enough." This was repeated several times and the audience burst into applause.

"We were all polite, but Pauli was obviously discouraged...It was obvious that his heart was no longer in their work," Yang recalled. He vividly remembered Pauli's gloom as they were on their way in Lee's car to a restaurant after the lecture. "Pauli oscillated back and forth in his seat and murmured some thing which I thought was, 'As I talked more and more, I believed in it less and less.' I was greatly saddened." The physicist Freeman J. Dyson, of the Inst.i.tute of Advanced Study, commented that it was "like watching the death of a n.o.ble animal."

So what had happened? How could Pauli have been so enthusiastic about this new approach and then so totally cast down? Presenting a lecture on a subject can shed an entirely new light on it. So perhaps that was what happened. Suddenly he realized that the theory was full of holes. He was beginning to have second thoughts about his work with Heisenberg.

The following day he lectured at the American Physical Society meeting in New York, at that time the biggest and most important annual gathering of physicists from around the world. There was standing room only. But the criticism meted out by a younger and brasher generation of American physicists was even harsher. Lee could not bring himself to attend.

From there Pauli went on to California-where Feynman, for one, had had no compunction about telling the great Bohr that he was an idiot. Audiences there too offered ruthless criticism. Pauli was beginning to conclude, as he wrote to Heisenberg later that year, that "something entirely new, in other words very 'crazy,' [was] needed" if he and Heisenberg were to crack the mystery of the ma.s.ses of elementary particles, one of the key aims of their unified theory.

Disillusioned, Pauli attacked Heisenberg's calculation of the fine structure constant as 1/250, which had seemed so promising and had played a part in his decision to join Heisenberg's project. He wrote to Fierz bitterly, "I have never considered it as correct. It's so totally stupid."

Some time later, Heisenberg's co-worker on that calculation, Renato Ascoli, recalled that he had originally deduced the fine structure constant as 8 on the basis of Heisenberg's theory. "Only after Heisenberg had doctored it up, was the value reduced to 1/250."

Later that month Heisenberg gave a lecture on his and Pauli's work at Heisenberg's Inst.i.tute in Gottingen. The room was packed. The great Heisenberg was about to announce a theory that could explain the behavior of every elementary particle in the world with a single equation-a "world formula"-that would surely prove to be an abstruse and highly technical piece of mathematics.

A press release was circulated reading (most offensively to Pauli): "Professor Heisenberg and his a.s.sistant, W. Pauli, have discovered the basic equation of the cosmos." The story was picked up by newspapers around the world. Pauli vented his anger in a letter to George Gamow, the physicist and prankster who had translated and ill.u.s.trated the Mephistopheles spoof at Bohr's Inst.i.tute in 1932. Pauli lampooned it by drawing an empty box saying, "This is to show that I can paint like t.i.tian: Only the technical details are missing"-a case of the emperor's new clothes. Pauli requested Gamow not to publish his comment but, miffed at Heisenberg's insulting press release, added, "please show it to other physicists and make it popular among them." Gamow certainly did. A week later Weisskopf wrote to Pauli about the press release and added that he read it with Pauli's comment about t.i.tian well in mind.

Combining Pauli's well-known obsession with 137 with Heisenberg's for his new theory, a colleague wrote jokingly to Pauli, "Since the Heisenberg equation is supposed to describe everything (see, for instance, New-York Herald Tribune, volume 137, p. i/137), it has as one of its solutions Heisenberg himself." Pauli replied, "Regarding Heisenberg I have the feeling, that the situation is slowly growing over his head; certainly he needs vacations." The problem of how to describe the properties of elementary particles remained open. Pauli summed up the situation thus, "Many questions, no good answers."

In fact, Pauli was furious. He wrote to C. S. Wu about Heisenberg's "poor taste" as far as the press releases were concerned: In some of these I had been, unfortunately, mentioned...but fortunately only in a "mild" form as a secondary (or tertiary) auxiliary person of the Super-Faust, Super-Einstein and Super-man Heisenberg. (He seems to have mentioned his dreams on gravitational fields-about which one has not worked at all in Gottingen recently-and his revival of the old idea of a "world formula"-which was never successful-in a quantized form.) He seems to have been relieved that he was not a.s.sociated too closely with Heisenberg's mistaken schemes. To Wu he recalled his hopes, dreams, and aspirations of thirty years earlier when he and Heisenberg were young and Heisenberg depended on his friend's criticism and inspiration. Now Pauli had had enough: Heisenberg's desire for publicity and "glory" seems to be insatiable, while I am in this respect completely saturated. I only need something in science which interests me sufficiently and with which I can play (without being a hero in the limelight of the "world.") Heisenberg's opposite att.i.tude, with which he certainly wishes to compensate earlier failures, may have many reasons lying in the whole history of his life.

No doubt the last words were an oblique reference to the role Heisenberg played in the war.

Soon afterward Pauli withdrew from the collaboration. Heisenberg persisted in making promise after promise as to the wonders his theory would produce. "He believes that if he publishes with me, then it is 1930 again! I have found it embarra.s.sing how he runs after me!" Pauli wrote to Fierz in May.

That July Pauli chaired a session at a conference at CERN at which Heisenberg was scheduled to speak. Pauli introduced Heisenberg with the words, "What you will hear today is only a subst.i.tute for fundamental ideas." He went on to make a request of the audience: "don't laugh in the wrong place, ha, ha, ha...." The audience was already in fits of laughter. Pauli let Heisenberg finish speaking, then mercilessly demolished his paper.

When Pauli and Heisenberg met again later that summer, Heisenberg noticed that Pauli looked dispirited. Pauli encouraged him to go on with his work and wished him well, but added, "For me, I have to drop out, I just haven't the strength, and that's that. Things have changed too much."

Could it have been that the great criticizer had met his match in the lambasting he encountered in America? To be on the receiving end must have been shattering. Heisenberg had been afraid this would happen when Pauli "in his present mood of exultation [encountered] the sober American pragmatists." Franca too had noticed this c.h.i.n.k in Pauli's armor which, up until then, he had concealed so successfully: "He was very easily hurt and therefore would let down a curtain. He tried to live without admitting reality. And his unworldliness stemmed precisely from his belief that that was possible."

But there was something else that brought Pauli to the point of spiritual exhaustion. He had grown attached to his work with Heisenberg. Their new theory had all the trappings that he thought a theory should have: a high degree of mathematical symmetry and Jungian meaning too, taking it one step closer to not merely a unified theory of elementary particles from which the fine structure constant could one day be deduced, but to a theory of the mind as well.

As he always did, Pauli interpreted the failure of the theory as personal failure. Genius though he was, he had failed yet again. Those who saw him in the autumn of 1958 recalled that he seemed beaten.

That year Pauli told an interviewer, "When I was young I thought I was the best formalist of my time. I believed that I was a revolutionary. When the great problems would come, I would be the one to solve them and to write about them. Others solved them and wrote about them. I was but a cla.s.sicist and no revolutionary." He began writing letters as if saying farewell.

A different side of Pauli.

It was not all gloom. During his visit to the United States that year, Pauli had visited Harvard. Among the delegation that greeted him was Roy Glauber.

Glauber had been a postdoctoral fellow at the ETH back in 1950, working under Pauli. "Pauli...had been a legendary figure since his early twenties. Some part of that legend, as Pauli well knew, was attached to his role as a critic, not always kindly, of the work of his colleagues. So no one who knew Pauli, it is fair to say, could be in his presence without feeling a certain defensive wariness," he remembered many years later.

Not long after young Glauber arrived in Zurich, he and the rest of Pauli's students went on a hike in the hills. They took a cable car and then followed a series of steep trails around the Vierwaldstatter See, a scenic lake. "Pauli, notwithstanding his ample girth," kept up a vigorous pace. Expecting a picnic, Glauber had brought a camera, a hefty Speed Graphic-made famous in the 1940s and 1950s by press photographers-which hung by a strap over his shoulder. He had not even brought much film. Pauli began teasing him. "Always you carry that awful camera," he kept saying, "but you are taking no pictures." Then he laughed uproariously.

At the end of the day, some of the group swam in the lake while others played soccer. Pauli kicked the ball into the lake so that someone had to swim out and fetch it. He roared with laughter as he kicked the ball further and further into the water.

A photograph of Pauli kicking the ball was too good to miss-but Glauber had only one exposure left. Trying not to draw Pauli's attention, he set up his camera, peered into the rangefinder and as inconspicuously as possible signaled a friend to kick the ball toward Pauli. Suddenly the camera smacked him square in the face. Instead of the lake, Pauli had decided to make Glauber's camera his next target. Glauber recalled hearing his bellowing laugh.

Pauli kicking a soccer ball, 1950.

He had, however, managed to snap the shutter. "Pauli," he concluded, "never discounted the element of luck in his practical jokes."

When Glauber was still at the ETH, his mother once wrote and complained to Pauli that her son never sent letters home. Thereafter, whenever Pauli saw Glauber, he always insisted on asking loudly, "And how is your dear mother?"

In 1958, when Pauli visited Harvard, Glauber was apprehensive. To his relief Pauli greeted him warmly and said nothing the entire time about his mother. "Thank G.o.d he has forgotten my mother," Glauber said after he had left. Pauli went with Weisskopf back to his lodging in Cambridge. The first thing he said once they were out of earshot was, "This time I fooled Glauber. I said nothing about his mother."

A nearly perfect sphere.

That same year Pauli attended the Solvay Conference in Brussels as that venerable meeting's vice president. There he and Franca invited the cosmologist Fred Hoyle and his wife to lunch. Honored, Hoyle happily accepted. He was eager to substantiate a story about Pauli that had been on his mind for some years, of how, in the 1920s, after a lecture by Einstein on relativity, Pauli had had the temerity to say to the audience that what Professor Einstein said "was not so stupid."

But Pauli had his own agenda. "Aha," he cackled, "I just read your novel The Black Cloud. I thought it much better than your astronomical work." Hoyle had recently proposed a theory a.s.serting that the universe around us has always existed exactly as we see it. He called it the "steady-state theory" to distinguish it from what he dubbed the "big bang theory"-that is, that the universe came into being at a specific moment in time and evolved into what we see today. Pauli was far from impressed with Hoyle's theory.

He told Hoyle that both he and Jung had read Hoyle's novel carefully and that he was writing a critical essay on it. Hoyle was mystified. After all, it was only a story-about how an intelligent life-form learns to communicate with earthlings. He had never felt it merited such deep a.n.a.lysis.

Finally Hoyle had the chance to ask Pauli about the Einstein story. "My abiding memories of Pauli," he wrote, "are of his helpless laughter as the youthful remark about Einstein came back to him and his rolling back and forth, a nearly perfect sphere." But Pauli said no more, "so I never quite had it from Pauli personally that the story was true, but those who knew him well a.s.sure me it was." Another lasting memory that Hoyle carried away from the lunch was the four bottles of fine wine on the table.

The Pauli effect strikes again.

That same year the physicist Engelbert Schucking visited Pauli in Zurich. Along with Pauli's a.s.sistant Charles Enz and another colleague they took a tram from the ETH to Bellevue Square, where they planned to have a "wet after-session," with plenty of drinking. Bellevue Square is a bustling intersection where several tram tracks cross each other in a seemingly random way. Just as they reached the square, two street cars collided right in front of them with an enormous bang. Schucking was standing with Pauli next to the driver of the street car. "Pauli's face was flushed as he excitedly turned to me and exclaimed, 'Pauli effect!'" Schucking recalled.

Enz told Schucking about a lecture Pauli had given to an audience of high-level government officials on an occasion honoring Einstein, the ETH's most famous graduate. "Pauli read from his ma.n.u.script. Whenever he found an error in his text, he stopped in mid-sentence, drew out his fountain pen, corrected the text and went on, oblivious of the squirming audience." It was a teaching style he had maintained throughout his career.

That November Pauli was in Hamburg. Schucking took a walk with him. As they walked along the Gojenbergsweg in the Bergdorf district, looking out over the marshland of the river Elbe, Pauli said several times how glad he was to have withdrawn his name from the paper with Heisenberg.

On Friday, December 5, 1958, as he was teaching his afternoon cla.s.s, Pauli suddenly began to suffer excruciating stomach pains. Up until then he had been fine. The next day he was rushed to the Red Cross Hospital in Zurich. Charles Enz visited him the day after. Pauli was visibly agitated. Had Enz noticed the number of the room, he asked him?

"No," replied Enz.

"It's 137!" Pauli groaned. "I'm never getting out of here alive."

When the doctors operated, they found a ma.s.sive pancreatic carcinoma. Pauli died in Room 137 on December 15. His last request had been to speak to Carl Jung.

PAULI was cremated on December 20 and later that afternoon an official funeral ceremony was held at the Fraumunster Church in Zurich, which dates back to the Carolingian period. The ceremony was non-religious. Niels Bohr, Markus Fierz, the party-giver Adolf Guggenbuhl, Pauli's treacherous colleague Paul Scherrer, and his one-time a.s.sistant Victor Weisskopf all gave addresses. Franca arranged the funeral. Only physicists spoke. Among the many who attended were Pauli's confidant Paul Rosbaud. Jung, now eighty-two, was relegated to a place at the back. Despite his long a.s.sociation and close friendship with Pauli, he was not invited to speak.

One notable absentee was Heisenberg. The ETH had sent Heisenberg's invitation on the sixteenth, giving him plenty of time to travel from his home in Munich to Zurich to pay his last respects to the man who had been his lifelong friend and colleague and had sparked his greatest discoveries. Heisenberg did not even bother to write a letter of condolence to Franca but left it to his wife. He was, she wrote, reading Pauli's philosophical writings, but due to the Christmas season they were too busy to attend.

It is extraordinary that Heisenberg would spurn his old friend in this way. Despite their recent falling out, one would have a.s.sumed that he would have put all that behind him and attended. The only possible explanation is to be found in Heisenberg's autobiography, written over a decade after Pauli demolished the theory he was so proud of. "Wolfgang's att.i.tude to me was almost hostile," he wrote of that episode. "He criticized many details of my a.n.a.lysis, some, I thought quite unreasonably." Presumably Heisenberg never forgot what had happened. The intensity with which these men treated their pa.s.sion-physics-went far beyond the grave.

Hertha also did not attend her brother's funeral. Perhaps travel was difficult financially for her; perhaps she wanted to remember Wolfgang the way he was; or perhaps she felt uneasy around Franca. Hertha had married E. B. Ashton, an immigrant from Munich, born Ernst Bach. He was a professional translator and they collaborated on several of her books. As she recalled, "we decided he would remain my 'better English'" and married in 1948. As Franca put it contemptuously, she "married her translator." The couple lived happily in a large farmhouse in Huntington, Long Island. Like her brother, Hertha had no children. She published several biographies and historical studies in addition to her books for children on Catholic themes. In the course of her prolific career she became an eminent member of PEN-the worldwide a.s.sociation of writers-and was awarded the Silver Medal of Honor by the Austrian government in 1967. Hertha died in 1973, predeceasing her husband by ten years. Their ashes were interred in the Schutz family grave in Vienna, near where she and Wolfi had grown up.

Pauli's ashes were interred in the graveyard in the town where he had lived, Zollikon, between Zurich, where the ETH is, and Kusnacht, where he used to visit Jung in his Gothic mansion-the two places that defined his two worlds of physics and psychology.

Franca was curious about the story Enz told about room 137. Pauli had never said a word to her about this mysterious number. Enz a.s.sured her that he was repeating "Pauli's own words." He told her about the significance of the number in physics and that Pauli had mentioned it many times.

Franca wrote a letter to Abdus Salam, a physicist whom Pauli had greatly respected, asking whether it was he who had written "an article connected with the subject Pauli and the number 137." She added, "it is a strange fact that Wolfgang Pauli actually died in the room Nr. 137." People thought that Pauli had requested that room, she said. In fact he had originally been in another room and was transferred to room 137 without being told where he was being sent.

It was Salam, in fact, who originated the story of Pauli going to heaven and asking the Lord to explain "Why 137?" That had been in 1957, the year before Pauli's death. Salam wrote to Franca, "of course it is a story which I would not repeat now." He sent her a copy of his lecture in which the story appeared.

Franca replied, "At last I got a written, beautiful explanation of this to me so elusive Number 137. I enjoyed the end of the story-I did not know-'convincing the Lord a mistake had been made.' One could not characterize Pauli better in so few words!"

FRANCA died in 1987. She spent the three decades after her husband's death finding suitable places for his books, personal papers, and correspondence. She also did her best to delay the publication of his correspondence with Jung. To the end Franca believed that it would detract from his image as a serious scientist.

Epilogue: The Legacy of Pauli and Jung.

PAULI AND JUNG were men who thought outside the box. Pauli made three discoveries that changed the course of science and our understanding of the world: the exclusion principle, the neutrino, and CPT symmetry. Jung pioneered a different way to explore the mind, by opening up psychoa.n.a.lysis to include alchemy, mysticism, and Far Eastern religions.

Today Pauli is remembered for the exclusion principle and the Pauli legend-as the man who loved to terrorize physicists. He's also remembered, of course, for his extraordinary effect on mechanical instruments. In 2000 the magazine Physics World asked scientists to vote for the top-ten physicists of the twentieth century. Pauli did not receive a single vote and was not even mentioned. Yet, beside his three major discoveries, his discussions with and suggestions to Heisenberg (who, of course, was high on the list) were invaluable to Heisenberg in achieving his breakthroughs, as were Pauli's critical evaluations of the work of others. Pauli was involved in some of the greatest advances in twentieth-century physics, but, as we have seen, he couldn't be bothered to step forward and claim the credit. He was more interested in pressing on with his work, in pushing forward the borders of science.

As for Jung, although his name is widely known to psychoa.n.a.lysts and the general public, what he actually did is less well known than the man himself. For many years the psychoa.n.a.lytic community spurned him because of his interest in what they saw as the occult. In part this was due to the lambasting he received from Freud's circle. He was later adopted by New Age movements, which did not help matters; nor did his alleged n.a.z.i sympathies. Today there is renewed interest in the connection between Freud and Jung. Scholars are also trying to understand Jung and his work within the culture of his day, both when he was forming his ideas and later as a pract.i.tioner. To this end scholars are examining his unpublished papers and preparing them for publication, seeking out further information about who this extraordinary man really was, who started a whole new school of psychology and whose work forms much of the basis of psychology as we have it today.

Today scientists, psychologists, and neurophysiologists routinely a.s.sert that the understanding of the mind, including consciousness, cries out for an approach that crosses disciplines. But when Pauli and Jung embarked on this same route it was so innovative-so totally out of the box-that they had to keep it to themselves, for fear their colleagues would laugh at them.

Many developments in the study of the mind have happened since their work together first appeared. Some scientists now a.s.sert that it should be possible to simulate the working of the mind on a computer, encapsulated as logical procedures for solving problems. This echoes the logical empiricists of the Vienna Circle in the early twentieth century.

Neurophysiologists such as Antonio Damasio investigate how parts of the brain are stimulated by images or problems. One of the instruments they use to study which sections of the brain become stimulated and in what order is functional magnetic resonance imaging (fMRI). This produces images of the brain derived from the way electrons line up their spins in a magnetic field, the understanding of which derives from Pauli's fourth quantum number. Another method is to measure the increased oxygen flow to a particular area of the brain that occurs when a subject solves a task. To do so the researcher injects radioactive oxygen into the subject's bloodstream. It produces positrons that collide with the electrons in the brain to produce light quanta which are detected by radiation counters around the patient's head (positron emission tomography [PET]). These are examples of the marriage of physics and brain research that Pauli might have thought up himself.

Neurophysiologists have also produced evidence showing how important visual images are to the working of the mind. Pauli's discovery of the fourth quantum number brought to an end the convenient image of the atom as a miniature solar system and led both him and Heisenberg to decide reluctantly to abandon the use of visual images. But Pauli hoped that some day, somehow, in a new theory, a usable visual image of atomic processes would be discovered. Richard Feynman's theory of quantum electrodynamics, formulated in 1949, produced just such an image. Feynman produced the Feynman diagrams, deduced from the equations of his new quantum electrodynamics which was free of the infinities that had rendered invalid Pauli's and Heisenberg's theory of quantum electrodynamics of the 1930s.

Pauli was well aware of Feynman's theory and was not satisfied because it concerned only electrons and light. It did not remove the infinities from theories that contained newly discovered elementary particles, nor those in Fermi's theory of weak interactions; and it did not produce the fine structure constant, either. Pauli did, however, agree that Feynman's procedure-which physicists called "renormalization"-was along the right lines. Jokingly he referred to a Feynman diagram as a "sentimental painting."

In recent years Roger Penrose has made a pioneering attempt to combine neurophysiology with physics. He suggested that structures within neurons-microtubules-could be the seat of the quantum computations that are the dynamics behind thinking. But these are not simply logical computations, because quantum physics, which includes the uncertainty principle and the concept of ambiguity, introduces an indefinable extra ingredient-intuition. This element is not addressed in any of the research programs mentioned here and is a critical shortcoming. Pauli and Jung emphasized its importance, as did Einstein and other scientists when they recalled how they had made their discoveries.

The puzzle of how we reason, how we think-of how we create knowledge from already existing knowledge and how we draw conclusions that go beyond the premises-cannot be solved by logic alone. Researchers in cognitive science have applied a cross-disciplinary approach. This includes simulating the mind on a digital computer; neurophysiology; notions from philosophy applied to the mind (philosophy of mind); linguistics (how metaphors arise and how they are used); and visual imagery (how visual images are generated and manipulated in problem solving). But they fail to include physics. And despite applying so much heavy intellectual machinery to the study of how the mind operates, they also omit data from the history of science in the form of testimonies, correspondence, and other biographical details of scientists themselves.

In this field Pauli's application of Jung's psychology to Kepler's thinking is an exemplary work. Applying data from case histories of great scientists as grist for the mill of theories of psychology is an adventurous and fruitful route.

In turn, Jung's psychology can throw light on how Pauli made his first great discovery of the exclusion principle: input from his conscious thinking energized the archetypes for three and four (constellated them, to use Jung's terminology), which sparked his insight. Jung, too, found number archetypes essential in transforming the neuroses in his life into a creative force.

Which brings us to 137 and Pauli's obsession with deriving the fine structure constant from quantum electrodynamics. Not only does this remain unsolved but the problem has widened. In Pauli's day there were seven known fundamental constants. Now there are twenty-six. This is due to the increase in the number of known elementary particles, their fundamental interactions, and their properties. While Pauli was able to focus on the fine structure constant and quantum electrodynamics, physicists are now trying to derive all twenty-six from a theory that will encompa.s.s not only the electromagnetic force-which is controlled by the fine structure constant-but the strong and weak forces, and eventually the gravitational force as well. This is the ultimate ambition of string theorists, among others whose grand aim is to come up with a theory that explains the large and the small, the universe and the atom-a theory of everything.

Notes.

Author's Note.