IS THERE a number at the root of universe? Is there a primal number? Is there a number that everything in the universe hinges on, that explains everything? Many of the major discoveries in science have emerged out of mathematics—Einstein’s general theory of relativity, black holes, parallel universes, string theory, and complexity theory are only a few of many examples. All of these can be expressed in equations; yet they also depict concrete aspects of the physical universe.
Could there be a single number at the root of the universe which is, as Douglas Adams has it in The Hitchhiker’s Guide to the Galaxy, “the answer to life, the universe and everything?” Physicists, psychologists, and mystics have pondered this question. Some have proposed the number three—as in the Trinity and the three dimensions of length, breadth, and depth. Some have argued for four—after all, we have four seasons, four directions (north, south, east, and west), and four limbs. Some have been convinced that the answer might be the very weird number 137, which on the one hand very precisely describes the DNA of light and on the other is the sum of the Hebrew letters of the word “Kabbalah.” This is a matter that exercised many of the great minds of the twentieth century, among them the physicist Wolfgang Pauli and the psychoanalyst Carl Jung.
137 is the story of two mavericks—Pauli, the scientist who dabbled in the occult, and Jung, the psychologist who was sure that science held answers to some of the questions that tormented him. Both made enormous and lasting contributions to their fields. But in their many conversations they went much further, exploring the middle ground between their two fields and striking sparks off each other.
In 1931 Wolfgang Pauli was at the height of his scientific career. He had discovered the exclusion principle—known to this day as the Pauli exclusion principle—which explains why the structure of matter is as it is and why certain stars die as they do.
Just a year earlier, he had made the audacious suggestion that there might be an as yet undiscovered particle—an outrageous suggestion in those days. Besides the electron, proton, and light quantum, which everyone took for granted, he insisted that there had to be another particle that became known as the neutrino. Twenty-six years later Pauli’s neutrino was finally discovered in the laboratory.
But while his friends and colleagues competed to win science’s glittering prizes, Pauli was a different kind of character. He seemed almost indifferent to success. His scientific work was not enough to give him satisfaction and his personal life too fell deeper and deeper into chaos as he trawled the bars of Hamburg, sampling the nightlife and chasing after women.
In 1932 a prize-winning film of Dr. Jekyll and Mr. Hyde came out, starring Frederic March as the tormented doctor. Pauli’s life too seemed to have fractured.
The solution was obvious. He turned to the world-famous psychologist Carl Jung who, as it turned out, lived not far from him just outside Zürich.
Pauli was thirty-one. Jung, his senior by twenty-six years, was firmly established and hugely famous. He was the toast of the wealthy ladies and gentlemen of European and American high society, who came to him hoping to solve their various psychological malaises.
At the time the world was still living through the aftermath of the 1929 Wall Street crash; two years earlier in Germany the Nazis had won 37 percent of the vote in a key election and Adolf Hitler was on the way to becoming chancellor; Japan had recently invaded Manchuria; and Franklin Delano Roosevelt had just been elected president of the United States. But none of this much affected Jung and his wealthy patients. They were interested in more arcane and intimate matters.
Along with Sigmund Freud, Jung had opened up the concept of the mind as something that could be studied and understood—and also healed. But the approaches of the two legendary psychoanalysts could not have been more different.
Right from the start Jung wanted to shed light on those deep recesses of the unconscious that were beyond Freud’s method, which dealt only with the areas of the unconscious generated by events in one’s daily life. Yet Jung was far more than just a psychologist. His interests ranged far and wide across Chinese philosophy, to alchemy and UFOs. He saw the same patterns underlying radically different ways of thinking across the world, and he was convinced that these patterns arose from the mind. He called them archetypes, essential elements of the pysche. Thus he developed the concepts of the collective unconscious and of archetypes, which are today taken for granted.
He then came up with the concept of synchronicity, which he always considered one of his most important ideas. He was sure that bonds as strong as those that linked Eastern and Western thinking could also link the apparently cold rational world of science with the supposedly irrational world of intuition and the psyche.
One area that brought all these interests together was numbers. Jung was fascinated by certain numbers—three and four—that popped up again and again in alchemy and also in religion, and in the power of numbers to predict occurrences in life, as codified in the I Ching (the Chinese Book of Changes). But it was not until he met Wolfgang Pauli that all this began to coalesce.
PAULI, a kindred spirit, was also fascinated by numbers. His infatuation with numbers had begun when he was a physics student, when his mentor Arnold Sommerfeld used to extol the wonders of whole numbers with all the fervor of a kabbalist. Among them was 137.
It was Sommerfeld who discovered this extraordinary number in 1915, while trying to solve one particular puzzling feature of atoms: the “fine structure” of spectral lines, the characteristic combination of wavelengths of light emitted and absorbed by each chemical element—the fingerprint or DNA, as it were, of each wavelength of light. It was dubbed the “fine structure constant” (which in fact equals 1/137, though for convenience physicists refer to it as 137).* From the moment 137 first popped up in his equations, he and other physicists saw that its importance went far beyond the fact that it solved this one puzzle. They quickly realized that this unique “fingerprint” was the sum of certain fundamental constants of nature, specific quantities believed to be invariable throughout the universe, quantities central to relativity and the quantum theory.
But if this one number were so important, should it not be possible to deduce it from the mathematics of these theories? Disturbingly, no one could.
The fine structure constant turns out to be exquisitely tuned to allow life as we know it to exist on our planet. Perhaps it was not surprising, then, that physicists began referring to 137 as a “mystical number.”
By the time Sommerfeld stumbled across 137 in 1915, whole numbers were beginning to crop up everywhere in atomic physics. Two years before, the Danish physicist Niels Bohr had worked out that the energy levels of the electrons within atoms could be expressed with whole numbers, so-called quantum numbers. He assumed that only three quantum numbers were necessary to locate an electron in the atom, just as it takes only three numbers to locate an object in space: its coordinates in the three dimensions. But then ten years later the twenty-four-year-old Pauli showed that in fact a fourth quantum number was needed. The problem was that the fourth quantum number could not be visualized.
For Pauli the problem came down to numbers: to the “difficult transition from three to four.” And 137 turned out to be linked with this transition.
Three hundred years earlier, a full-scale row over a very similar issue had broken out between the mystic and scientist Johannes Kepler and the Rosicrucian Robert Fludd. Kepler argued that three was the fundamental number at the core of the universe, using arguments from Christian theology and ancient mysticism. Fludd, however, argued for four on the basis of the Kabbalah, of the four limbs, the four seasons, and the four elements (earth, water, air, and fire): God’s creation of the world was a transition from two to three to fourness, he asserted.
But where did 137 come in? Pauli became convinced that the number was so fundamental that it ought to be deducible from a theory of elementary particles. This quest took over his waking and sleeping life. Driven beyond endurance, he sought the help of Jung.
Jung’s theory of psychology offered Pauli a way to understand the deeper meaning of the fourth quantum number and its connection with 137, one that went beyond science into the realm of mysticism, alchemy, and archetypes. Jung, for his part, saw in Pauli a treasure trove of archaic memories, as well as a great scientist who could help him put his theories on a firm footing.
THE EARLY YEARS of the twentieth century were a watershed not unlike the Renaissance. Freud’s discovery of the mind as a field of study and Max Planck’s discovery of the quantum nature of matter were quickly followed by Einstein’s relativity theory and Bohr’s theory of the atom. Then came the horrors of the First World War, which inspired a trend toward spiritualism and a return to ancient beliefs, especially in Germany. Just before the war the great German physicist Werner Heisenberg was finding solace in reading Plato. In 1927 Sommerfeld, in response to a request by a periodical for an article on astrology, wrote:
Doesn’t it strike one as a monstrous anachronism that in the twentieth century a respected periodical sees itself compelled to solicit a discussion about astrology? That wide circles of the educated or half-educated public are attracted more by astrology than astronomy? [We] are thus evidently confronted once again with a wave of irrationality and romanticism like that which a hundred years ago spread over Europe as a reaction against the rationalism of the eighteenth century.
Yet he himself wrote ecstatically of the mystical qualities of 137.
The search for some point of contact between physics and the mind was of key interest to many physicists, including Max Born and Werner Heisenberg—two other pioneers of quantum physics—and Pauli and Bohr. As Pauli put it:
I do not believe in the possible future of mysticism in the old form. However, I do believe that the natural sciences will out of themselves bring forth a counter pole in their adherents, which connects with the old mystic elements.
All this was taking place at a time when philosophy was shifting from a positivistic approach, which excluded anything that could not be reduced to sense perceptions, to a search for a reality beyond appearances. The search for this reality became a passionate quest in the arts as well: Pablo Picasso and Wassily Kandinsky were discovering new ways to represent reality as they developed cubism and abstract expressionism; composers such as Igor Stravinsky and Arnold Schönberg were rebelling against the traditional canons of music; while writers such as James Joyce were incorporating relativity into their fiction.
PAULI told very few colleagues about his discussions with Jung. He feared their derision. Nevertheless his sessions with Jung convinced him that intuition rather than logical thought held the key to understanding the world around us. Many scientists see Pauli as the epitome of rationality and logical thinking. They assume that a scientist who worked as hard as he did, and achieved as much, must have lived strictly a life of the mind, devoted to physics. This still tends to be the image that both ordinary people and scientists themselves have of scientists.
It is important to remember Isaac Newton, who laid the foundations of modern science. For over two hundred years after his death people imagined he was a man devoid of emotions—“with his Prism and silent Face,” as William Wordsworth wrote—who sat at his desk day after day working out equations.
A colleague once asked Newton what he was working on. He replied that he did physics—but only in his spare time. In the 1930s, a bundle of papers which he had kept secret came to light. These revealed that Newton had been very much a man of his time, concerned less with physics than with issues such as how big the new city of Jerusalem would have to be to receive the souls on Judgment Day, with biblical chronology and how to discern the motion of material objects relative to God. As far as he was concerned, his famous laws of motion were simply a means to work toward this end.
As the English economist John Maynard Keynes, who bought many of Newton’s newly discovered papers, wrote, “Newton was not the first of the age of reason. He was the last magician.”
Newton’s first biographer, the nineteenth-century Scottish scientist David Brewster, was adamant that there was “no reason to suppose that Sir Isaac Newton was a believer in the doctrines of alchemy.” But Newton’s papers reveal just the opposite—that Newton was among the most knowledgeable alchemists of his day. We now take for granted that he should be understood as a man of his time, who lived in a world of alchemy, magic, and mysticism, like his near-contemporary, the seventeenth-century German astronomer Johannes Kepler, whom Pauli saw as an image of himself.
Scientists who have not examined Pauli’s vast correspondence and writings still place him in the old Newtonian straitjacket. But Pauli was alive to the alchemical roots of science. Modern science, he believed, had come to a dead end. Perhaps the means to break through and to develop new insights was to take a radically different approach and return to science’s alchemical roots.
Although a twentieth-century scientist, Pauli felt an affinity with the seventeenth century—perfectly natural to anyone who, as he did, accepted that there was, as Jung postulated, a collective unconscious.
Today a vocal minority of scientists believe in paranormal phenomena. For twenty eight years a laboratory at Princeton University tried to establish evidence for extra-sensory perception (ESP)—using card-guessing methods—as well as evidence for telekinesis, the ability of the mind to move objects. It had been privately funded to the tune of ten million dollars and closed down in 2007. Its founder, Robert G. Jahn, a pioneer in jet propulsion systems said, “it is time.” He claimed to have demonstrated that test subjects “thinking high” and “thinking low” could alter a sequence of numbers flashed from a random number generator—very slightly, however, two or three flips out of ten thousand. Pauli and Jung discussed experiments of this sort. They, too, believed in powers of the mind inexplicable by the logic of physics.
The two men also discussed at great length the notion of consciousness, considered by most scientists at that time to be sheer nonsense—“off limits.” Today it is a burgeoning field of research using concepts from quantum mechanics, some of which Pauli had speculated on.
MORE THAN TWENTY YEARS ago I was intrigued to discover that Pauli and Jung had co-authored a book entitled The Interpretation of Nature and the Psyche. I tracked it down and read it with growing fascination. I was gripped by the new aspects of both men it revealed. As a physicist I knew about Pauli and his contributions to science and of course was well aware of Jung. But the two together, the rational Pauli with the iconoclastic Jung?
I was determined to find out more about their story. Nevertheless, many years passed before I finally had the chance. I began my research in Zürich where I studied their letters, housed in the library of the very famous technological university, the ETH (Eidgenössische Technische Hochschule). I visited the areas where Pauli had lived, the restaurants and bars where he used to go, and the streets he used to walk, and stood outside his home in Zollikon, just outside Zürich. It was a large, nondescript, suburban detached house surrounded by trees, not the grand house I had imagined.
In Hamburg I walked the streets where Pauli had lived, worked, and played. Some of the bars he frequented in the Sankt Pauli red-light district are still there and still carry the same edge of violence.
At La Salle Pauli at the huge nuclear physics research laboratory CERN (Conseil Européenne pour la Recherche Nucléaire), outside Geneva, where Pauli’s library is housed, I looked through his books, marked in his own handwriting with his code for important passages, both books he read before meeting Jung and during the time he knew him.
Jung’s Gothic mansion, two stops on the train from Zollikon, was, I had heard, no longer open to visitors. Nevertheless I sent a letter there, addressed simply to “The resident of 228 Seestrasse.” A few days later I received an email from Jung’s grandson Andreas, inviting me to visit. A gracious and friendly man—and the spitting image of his grandfather—he showed me around Jung’s vast and splendid residence. I was thrilled to step inside the spacious high-ceilinged library where Jung and Pauli used to sit, first as patient and analyst and then as friends, mulling over the mind, the times in which they lived, and the civilization they knew. I looked around the dining room and put my hand on the table where they had dined. Outside the grand windows the lawn stretched down to Lake Zürich. It was the same view that the two friends used to admire as they chatted over fine wine and fine tobacco.
The table in Jung’s dining room, the seventeenth-century alchemical books in his library, and Pauli’s own books, with his markings, brought home to me the intensity of their common quest. For Pauli realized that quantum mechanics—despite its grandeur, and in the face of his distinguished colleagues—lacked the power to explain biological and mental processes, such as consciousness. It was not a complete theory. As he put it, “Though we now have natural sciences, we no longer have a total scientific picture of the world. Since the discovery of the quantum of action, physics has gradually been forced to relinquish its proud claim to be able to understand, in principle, the whole world.” To Pauli the only hope was an amalgam of quantum mechanics and Jung’s psychology.
Jung’s and Pauli’s was a truly unique meeting of the minds. It was, as Jung wrote, to lead both of them into “the no-man’s land between Physics and the Psychology of the Unconscious…the most fascinating yet the darkest hunting ground of our times.”