137: Jung, Pauli, and the Pursuit of a Scientific Obsession Part 2

In the evenings, instead of turning left on Theresienstra.s.se to go to the university, Pauli would turn right. The road took him to the bohemian Schwabing district teeming with cafes, bars, beer gardens, and a huge number of cheap apartments. It was like a fusion of the Latin Quarter in Paris, where debates over the latest trends in art, music, and politics took place, with Montmartre, populated by the creators of these movements who generally lived in squalid conditions. Like the avant-garde scene in Paris there were publishing houses turning out new-wave literary magazines and satiric journals. It was the locus of radical experiments in art, politics, and s.e.x. In Schwabing, anything went.

The area a.s.similated a spectrum of people. Before the war Vladimir Ilyich Lenin lived there while on the run from the tsar's secret police and schemed with a.s.sociates such as Rosa Luxemburg. Among other denizens were the writers Thomas Mann and Rainer Maria Rilke and the artists Wa.s.sily Kandinsky and Paul Klee. It was a place where up-and-coming artists aspired to achieve their first success. Among these was a young man who arrived in 1913 and made a living by selling his paintings of the area to tourists. He tried to fit into the bohemian culture, but never really did. Twenty years later Adolf Hitler, in his autobiography Mein Kampf (My Battle), recalled the "Schwabing decadents."

Despite the upheavals in Munich, in October 1918 Schwabing was an island of calm. Cafe society was still bustling. Young Pauli, newly released from home, found it irresistibly attractive. He came to drink, to meet men and women, and perhaps to think about physics, while sitting at a table with a gla.s.s of wine or a cup of coffee. He had found the rhythm of his life.

Pauli spent longer and longer in Schwabing, though he was always careful to stay sober enough to be able to spend the small hours of the night working. It soon became impossible for him to make it to Sommerfeld's morning lecture, which began at 9.00 a.m. Instead Pauli took to dropping in at noon to check the blackboard to see what the topic had been so he could work it out for himself.

Sommerfeld reprimanded him. "In order for you to become a genius I have to educate you," he told him. "You have to come at eight o'clock in the morning." Unusually in the stiff world of the German Herr Professor Doktor, he was prepared to tolerate erratic behavior if the student was undoubtedly brilliant. Touched that Sommerfeld took such personal interest in his well-being, Pauli began to turn up at 8.00 a.m., at least for a while.

Pauli was particularly gripped by Sommerfeld's course on cutting-edge atomic physics, which focused on problems that the master himself was still struggling with. Fortunately for Pauli, the seminar took place once a week for two hours-in the evening.

After cla.s.s a group of students often went to the cafe Annast, now part of the Hofgarten-Cafe, in the southernmost part of Ludwigstra.s.se, a short walk from the university's main entrance. For scientists the attraction of the Annast was its marble-topped tables, which provided excellent surfaces for scribbling equations during animated conversations. According to one story, Sommerfeld was once stuck on a particular equation. When he left the cafe he forgot to erase his attempts to solve it. The next evening he returned and found that another customer had solved it for him.

War zone in Munich.

A short three months after Pauli arrived in Munich, this idyllic world of pondering the universe came to an abrupt end. Suddenly Munich was in the grip of anarchy. The moderate Soviet Republic formed just a few months earlier had lost the support of the populace. It was not surprising. Every day Pauli would have seen people standing hungry in the streets, lining up for food in the snows of one of the worst winters on record. A host of political factions sprang up and with great speed coalesced into two groups: a moderate to extreme right-wing group and a left-wing communist one. Both sides had no trouble recruiting an army. Central Europe was swarming with thousands of armed, disgruntled, and starving soldiers looking for a fight. The situation was ominous. News traveled fast around Munich that there had been a gun fight in the Bavarian diet, and that two representatives had been killed.

For sizable periods of time the university was shut down. Cafes became cla.s.srooms for Pauli and his fellow students and teachers. They also offered front-row seats for the street fighting carried on by uniformed soldiers as well as local citizens. Sometimes it was difficult to tell one side from another. By April there was a second Soviet Republic.

But this second Soviet regime also failed to contend with the food and fuel crisis and in April 1919 total chaos descended on Munich. Having suppressed an attempted communist coup in Berlin, the federal government dispatched an army to Munich to put down the last vestiges of rebellion against it. They blockaded the city, exacerbating the already critical food and fuel shortages. The struggle boiled down to a confrontation between the Communist army of the Soviet Republic-the reds-and the army from Berlin-the whites. The Red Army had 15,000 soldiers. The whites had about 40,000 soldiers, committed to eradicate by any means the Communists who they saw as a threat to the new republic.

Even walking the streets was risky because the reds were arresting and summarily shooting anyone suspected of spreading discontent or who looked suspicious.

The backbone of the white army-the Berliners-was the Freikorps (Free Corps). This was made up of extreme right-wing fascist paramilitary units manned by combat-hardened ex-soldiers serving as mercenaries, former officers often with royal t.i.tles and students who had been too young to fight in the war and sought instant action against easy targets. They were financed privately by German industry and hated Communists. One unit of the Free Corps called itself the defender of the democratic spirit against Communists and Jews. From it emerged such staunch "defenders of democracy" as Rudolf Hess, who was to become Hitler's deputy chancellor, and Ernst Rohm soon to command Hitler's storm troopers. It was also to provide the start in life for the man who was to become Pauli's closest colleague-Werner Heisenberg.

Preceded by a heavy artillery and mortar bombardment that created enormous damage and caused numerous civilian deaths, at the end of April the white army stormed Munich. Planes flew over, dropping leaflets telling people to surrender. There was heavy street fighting and ma.s.sacres by both sides.

The fighting ended on May 8. Thousands of Red Army soldiers and civilian supporters had been killed-some estimates were as high as 20,000-in what became known as the white terror, wreaked mainly on the reds by the trigger-happy Free Corps. The white army estimated its losses at around 60. But the white terror was not yet over. People suspected of collaboration were summarily shot, stabbed, or beaten to death with rifle b.u.t.ts. Often they had been identified by spies who had infiltrated communist organizations, such as Corporal Hitler who had returned to decadent Schwabing. Munich, his favorite city, soon became the hot bed of his right-wing politics. The excesses of the Free Corps were so blatant that Lenin threatened to unleash Soviet forces on the area.

For Pauli, as for everyone, it must have been a traumatic and exciting time and also certainly dangerous. No doubt he wrote home about his experiences but sadly none of those letters remain. Perhaps Pauli's father destroyed them when he fled Vienna in 1938. Pauli, himself, may have destroyed others when he left Europe in 1940.

Pauli meets Heisenberg.

By 1920 peace had returned to the city. Pauli was now Sommerfeld's deputy a.s.sistant. Among the students whose homework he had to correct was a young man called Werner Heisenberg.

Heisenberg was destined to become one of the great names in the history of physics. Even as a boy he was immensely compet.i.tive. He was not a natural athlete but trained with great determination and became an expert skier, runner, and Ping-Pong player. Like Pauli, he breezed through his cla.s.ses at school and spent much of his time reading on his own, almost exclusively mathematics.

He had the look of "a simple farmboy with short, fair hair, clear blue eyes, and a charming expression," his friends recalled. Heisenberg first encountered atomic physics at the age of eighteen, in 1919, reading Plato's Timaeus while lying on a rooftop at the University of Munich during a break from his military duties as a member of the Free Corps, while rioting went on below him. (Five decades later Heisenberg was to recall those days as youthful fun, like "playing robbery [cops and robbers] and so on; it was nothing serious at all." Perhaps. Or perhaps not.) Heisenberg was entranced with Plato's description of atoms, visualized as geometrical solids. He knew this was now fantasy but was struck by the way in which the ancient Greek scientists were prepared to consider even the most unlikely speculations.

He had developed a keen interest in the theory of numbers and a year later entered the university. He had also tried studying Einstein's relativity theory. The reigning power in the mathematics department, Professor Ferdinand von Lindemann, convinced that Heisenberg's brush with relativity theory had spoiled his mind for a career in mathematics, rejected him outright. Sommerfeld, on the other hand, delighted with his enthusiasm and obvious brilliance, sent him straight to his graduate-level seminars, plunging him into advanced quantum physics.

Heisenberg and Pauli quickly struck up a friendship, cemented by their mutual pa.s.sion for physics-although the two young men had diametrically opposite tastes when it came to what const.i.tuted a good time. Heisenberg recalled: "While I loved the daylight and spent as much of my free time as I could mountain-walking, swimming or cooking simple meals on the sh.o.r.e of one of the Bavarian lakes, Wolfgang was a typical night bird. He preferred the town, liked to spend his evenings in some old bar or cafe, and would then work on his physics through much of the night with great concentration and success." It was often said that in Germany just after the war, in the pre-Hitler years of the Weimar Republic, there were two types of people: those who went in for night life and those who dedicated themselves to the youth movement. Pauli typified the former, Heisenberg the latter.

Whenever they were apart, they corresponded, though their letters were more like scientific articles as they bounced ideas off one another. Just as he had corrected Heisenberg's homework in Munich, so Pauli continued to comment critically on Heisenberg's ideas. "Pauli had a very strong influence on me," Heisenberg recalled. "I mean Pauli was simply a strong personality.... He was extremely critical, I don't know how frequently he told me, 'You are a complete fool,' and so on. That helped me a lot."

"When I was young I believed I was the best formalist of my time," Pauli said later in life, referring to his extraordinary understanding of mathematics and how to use it in solving problems in physics. Mathematics had served him well in his papers on relativity theory. Now Pauli was to apply his mathematical ac.u.men to another puzzle that he was determined to crack and which formed the subject matter of his PhD thesis. It related to the great Danish physicist Niels Bohr and his seminal model of the "atom as universe."

Niels Bohr and his theory of the atom.

Bohr was another scientific prodigy. He arrived in England from Copenhagen in 1911, when he was twenty-six, and became fascinated by the work of Ernest Rutherford at Manchester University. Rutherford had just unraveled the structure of the atom in a series of experiments that suggested that the atom was made up of a nucleus with a positive charge, surrounded by enough negatively charged electrons to produce an electrically neutral atom.

In other words, it was a sort of miniature solar system. But the model was unstable. Science was out of step with nature.

Bohr set out to solve this problem. He showed that electrons in an atom could not revolve in just any orbit-like planets-but that only certain orbits were allowed. Given that atoms are generally stable, their planetary electrons cannot be pulled into the nucleus. If they did then the atom would collapse. Bohr interpreted the stability of atoms as proof that there had to be a lowest orbit. He found it by altering Newton's theory of planetary motion using Planck's constant.*

In his atomic "bookkeeping" Bohr a.s.signed to each allowed orbit a whole number, which he called the "princ.i.p.al quantum number." The lowest orbit was number one. As the princ.i.p.al quantum number increased, the orbits became closer and closer. Bohr called allowed orbits "stationary states."

(a).

(a) This figure shows the hydrogen atom with its single orbital electron from Bohr's theory of the atom, where n is the princ.i.p.al quantum number tagging the electron's permitted orbits. When the electron moves from a higher to a lower orbit there is a burst of radiation, and the frequency of this emitted radiation can be measured as a spectral line. The Lyman series, Balmer series, etc. are series of spectral lines.

(b)

(b) This figure shows the Balmer series.

Since the late nineteenth century scientists had been aware that when light illuminated a collection of atoms, they emitted light in response. When the light the atoms emitted was pa.s.sed through an instrument that separated its frequencies-a spectroscope-lines appeared. Dubbed spectral lines, these lines were unequally s.p.a.ced and bunched up more and more as their frequency increased. Most strikingly the series of lines were different for each sort of atom. In fact, an atom's spectral lines were its fingerprint, its DNA. Scientists had made a stab at writing equations to describe these lines, but there was no theory of the atom to explain the equations. Bohr's was the first to succeed.

According to Bohr's theory atoms emitted light when an electron moved from an upper to a lower orbit. The light that was emitted by an electron had the same frequency as a spectral line that had been observed. An oddity of the theory was that the electron's transition from one orbit to another could not be visualized-it disappeared and appeared again like the Cheshire cat's smile. In this sense the electron's quantum jumps were discontinuous.

Bohr's was a magnificent theory and it worked more than adequately. When applied to the hydrogen atom, the difference between the spectral lines observed in the laboratory and the spectral lines deduced from his theory was only 1 percent.

Scientists were impressed not only by its accuracy but also by its iconic visual imagery: the atom as a miniscule solar system with the electrons revolving in circular orbits around a central "sun," or nucleus. It was a momentous fusion of large and small, of the universe and the atom, the macro-and microcosmos.

Bohr's theory depicted the simplest element, hydrogen, as a single electron orbiting a positive charge-its nucleus. The atom had no total electrical charge; it was electrically neutral, just as atoms are in nature. Helium, the next element in the periodic table of the chemical elements, differs from hydrogen in that it has two electrons that orbit around a nucleus that has two units of positive electric charge. Because helium does not react chemically-it cannot bond with any other element-Bohr deduced that the innermost orbit needed to be filled up with two electrons. He went on to infer that the next orbit can take on eight electrons.

Atoms depicted according to Bohr's atomic theory. (Kramers and Holst [1923]).

As another of the pioneers of atomic physics, Max Born, head of the Inst.i.tute for Atomic Physics at the University of Gottingen, put it: A remarkable and alluring result of Bohr's atomic theory is the demonstration that the atom is a small planetary system.... The thought that the laws of the macrocosmos in the small reflect the terrestrial world obviously exercises a great magic on mankind's mind; indeed its form is rooted in the superst.i.tion (which is as old as the history of thought) that the destiny of men could be read from the stars. The astrological mysticism has disappeared from science, but what remains is the endeavor toward the knowledge of the unity of the laws of the world.

Pauli's work on Bohr's theory.

No one had attempted to apply the Bohr theory to anything more complex than the hydrogen atom. Pauli set out to do so.

He began the year after he arrived in Munich and decided to apply Bohr's theory to the next simplest atomic system to the hydrogen atom, that is, two protons...o...b..ted by a single electron-the hydrogen-molecule ion, H+2. The mathematics he had to grapple with was extremely complex. The problem gnawed at him. It took over his life. He ended up thinking about it night and day.

The last thing Pauli wanted was to disprove Bohr's iconic model. But after two years of working on the problem he had to conclude that he had proved beyond doubt that Bohr's theory could not produce the necessary orbits-or "stationary states"-for a stable H+2 ion. When he applied Bohr's theory, he discovered that a small disturbance to the electron orbiting the two protons would make it fly away from them. But that couldn't be right because stable H+2 ions had already been found in the laboratory. This could only mean that there was something fundamentally wrong with Bohr's model-not at all the result Pauli had hoped for.

Pauli was deeply discouraged. But Sommerfeld praised his mathematical skill and thoroughness. Heisenberg considered Pauli's result ominous. "In some way this was the first moment when really this confidence [in Bohr's theory] was shaken," he said.

Then Pauli received an invitation from Max Born. Born had done important work in electromagnetic theory, relativity, acoustics, crystallography, and most recently atomic physics. He was highly impressed with Pauli's mathematical skills and invited him to spend six months at the inst.i.tute. Pauli accepted.

"W. Pauli is now my a.s.sistant; he is amazingly intelligent and very able. At the same time he is very human and, for a 21-year-old, normal, gay, and childlike," Born wrote to Einstein. By Pauli's own account, he was actually rather miserable. Born and Pauli applied Pauli's mathematical methods to the helium atom (He)-two electrons...o...b..ting a nucleus. But Bohr's theory failed here, too. It horrified Pauli that all his work seemed to result only in undermining this iconic theory. As far as he was concerned, it was he who had failed, not the theory. This failure loomed over him and grew into a general sense of gloom.

Despite Born's presumption of his "gaiety," he had also noted that Pauli "cannot bear life in a small city." Nor was Pauli particularly enamored of working with Born. While Born was neat and well organized, Pauli was not. Born was an early riser, Pauli far from that, especially after late nights working. Born often had to send someone to Pauli's apartment at 10:30 in the morning to awake him for his 11 o'clock lecture. Born recalled: "Although a place like Gottingen is accustomed to all kinds of strange people, Pauli's neighbors were worried to watch him sitting at his desk, rocking slowly like a praying Buddha, until the small hours of the morning."

Pauli also did not appreciate Born's overly heavy mathematical style of physics. He felt that the time was not yet ripe for such a rigorous approach. For him adroit guesswork backed up by mathematics was the best way to proceed.

Three months after his arrival in Gottingen, Pauli was offered a position as a.s.sistant to Wilhelm Lenz, professor of physics at the newly established University of Hamburg. He immediately accepted.

When Pauli had first arrived in Gottingen, Born lamented to Einstein that, "Young Pauli is very stimulating-I shall never get another a.s.sistant as good." In fact he did. Two years later Heisenberg appeared. Born wrote to Einstein, "He is easily as gifted as Pauli, but has a more pleasing personality. He also plays the piano very well." The two tried again to tackle the helium atom using other mathematical approaches to solar system models and failed. "All existing He[lium]-models are false, as is the entire atomic physics," was Heisenberg's bleak a.s.sessment.

Pauli meets Bohr.

In June 1922 Pauli returned to Gottingen to attend a Bohr-Festspiele (Bohr festival) Born had organized to launch his new Inst.i.tute for Atomic Physics. Sommerfeld, too, was there along with Heisenberg.

"A new phase of my scientific life began when I met Niels Bohr personally for the first time," Pauli later recalled. For both Pauli and Heisenberg it was hugely inspiring to meet this giant of physics.

Fifty years later Heisenberg still remembered the mesmerizing way in which Bohr presented his theory. He "chose his words much more carefully than Sommerfeld usually did. And each one of his carefully formulated sentences revealed a long chain of underlying thoughts, of philosophical reflections, hinted at but never fully expressed. I found this approach highly exciting.... We could clearly sense that he had reached his results not so much by calculation and demonstration as by intuition and inspiration, and that he found it difficult to justify his findings before Gottingen's famous school of mathematics." As physicists used to say, at Munich and Gottingen you learned to calculate, but at Bohr's center at Copenhagen you learned how to think. This was certainly the case for Heisenberg and Pauli.

One of the ways in which Bohr's original theory had been developed was to allow electrons to move in three dimensions, transforming the orbits into sh.e.l.ls. In his lecture he described his latest work, which concerned how the electrons in an atom distributed themselves. The essence of the problem was the way in which atoms were built up, beginning with the hydrogen atom with its single electron. Understanding this would be a first step to explaining why the periodic table of chemical elements fell into place as it did, a key problem that everyone recognized needed to be cracked.

Examining the experimental data, Bohr proposed that there were two electrons in the first sh.e.l.l, eight in the second, and so on. He was then able to deduce these numbers from a series, each of which could be obtained from the formula 2n2, where n is the princ.i.p.al quantum number for the sh.e.l.l (in Bohr's original model, n was the princ.i.p.al quantum number for an orbit, but orbits had now been replaced by sh.e.l.ls). If n is 1 then the total number of electrons in the first sh.e.l.l is 2; if n is 2, the number of electrons in the second sh.e.l.l is 8; the next sh.e.l.l becomes 18, and so on. The a.s.sembled scientists discussed this series of numbers with great intensity. But as they listened, both Heisenberg and Pauli realized that there was no basis in fact to what Bohr referred to as the "building up principle." As for Sommerfeld, he dismissed Bohr's reasoning as "somewhat Kabbalistic."

Bohr's reasoning also failed to answer the problem of why every electron did not simply drop into the lowest sh.e.l.l-at least for atoms other than hydrogen and helium.

Pauli and Heisenberg argued fiercely with Bohr, who was impressed with their knowledge of physics and their uninhibited critical give-and-take. Bohr was also impressed with Pauli's work on the H+2 ion and the helium atom, although in each case he had come up with a result that seemed to disprove Bohr's own theory. Discussions continued into the evening in coffeehouses and on walks. Heisenberg complained that no one went to bed before 1 a.m. Pauli, of course, was in his element.

After the meeting, Bohr invited Pauli to visit Copenhagen for a year, from September 1922, to help in his research. Pauli replied rather arrogantly, "I hardly think that the scientific demands which you will make on me will cause me any difficulty, but the learning of a foreign language like Danish far exceeds my abilities." He accepted nonetheless.

In Copenhagen Bohr set a problem that was to haunt Pauli for years and was one of the factors that led to his breakdown. The problem was on the anomalous Zeeman effect. To understand it, we have to go back to Pauli's old mentor at Munich, Arnold Sommerfeld, and his work on the structure of spectral lines.

The discovery of 137.

According to Bohr's theory, when an electron drops from a higher to a lower orbit it emits light, which is recorded in the laboratory as a spectral line. Bohr was able to work out equations for these spectral lines that could be compared with the data obtained in the laboratory.

By 1915 scientists had more accurate spectroscopes that enabled them to make closer inspection of spectral lines. This revealed that many of the individual lines were in turn made up of several more closely s.p.a.ced lines: they were said to have a "fine structure." Certain spectral lines also split into several lines or "multiplets" when the atom was placed near a magnet, but the fine structure was always there. "It was given by Nature herself without our agency," Sommerfeld wrote.

Sommerfeld's primary contribution to atomic physics was his work on the fine structure problem. His brainwave was to apply relativity theory to Bohr's theory, changing the ma.s.s of the electron following Einstein's famous equation E = mc2. The result was astounding: an extra term appeared in Bohr's equation for a single spectral line. This extra term made it possible to predict that certain lines would actually split and reveal their fine structure.

Sommerfeld called the quant.i.ty that set the distance between the split spectral lines in this extra term the "fine structure constant" and designated it with the Greek letter (alpha). His equation was: The fine structure constant is made of three fundamental constants: the charge of the electron e (1.60 10-19 coulombs-a coulomb is the unit of electric charge); the speed of light c (3 108 meters/second), which defines relativity theory; Planck's constant h (6.63 10-34 Joule-seconds), which defines quantum theory and determines the size of the grains into which the microscopic world is part.i.tioned, be it grains of energy, ma.s.s, or even of s.p.a.ce itself. (pi) is the ratio of the circ.u.mference of a circle to its diameter (3.141529). The constants e, c, and h had already been measured. Thus the discovery of the fine structure constant was a step toward the great goal of finding a theory that would unite the domains of relativity and quantum theory, the large and the small, the macrocosm and the microcosm.

There was one extraordinary feature of the fine structure constant. The three fundamental constants that make it up have dimensions-such as s.p.a.ce and time-and therefore depend on the units in which they are measured, whether metric, imperial, or some other. So although they would certainly play an essential part in a relativity or quantum theory formulated by physicists on a planet in another galaxy, they might not have precisely the same values as they have on earth.

But when they come together to form the fine structure constant, something extraordinary happens. All of their units cancel out and as a result the fine structure constant is a pure number without any dimensions. No matter what the number system this will always be true. Sommerfeld calculated it as 0.00729-a rather unexciting way of expressing such a momentous result.

Sommerfeld's extension of relativity into atomic physics was "a revelation," wrote Einstein. Bohr wrote to Sommerfeld, "I do not believe ever to have read anything with more joy than your beautiful work."

A dimensionless number of such fundamental importance had never before appeared in physics. Of course dimensionless numbers had always been present in equations, but never one that was deduced from fundamental constants of nature. Scientists later realized that if the numerical value of the fine structure constant were to differ by a mere 4 percent, almost all carbon and oxygen would be destroyed in every star in the universe and life on our planet would not exist or would be dramatically different. The fine structure constant was one of the primal numbers that bound all existence together.

One of the many puzzles that arose was the question of why spectral lines of atoms split when they were placed in a magnetic field, between the pole faces of a magnet. Back in the mid-nineteenth century the British scientist Michael Faraday had identified the phenomenon but his equipment was not yet precise enough to enable him to pursue it.

In 1896 Pieter Zeeman, a young Dutch researcher at the University of Leiden, was looking for a research problem. Going through physics journals from decades earlier, Zeeman came upon Faraday's ruminations over the behavior of atoms in magnetic fields. With the more precise equipment at his disposal, he succeeded in discovering the additional split spectral lines caused by a magnetic field. This was dubbed the Zeeman effect.

Two years later all was not well again. When Zeeman tried using a weaker magnetic field, he found that the spectral lines split into different patterns of even more lines-multiplets. This peculiar situation became known as the "anomalous Zeeman effect."

The puzzle that Bohr set to Pauli was to find an equation that described this behavior. The effect existed; it had been identified. Therefore it must be possible to deduce an equation from Bohr's iconic theory of the way atoms worked-electrons revolving like planets in small solar systems. Despite its shortcomings Bohr's theory offered the only means to deal with problems of atomic physics. Perhaps it could be modified to suit the one at hand.

Day and night Pauli thought about it. He calculated and calculated, he tried this approach and that approach, and eventually he fell into a fit of despair. Everything had been going so well. The boy genius's triumphant entry into Munich had been heralded by an important paper on relativity theory and two more quickly followed. Even Einstein had been impressed. But ever since it had been nothing but one failure after another: "A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, 'You look very unhappy,' whereupon I answered angrily, 'How can one look happy when he is thinking about the anomalous Zeeman effect?'"

There had to be a way. But how?

The Philosopher's Stone.

Jung's a.n.a.lytical psychology: The four function types.

MEANWHILE, in Zurich, Carl Jung was establishing a vocabulary and framework for his budding new field of a.n.a.lytical psychology. In 1921 he published his seminal book on the subject, Psychological Types.

In this he argued, based on his vast experience with patients, that there were two opposing modes of being that determined and limited a person's reaction to the world and to himself-introversion and extraversion. In Jung's initial definition, introversion is a turning inward from an object, while extraversion is the reverse. Jung was the first to coin these two terms, which have since become common currency. He then broke these two categories down further and proposed four basic functions or function-types: thinking, feeling, sensation, and intuition. He was intrigued that there appeared to be four function types rather than three or some other number. But for the moment he set the problem aside.

Jung defined what he called the four orienting functions of consciousness thus: thinking leads to logical conclusions; feeling is a means to establish a subjective criterion of acceptance or rejection; sensation directs one's attention outside oneself and is caused by conscious perception through the sense organs. As for intuition, it is somewhat like sensation but there is no cause for directing one's attention. Rather, there is a hunch, an inspiration, or gut feeling. Conclusions surface not by logical means but as if bursting out of nowhere, such as in suddenly realizing how to solve a problem when you are not consciously thinking about it.

The two opposing modes of being and four function types.

Jung then divided these four functions into two groups of two: thinking and feeling, which are to do with rationality and logic; and intuition and sensation, which he cla.s.sified as irrational, outside of reason. Besides his clinical experience, Jung drew upon his knowledge of Eastern and Western religions and of myths, philosophy, and literature to support his theory of types. In particular, he drew on the notion of pairs of opposites such as evil/good, darkness/light, matter/spirit, which he saw as emerging from deepest history-before Christianity, the Hebrews, the Egyptians, and the Chinese-and providing the energy for creativity and for life itself.

The extent to which these four functions predominate in an individual, Jung argued, gives each person a mode of being. Specifically, thinking types direct their mental energy toward thought at the expense of feeling, which disturbs the flow of logic; feeling types are governed by their feelings. Similarly, to understand a situation with one's senses-by sensation-requires concentration and focus, whereas trying to intuit a situation requires taking in its totality and flitting around it. These are opposites because no one can do both at once.

When one function is particularly dominant, the opposite one may lapse into the unconscious and return to its earlier archaic state. The energy generated by this inferior function drains into the conscious and produces fantasies, sometimes creating neuroses. One goal of Jungian psychology is to retrieve and develop these inferior functions. Jung was careful to point out that no one is strictly a thinking or feeling type. We are all combinations of the two types and the four functions. Our personality, or psychology, results from a struggle among these opposites for equilibrium.

At this time Jung had also begun to study the Gnostic writers, spurred on by his interest in myths. He was aware that Freud had derived his influential myth of the primal father and its effect on the superego from the Gnostic motifs of s.e.xuality and Yahweh, which dated back to ancient Egypt and early Judaism. The Gnostics speculated that the content and images of the primal world of the unconscious might be clues to uncovering the mysteries of the universe. But at first Jung could find little relevance in their writings, nor could he find any historical bridge between Gnosticism and the contemporary world.

And still he dreamed. What could these images mean? Where did they come from?

Among the most vivid of his dreams were two in which he found himself in a huge manor house. In one he wanders from room to room and eventually ends up in a s.p.a.cious library full of books from the sixteenth and seventeenth centuries. The engravings on the books are unfamiliar and the ill.u.s.trations include curious symbols. In the second he is in a horse-drawn coach that enters a courtyard. Then the gates slam shut and a coachman screams that they are trapped in the seventeenth century. His efforts to explain this dream sent him delving into books on history, religion, and philosophy, particularly of that period.

Meanwhile, he was shaping his own method of treating neuroses. Freud interpreted a boy's incestuous desires for his mother as a literal return to the womb, to a state free from responsibility and decisions. Jung preferred to see the positive side, as breaking down the bond between mother and son and thus freeing psychic energy to be transferred to other archetypal components. In this way he removed the purely s.e.xual connotation of incest, choosing rather to explore it in terms of archetypal metaphors and symbols. By now Zurich had become the center for this developing technique of a.n.a.lysis, Jung's "a.n.a.lytical psychology."

Alchemy.

Back in 1914, Jung had come across a book by Viennese psychologist Herbert Silberer, who was part of Freud's circle. In Problems of Mysticism and Its Symbolism, Silberer discussed whether there might be a relationship between the imagery in alchemical texts, the imagery experienced by patients in the mental state between dreaming and waking, and Freud's a.n.a.lysis of dreams. At first Jung was fascinated and corresponded with him. He was looking for something deeper than Silberer-to understand the imagery that had never been conscious, the imagery in the deep or collective unconscious. But he soon concluded that alchemy was "off the beaten track and rather silly."

Nevertheless Jung began collecting ancient alchemical texts. Then, in 1928, his friend Richard Wilhelm sent him a copy of his translation of the thousand-year-old Taoist-alchemical text The Secret of the Golden Flower.

At first The Secret of the Golden Flower did not seem to make any sense. But Jung was intrigued. Silberer's book came to mind and he suddenly realized that although he had appreciated what Silberer was suggesting, he had not understood how to interpret the alchemical texts Silberer used. For the next two years Jung pored over alchemical texts and began to find more and more pa.s.sages that he could understand. Then he had a revelation. "I realized that alchemists were talking in symbols-those old acquaintances of mine," he wrote. It was the symbols not the text that were the essence. He decided to learn alchemy from the ground up and then return to Silberer's and Wilhelm's books.

Alchemy was conceived of as a means toward understanding the "great chain of being"-in other words, all life-stretching from our "corruptible world" to heaven. There were two sorts of alchemist. Scientific alchemists, the forerunners of modern chemists and metallurgists, searched for ways to trans.m.u.te base metals into gold and jealously guarded their recipes. The mystical school of alchemy, however, interpreted trans.m.u.tation as a spiritual path to redemption. They considered their laboratory experiments to be part of an inner process of maturing while nurturing a contemplative att.i.tude. Alchemy embraced the teachings of the Greek philosopher Proclus as well as mystery religions such as Zoroastrianism and the ancient cults of Isis, Mitre, Cybel, and Sol Invictus.

Alchemists postulated that everything, even metals, was made up of the four elements-earth, water, air, and fire-and that these four elements could be transformed one into another. They called this process of transformation the "circle" or the "rotation of the elements." The goal of alchemy was to bring about a union of all four elements to produce the mystical fifth element-the quintessence, or the legendary "philosopher's stone," the ultimate state of enlightenment. In alchemical books the four elements were represented by the four sides of a square. The philosopher's stone-referred to as the one, the perfection, and imbued with the power both to trans.m.u.te base metals to gold and to transform man into the illumined philosopher-is represented by a circle. It is the light hidden in dark matter; it combines creative divine wisdom and creative power. Christians sometimes identified it with Christ, while Buddhists symbolized it as the jewel in the lotus.

The first step in creating the philosopher's stone was to obtain the prima materia, the basic material from which all metals are derived, "philosophical mercury"-Mercurius, known also by his Greek name, Hermes, symbolizing the universal agent of transformation as opposed to the vulgar physical mercury of the scientific alchemists. Mercurius is present throughout the process of transformation from its dark beginnings (as prima materia) to its triumphant end (as the philosopher's stone). In this way Mercurius partic.i.p.ates in both the dark and light worlds.

Prima materia, in its turn, comes out of the union of male-sulphur (the hot, dry, active principle)-and female-argent-vive, or mercury (the cold, moist, receptive principle). In alchemical philosophy this union symbolized the wedding of man and woman, the coniunctio of King Sol and Queen Luna (sulphur and argent-vive). Sol (the Sun) is the male force of the universe, creative will. Luna (the Moon) represents the receptive female force, wisdom. The material world is generated out of sulphur (fire and air) and argent-vive (earth and water), that is, out of the four elements. Thus the conjunction of all these gives rise to the world of mysticism.