137: Jung, Pauli, and the Pursuit of a Scientific Obsession Part 3

Alchemy and psychology.

As he read more and more deeply in alchemical works, Jung realized that he had discovered the "historical counterpart of [his] psychology of the unconscious." Alchemy provided an unbroken historical link between the ancient Gnostics of first-century B.C. and the contemporary world. Its roots went back through Gnostic writings to Plato, Pythagoras, texts attributed to the magus Hermes Trismegistus of ancient Egypt (referred to as Moses in the Kabbalah), and ancient creation myths such as the Enuma Elish from seventh-century-B.C. Babylonia.

The Hermetic view was that after the fall humankind had divided into two states, the male and the female. The alchemical wedding returns man to the original Adamic state-to Adam-thus reconciling opposing forces and creating the highest wisdom, which is the philosopher's stone. The alchemical wedding releases the world-soul-the soul of the whole world-which had lain dormant until this reconciliation and which unites the souls of individuals and also of the planets, which are living ent.i.ties and not merely matter.

Thus Jung finally understood the meaning of his two dreams about being trapped in the seventeenth century, the period when alchemy was at its height. Hereafter primordial dream images, which he saw as visual symbols of archetypes, began to play a central role in Jung's a.n.a.lytical method, along with ancient myths and religion.

Jung's a.s.sociates warned him that he might be considered a charlatan if he dabbled in alchemy. If a scholar of Wilhelm's standing could publish a book on alchemy, Jung replied, then so could he. Furthermore, he was convinced that alchemical imagery and notions of transformation could provide another approach to understanding the psyche.

So Jung set to work to incorporate alchemy into his a.n.a.lytical psychology. One of his patients, Aniela Jaffe, later to become his personal secretary and collaborator, recalled a particularly startling yet productive a.n.a.lytic session. She was describing her problems with her mother when Jung abruptly cut her off with the words, "Don't waste your time." He went to his bookcase and took down the Mutus Liber, an alchemical book from the seventeenth century that contained only images, no text, and they spent the rest of the session discussing the images. Looking back on this and similar sessions in later years, she recorded that they had a more lasting influence on her than any of those spent in conventional therapy.

Thus by incorporating alchemy into his a.n.a.lytic psychology, Jung began to evolve a dramatic new way to understand the unconscious.

Dr. Jekyll and Mr. Hyde.

The pesky anomalous Zeeman effect.

IN THE AUTUMN of 1923 Pauli left Copenhagen to go back to Hamburg. He had still made no progress with the anomalous Zeeman effect. The problem, to recap, was to find the correct equation to describe the spectral lines of an atom placed in a weak magnetic field. He worried at it like a dog with a bone. But no matter how hard he tried, he just couldn't crack it.

Pauli was growing more and more despondent. He had become friendly with Bohr's a.s.sistant, Hendrik Kramers, who promised to visit him in Hamburg to cheer him up. Then Bohr decided that Kramers must go to England with him. Pauli wrote telling Bohr how deeply offended he was by this decision and how much he had looked forward to seeing his friend, whose presence "would mean a great deal for me psychically." "I feel myself so unwell," he added. He had just returned and already he was writing to Bohr about how unhappy he was. His letter was in effect a cry for help.

Not long after he had settled back in Hamburg he gave his inaugural lecture. His subject was the periodic table of chemical elements, but his heart was not in it. He was all too aware that the most basic problem in understanding it had yet to be resolved: what was the reason that the sh.e.l.ls of electrons in each atom filled in the way they did? He had a hunch that it was related in some way to the multiplets in the anomalous Zeeman effect. Surely it was all tied together. After all, the way in which the sh.e.l.ls filled up with electrons determined the numbers of spectral lines.

In struggling to find a mathematical description for the effect, he began by reworking equations from the normal Zeeman effect-where Bohr's theory produced equations that agreed reasonably closely with the spectral lines that had been observed. Pauli's goal was to apply the new equations to the anomalous Zeeman effect. Sommerfeld had already made some progress along these lines.

To study the anomalous Zeeman effect, physicists focused on alkali atoms-primarily sodium, pota.s.sium, and cesium-which displayed behavior similar to the hydrogen atom for which Bohr's theory seemed to work. Like the hydrogen atom, alkali atoms have only one electron in their outer sh.e.l.l and this is the only electron that can bond with other chemical elements. The other electrons are in the inner sh.e.l.ls, which have already been filled and thus cannot react.

Sommerfeld set Heisenberg, who was just nineteen, to work on the problem. Since the Bohr theory now dealt with an electron in an atom moving on a three-dimensional sh.e.l.l, in addition to a princ.i.p.al quantum number each electron had two more a.s.sociated with it. Locating an object in a room requires three numbers, two to give its location from the walls and the third its height from the floor. An electron can be located in an atom in a similar way, with three numbers identifying its position within the Bohr atom relative to the nucleus. These are taken to be whole numbers and are called quantum numbers.

Sommerfeld supplied Heisenberg with the newest data as well as his own unpublished research, including speculation on new ways to combine the three quantum numbers at the very basis of Bohr's theory of the atom. "All right, you have an interest in mathematics; it may be that you know something; it may be that you know nothing.... We will see what you can do," he said. Heisenberg quickly came up with his own ideas on how to tackle the anomalous Zeeman effect. He rewrote one of Sommerfeld's equations using half figures-1/2, 3/2, and so on-and discovered he could produce an equation that described most of the observed multiplets.

Then he turned to Bohr's model of the atom-with the nucleus as a rigid core surrounded by filled sh.e.l.ls of electrons, the whole thing spinning like a ball. Heisenberg made the audacious a.s.sumption that the core and the surrounding electron shared a half unit of angular momentum by means of an interaction that he left unspecified. (An object moving in a line has linear momentum [ma.s.s times velocity]. Similarly an object spinning like a top has angular momentum [which is related to ma.s.s times angular velocity].) The mysterious interaction between the core and the lone electron could be the explanation for the anomalous Zeeman effect. Sommerfeld was stunned, as was Pauli. Surely this would result in an atom emitting a half quanta of energy. But that had to be wrong because quanta were a.s.sumed to be indivisible. This was a basic postulate of the quantum theory. All the same, Heisenberg's equation produced multiplets for the alkalis which precisely duplicated data from experiments. "Success sanctifies the means," Heisenberg wrote to Pauli.

Sommerfeld was astonished that this novice dared take such a dramatically different approach to problems with which experienced scientists had struggled. Instead of getting tied up in endless complicated calculations, Heisenberg came up with instant solutions. Eventually Sommerfeld had to give in and accepted that there had to be half quantum numbers. After all, he reasoned, cla.s.sical physics was frequently proved wrong. Why not atomic physics, too?

Bohr, however, insisted that while breakdowns in cla.s.sical physics were fine, it was not acceptable when it came to his own theory of the atom. At the Bohr-Festspiele in Gottingen, he had discussed Heisenberg's new approach and referred to it as "very interesting," by which he meant that it was almost certainly wrong. Although it happened to fit existing data, Bohr argued, it was not an end in itself. Bohr was more interested in unraveling a problem than in instant solutions.

Bohr now suggested that there might be a force that linked the core and the lone outer electron in an alkali atom and that this force might distort the core in two different ways, giving rise to a "double-valuedness," which he, too, was willing to include as a half quantum number. Thus Bohr was able to reproduce the required multiplets, while avoiding the other half quantum numbers that were essential to Heisenberg's model. But what was this strange force? Pauli couldn't accept it and argued tooth and nail with Bohr. He continued to torture himself over the problem of the anomalous Zeeman effect but could make no sense of it. Bohr insisted that Pauli publish his own contribution to these mathematical models and he did so "with a tear in my eye," as he wrote to Sommerfeld. As for Heisenberg's theory of the anomalous Zeeman effect, Pauli found it "unsightly" and "monstrous." "I am deeply insulted by it," he wrote to Bohr.

Ten days later Pauli wrote to Bohr again, offering his own deeply critical a.s.sessment of the situation: "The atomic physicists in Germany can now be divided into two cla.s.ses. Some work out a given problem first with half quantum numbers, and if it doesn't agree with experiment, they do it again with integral ones. The others calculate first with integral values, and if it doesn't work, do it again with halves." In other words, they had all been reduced to desperate measures.

As far as he was concerned the problem of the anomalous Zeeman effect was far from solved. He was becoming convinced that "there is no [satisfactory] model for the anomalous Zeeman effect and that we have to create something fundamentally new."

But he had no idea what this might be. The whole farrago was getting him down. "I myself have no taste at all for this sort of theoretical physics," he wrote to Bohr, and wanted to withdraw from it. Atomic physics had all become "too difficult."

Dr. Jekyll and Mr. Hyde.

Physics was Pauli's heart and soul. His physics research gave definition to his life and his fruitless attempts to solve the anomalous Zeeman effect, on top of what he regarded as his lack of success with the hydrogen-molecule ion and helium atom, began to take a heavy toll on his already fragile psyche. His early successes-his maiden papers on relativity theory-suddenly seemed in the distant past. He began drinking more and more heavily. "I have noticed that wine agrees very well with me," he wrote to a friend. "After the second bottle of wine or champagne I usually adopt the manners of a good companion (which I never have in the sober state) and then may under these circ.u.mstances enormously impress the surroundings, particularly if they are women."

By day he behaved like a staid Germanic professor. By night he roamed the Sankt Pauli, Hamburg's notorious red-light district full of risque cabarets and bars catering largely to a rough clientele. He described his life to a friend: "During the day, calming work, in the night, s.e.xual excitement in the underworld-without feeling, without love, indeed without humanity." Much later, writing to Jung, he recalled "the complete split between my day life and my night life in my relations with women." He seemed to have split into Dr. Jekyll and Mr. Hyde. Robert Louis Stevenson's celebrated novel had been published some forty years earlier. No doubt Pauli had read the story of the scientist who is taken over and destroyed by his darker impulses. Perhaps he saw a parallel between Dr. Jekyll and his own increasingly erratic behavior.

Hamburg was a vibrant city that welcomed all comers and in which one could savor the steamy side of postwar Germany. Munich banned the American cabaret performer Josephine Baker, who was famous for her nude dancing; Hamburg welcomed her with open arms.

The real action was on the side streets off the main Sankt Pauli avenue, particularly on a street called Grosse Freiheit. Even during the day it was difficult to see inside the bars there. The odor of spilled beer and the sticky unmopped floors made the interiors stifling. When Pauli walked in in his fine suit and went to the bar, no doubt in the early days at least conversation would grind to a halt and everyone would stare until he had finished his drink and left. But he soon became a regular. To make things worse, the more he drank, the more obnoxious he became.

Often he ended up getting beaten in a brawl. Once he was eating in one of his favorite restaurants in the area. A row broke out and Pauli found himself right in the middle of it. He only pulled himself together when someone threatened to throw him out of a second-floor window. Afterward, he said, he could not understand how he had gotten into such a situation.

He began to feel as if he were losing control. He was frightened of the person he was becoming. "[I] tended toward being a criminal, a thug (which could have degenerated into my becoming a murderer)," he later recalled. By day, immersed in his research, he felt "detached from the world-a totally unintellectual hermit with outbursts of ecstasy and visions." His two parallel worlds were in danger of colliding with potentially fatal effect.

The women Pauli found in the bars there offered a way to forget his growing frustration and anger. Typical of his Sankt Pauli girlfriends was a beautiful blond woman some two years younger than he. They had a short and pa.s.sionate affair that Pauli broke off when he discovered she was a morphine addict. Then one day she turned up at his office at the university. Somehow she had found him, despite his secrecy and desperate attempts to keep his night and day lives separate. Pauli was horrified. Poor, sick, and stick thin from her continuing morphine abuse, she stood like a specter, begging him for help. Pauli threw her out, and told her never to come back-and she disappeared back into the Sankt Pauli. He forgot about her, hoping she was gone forever. Little did he guess that in later years she would come back to haunt him.

Pauli always kept his visits to the Sankt Pauli secret, even from his closest friends and colleagues. These included the always upbeat Otto Stern, Emil Artin, Walter Baade, and Gregor Wentzel. Wilhelm Lenz, director of the Inst.i.tute for Theoretical Physics, joined them from time to time, particularly for departmental lunches, which were always held in top restaurants scouted out by Stern. Like Pauli they were all bachelors.

Lenz was a man of some means who lived in a fashionable area of Hamburg at 18 Armgartstra.s.se, on a beautiful ca.n.a.l with gra.s.sy banks and the city's largest lake, the Aussenalster, glittering in the distance. When Pauli first arrived Lenz offered him a room in his house. Pauli later moved around the corner to 16 Papenhude, where he had an apartment on the second floor. Miraculously the area escaped damage in World War II and remains today much as it was then. Lenz was noted for his reserve.

Otto Stern, an unusually gifted experimental physicist, was another recent addition to Hamburg. Like Lenz, Stern was a rather wealthy man. But unlike Lenz he was outgoing-a bon vivant who sometimes flew to Vienna just for lunch. Artin was a mathematician who specialized in number theory, Baade an astronomer, and Wentzel a physicist. These last three were Pauli's exact contemporaries.

Wentzel was Pauli's closest friend. Not only did their research interests overlap but so did their idea of a good time. Wentzel frequently went to Paris on the slightest pretext. On one occasion he sent Pauli two of his papers to comment on and signed the letter giving his address simply as "Paris." Pauli swiftly replied, "The question is this, whether indicating Paris at the end of your work suffices at least to justify all this psychologically and whether in the corrections you should not change it more specifically into Paris, Moulin-Rouge, or something a.n.a.logous."

Pauli enjoyed visiting Baade and the astronomers at their observatory in Bergedorf. On full-moon nights it was impossible to observe the stars and they would have a party instead. On one occasion Pauli was present at the observatory when it was discovered that a terrible accident had befallen the great refractor telescope. It was almost destroyed. Naturally everyone chalked it up to the Pauli effect.

Cases of the dreaded Pauli effect were beginning to pile up. Physicists at the university became convinced that Pauli's presence in or even near a laboratory led to severe breakdowns in the equipment. Stern was reduced to desperate measures. He recalled that the only way he could protect his laboratory from the Pauli effect was that Pauli "was not allowed to enter." The Hamburg scientists were surprisingly superst.i.tious. One brought a flower and gave it to his apparatus every day. Stern kept a hammer lying next to his as a veiled threat to it not to break down. Pauli himself fervently believed in the Pauli effect and began to wonder whether he emanated powers.

Pauli's exclusion principle: Four quantum numbers instead of three.

Pauli had given up trying to solve the anomalous Zeeman effect, but he kept up with the flood of papers that poured out on the subject. Then in autumn 1924 two ideas suddenly came together for him.

The first was this: Suppose relativity had something to contribute on the subject. Pauli looked into it. He found that in the models of the atom proposed by Bohr and Heisenberg, electrons within the core moved at speeds comparable to that of light. They should therefore be expected to display variations in ma.s.s consistent with Einstein's equation E = mc2. These variations should show up in the s.p.a.cing between the multiplets, but experiments had not revealed any such effect and could mean only one thing: the core in these models had to be inert; it did not interact and so played no role at all. In other words, every model of the atom that featured a core was wrong.

Then he came across a paper by Edmund Stoner, a twenty-five-year-old physicist at Leeds University. Stoner went far beyond the anomalous Zeeman effect, although he himself had not realized the full significance of what he had found. It had to do with the problem constantly on Pauli's mind: What stopped every electron in an atom from falling into the atom's lowest energy level-its ground state?

By clever manipulation of the three quantum numbers for an electron in an atom, Stoner had succeeded in calculating the total number of multiplets of an alkali atom undergoing the anomalous Zeeman effect (that is, when it is placed within a weak magnetic field). He did this, as Heisenberg and Bohr had, by imagining the alkali atom to be made up of a closed core-made of sh.e.l.ls filled to their maximum with electrons and so inactive chemically-with a single lone electron revolving around it. From this he was able to show that the total number of electrons in each closed sh.e.l.l was related to twice the total amount of angular momentum of the closed core with the lone electron.

What struck Pauli was the appearance of the number two. Bohr had inserted this number into his model of the core simply so that only halves would appear in formulas for the anomalous Zeeman effect. In other words, when the atom was in a magnetic field, the core containing the closed sh.e.l.ls full of electrons could be distorted in two ways, which would give one of its quantum numbers a value of plus or minus a half.

But Pauli had established that the core was inert and that only the lone electron played any role in the chemical activity of an alkali atom. So why not transfer the two possible values of the core to this electron? Pauli began to suspect that Stoner's work contained the seeds of something new and exciting. He decided to see what would happen if he extended Stoner's method of manipulating quantum numbers to include a fourth quantum number that had the values of plus and minus a half for the lone electron. The result was astounding. He figured out that the total number of electrons in each closed sh.e.l.l was twice the princ.i.p.al quantum number of that sh.e.l.l squared. It was 2n2, the same number that Bohr had proposed with no basis from his theory of the atom. Now there was one.

Pauli went yet further, proposing that the two possible values for the fourth quantum number be a.s.signed to every electron in every atom, regardless of whether the atom was in a magnetic field.

The conclusion had to be that each electron in an atom required four not three quantum numbers, and, to explain the periodic table of chemical elements, that no two electrons in an atom could have the same four quantum numbers. Basically, two electrons with the same quantum numbers cannot occupy the same sh.e.l.l. (This is Pauli's famous exclusion principle. The name was given it by Paul Dirac, a physicist at Cambridge University.) This was the reason why Bohr's building-up principle for atoms worked-why there are precisely two electrons in the inner sh.e.l.l, eight in the next, then eighteen, and so on. This was also why every electron in an atom did not fall into its lowest stationary state. They were prohibited from doing so.

To get a grip on this complicated concept, imagine that an atom is an apartment building with many rooms on many different floors and no elevators. In fact, it is an upside-down pyramid with two rooms at the bottom, eight on the second floor, eighteen on the third, and so on. To avoid overcrowding, the local housing authority pa.s.ses a law that only one electron can occupy a room. A crowd of electrons enters the building and jostles around, trying to occupy as low a floor as possible. No electron wants to be the only one on a floor-the lone electron, as in an alkali atom. Such an electron cannot relax because on its shoulders rests the chemical activity for the entire atom. This is a very simplified description of the way that Pauli's exclusion principle works.

Pauli's paper on the exclusion principle contained none of the mathematical fireworks for which he had become famous. Rather, it was the fruit of his patient examination of data. By searching out patterns among numbers, he came up with what scientists call a restrictive or prohibitive principle. Another example is the principle of relativity, which a.s.serts that the laws of physics must be the same in every laboratory, regardless of its motion. There is no reason for this to be so. Yet it must be, to formulate a systematic theory of how objects from the size of basketb.a.l.l.s to planets move. It also enables scientists to predict numerous phenomena, such as the bending of starlight by ma.s.sive objects, a prediction of relativity theory that was later proved to be true in real life. There is no way of deriving the principle of relativity mathematically. It is simply an axiom.

But what about the exclusion principle? Could it be derived? Pauli was not sure, nor was anyone else.

Hard though it was to understand its deeper meaning, scientists quickly realized the exclusion principle's importance in explaining the periodic table of chemical elements and thus, also, atomic structure. It also helped clarify why metals are hard and what the fate of stars might be. Pauli had made a discovery that would shape the path of physics in the future and change our understanding of the cosmos.

The search for the meaning of the exclusion principle.

Pauli immediately notified Bohr and Heisenberg of his discovery and sent them the draft ma.n.u.script of his paper. It was, he wrote them firmly, at the very least "not a bigger nonsense" than the schemes other scientists proposed for understanding the structure of the atom. At least Pauli had avoided hypotheses with no basis such as Bohr's force of unknown origin, which distorted a core in two different ways. He suspected that his exclusion principle could not be derived from Bohr's theory of the atom. Understanding it lay rather, he suggested, in the as-yet-unknown properties of "motion and force in quantum theory." Remembering his many attempts to support Bohr's theory-the hydrogen-molecule ion, the helium atom, and the core models of atomic structure-all of which ended in failure, he wrote that he would prefer to interpret the exclusion principle free of any model of the atom, especially a model containing the concept of electron orbits. He was sure that the key factors in describing the characteristics of an electron had to be its energy and momentum. Those were real because they were measurable; electron orbits and sh.e.l.ls were not. In this Pauli was true to his G.o.dfather Ernst Mach's philosophy-to avoid any unmeasurable concepts in a theory of physics, for those were purely metaphysical.

Heisenberg and Bohr were amused by Pauli's exclusion principle. Here was proof, Heisenberg wrote to Pauli, that Pauli was entering the "land of the formalist philistines," practicing a style of physics "of which you had insulted me. [In fact, you] had broken all hitherto existing records [in rising] to an unimagined, giddy height (by introducing individual electrons with 4 degrees of freedom)." Everyone knew that electrons had to move in three-dimensional s.p.a.ce like everything else in the universe, and therefore three quantum numbers should surely suffice. Pauli had frequently accused Bohr and Heisenberg of coming up with "swindles." Now Heisenberg accused Pauli of coming up with a swindle of his own; "swindle x swindle does not yield something correct," he wrote.

A week later, Bohr had clearly thought more seriously about Pauli's new theory. He wrote to him, "I have the impression that we stand at a decisive turning point, now that the extent of the whole swindle has been so exhaustively characterized." What struck him about Pauli's proposal, he said, was its "complete insanity." Bohr always condemned new proposals with the words "interesting but not crazy enough." Saying that Pauli's was completely insane meant he thought it was most probably right.

Pauli had still not solved the anomalous Zeeman effect, but he had accomplished something far more important. He suspected that the full significance of the exclusion principle would not become clear until there was a deeper understanding of quantum theory. "I will wait patiently; and be satisfied if I live to see the solution," he wrote to Bohr. He hoped his "insane idea" would help toward understanding the structure of atoms made up of many electrons. If it did, "I would be the happiest man on earth."

The fourth quantum number.

The problem people had with understanding the exclusion principle was the lack of a visual model for the fourth quantum number. Pauli was well aware that it was essential for physicists to be able to visualize a theory-which was what made Bohr's image of an atom as a miniscule solar system so pleasing. Nevertheless, he wrote to Bohr, although this need for visual images was "in part legitimate and healthy, it should never count as an argument for retaining systems of concepts. Once the systems of concepts are settled, then will visualizability be regained." In effect, Pauli was suggesting strongly to Bohr that he should drop all visual images from his theory because they had proved to be incorrect and misleading. It was only once a new theory of atomic physics had emerged that it would be possible to develop a visual language to describe the atomic world.

Then Ralph Kronig, a twenty-year-old German American, noticed something Pauli had overlooked. The fourth quantum number of an electron has the mathematical properties of angular momentum, the momentum of an object moving in a circle. Every electron has an angular momentum from its...o...b..t around the nucleus of the atom, like the earth revolving around the sun. Perhaps, thought Kronig, each electron also has an angular momentum of its own, like the earth spinning on its axis.

But whereas the earth's spin is variable, the electron's always remains the same. Kronig gave electron "spin" a value of a half, using the units of angular momentum. To explain spectral lines physicists had always a.s.sumed that the electron acted like a tiny magnet that could align itself in a magnetic field. Pauli's and Kronig's discovery had transformed it into a spinning magnet that could align itself along a magnetic field in one of two directions, depending on whether it had a spin of plus or minus a half. These were precisely the two values that Pauli had transferred from the inert closed core to the lone electron in the outermost sh.e.l.l of an alkali atom. Thus spin was recognized as a distinguishing feature of an electron. Every electron has its own spin, just as each of us has a nose, eyes, and lips that distinguish us from one another. Spin is an intrinsic property of an electron, and no matter where the electron is located it has a spin of a half.

Initially Pauli dismissed Kronig's proposal, saying merely that it was "indeed a witty idea." For imagining an electron as a spinning top, as Pauli and everyone else did, led to a serious conflict with relativity theory. It meant that a point on the surface of the electron might move with the velocity of light, which according to relativity theory is impossible. When Kronig visited Copenhagen, Bohr dismissed his proposal with the words "very interesting" Kronig dropped the idea.

Then, nine months later, two Dutch physicists, George Uhlenbeck and Samuel Goudsmit, rediscovered spin and staked their claim in print, warning that one should not visualize the electron as a spinning top. Pauli was deeply embarra.s.sed at having discouraged Kronig from publishing his idea and thereafter always spoke highly of him.

Spin was undeniably a property of an electron but it was entirely impossible to visualize it in a way consistent with relativity theory. Scientists had to accept that the fourth quantum number had no accompanying visual image. It was time for atomic physics to move on from trying to visualize everything in images relating to the world in which we live.

Intermezzo-Three versus Four: Alchemy, Mysticism, and the Dawn of Modern Science.

My branch of science, physics, has got somewhat bogged down. The same thing can be said in a different way: When rational methods in science reach a dead end, a new lease on life is given to those contents that were pushed out of time consciousness in the 17th century and sank into the unconscious.

-WOLFGANG PAULI.

SINCE his student days and before, Pauli had been interested not just in the rational world of physics but also in the role of the irrational. Arnold Sommerfeld, his professor and lifelong mentor, was fascinated by the sixteenth-century pioneer of modern science, Johannes Kepler. Science, Sommerfeld reminded his students, emerged out of mysticism and had never completely separated itself. Besides his purely scientific work, Sommerfeld also pursued kabbalistic lines of research based on pure numbers and spoke of Kepler as his precursor.

In fact, he saw a direct connection between the developments of modern science and the harmony that Kepler had been searching for. Writing of his own research into spectral lines, the "fingerprint" of the atom, he said, "What we are nowadays hearing of the language of the spectra is a true music of the spheres within the atom, chords of integral relationships, an order and harmony that becomes even more perfect in spite of manifold variety."

Pauli, too, sought out links between his work and these ancient esoteric systems of understanding the universe. Many years later he was to write to Sommerfeld that he had finally succeeded in using the exclusion principle to establish the reason why the electron sh.e.l.ls fill up as they do in the series 2, 8, 18, 32, a grouping that Sommerfeld had described as "somewhat kabbalistic." In 1923, when Sommerfeld wrote those words, no one had been able to find any reason why electron sh.e.l.ls should fill up in this way and not some other. There was, in fact, no firm basis for almost all of the rules of atomic physics. "Some of the rules recall irresistibly the teaching of the alchemists or the witches' kitchen of Faust," wrote one physicist. Writings on the subject were nearly as mysterious as the Kabbalah, the Jewish book of mysticism that claimed that numbers could yield insight into the world beyond sense perceptions, just as Bohr's theory of the atom promised.

From time to time Pauli could not resist poking fun at his mentor's obsession with numbers. Once he noticed an advertis.e.m.e.nt posted around Munich, promoting an optical firm: "If you have trouble with your eyes, see Herr Runke." Pauli added the coda, "For integers, go to Sommerfeld."

In a tribute to Sommerfeld on his eightieth birthday, Pauli wrote that he "would not hesitate to set as a superscription over Sommerfeld's works in a wider sense the t.i.tle of Kepler's magnum opus-Harmonices Mundi."

Inspired by Sommerfeld, Pauli became fascinated by Kepler and may well have read him in the original Latin. In Hamburg he could have followed up his interest by attending lectures by Erwin Panofsky. A historian of art who specialized in symbolism and iconography, Panofsky had a great deal of knowledge about early science, particularly Kepler.

But what was it about Kepler that particularly piqued Pauli's interest?

It seems likely that Pauli read Kepler's Harmonices Mundi (Harmonics of the World) at this early stage of his life, when he was working on the exclusion principle. If so, he could not fail to have noticed the Appendix to Book V, about Robert Fludd, with whom Kepler had clashed. Kepler had stood up for the number three as the key number necessary to explain the workings of the universe. Fludd, conversely, a.s.serted that it was four. "I, myself, am not only Kepler, but also Fludd," Pauli was to write many years later. For Pauli had been in exactly the same quandry. "Once (in Hamburg) my path to the Exclusion Principle had to do precisely with the difficult transition from 3 to 4, namely with the necessity to attribute to the electron a fourth degree of freedom (soon explained as "spin") beyond the three translations.... That was really the main work." Bohr and Heisenberg had a.s.serted firmly that there could only be three quantum numbers for an electron. But Pauli, almost despite himself, realized there had to be four.

A few years later he was to come across the same numbers again in Carl Jung's psychology, based as it was in alchemy. He was adamant that "in neither case was it by any means Mr. C. G. Jung who suggested it to me, nor was there an advance conscious intention for me to grapple with figuring out the problem of three and four. Consequently I am rather certain that objectively there is an important psychological and, perhaps, natural philosophical problem connected with these numbers."

Pauli's study of Kepler and Fludd.

Pauli's study of Kepler and Fludd, "The Influence of Archetypal Ideas on the Scientific Theories of Kepler," published in 1952, is the definitive work on the two and indicative, incidentally, of Pauli's creative ability as a historian of science. His goal, as he wrote, was not so much to enumerate facts as to explore the "origin of and development of concepts and theories." Scientists such as Einstein and Poincare had insisted on the importance of intuition in creative thinking. Logic alone cannot lead to the discovery of scientific theories, they said. But neither man suggested a way to bridge the gap between intuition and the precise concepts required of a scientific theory.

Pauli's inspiration was to look into the practice of science in the Middle Ages, when alchemy, astrology, myths, the Kabbalah, and magical symbolism were all accepted modes of thought. It was a time of enormous change, when thinkers were daring to question the authority of the Church in understanding nature and the process of learning itself was becoming secularized. As scholars debated what questions they should ask about the world around them, brilliant men were developing the fundamental methods of science. Gradually a strongly rationalistic, logical science developed, forcing the more irrational, mystical elements into the background, where perhaps they remained in the unconscious of modern scientists.

Kepler was sure there was an order and harmony in the world and struggled to find a means to comprehend it. Straddling two worlds, he suffered great personal anguish in his quest to find the proper place for G.o.d. Again and again his research came up with precisely the symmetries and harmonies he was expecting, yet it always seemed to result in a universe without a G.o.d. Robert Fludd, meanwhile, remained firmly entrenched in the Middle Ages and in the end the two had to clash. It was a collision between two opposing intellectual worlds, leading each of them to produce a one-sided and incomplete understanding of nature. The forces of mysticism were at the time still overwhelming while science as we know it today was still in its infancy-but a beacon of light.

Early travails.

Johannes Kepler was born on May 16, 1571, in the town of Weil-der-Stadt in Germany. His father was a swashbuckling soldier of fortune who fought for anyone willing to pay for his services, even the Catholics, which disgraced the Keplers in the eyes of the Protestant families of Weil. He vanished in the course of a mercenary adventure. Kepler's mother, Katharina, was said to be quarrelsome and generally unpleasant, just like her husband.

A sickly child, Johannes grew up in what he described as a virtual madhouse surrounded by his squabbling parents and grandparents and six siblings, one of whom suffered from epilepsy. At four he almost died of smallpox, and two years later his hands were badly crippled. At sixteen, he wrote, he "suffered continually from skin ailments, often severe sores, often from the scabs of chronic putrid wounds in my feet which healed badly and kept breaking out again. On the middle finger of my right hand I had a worm, on the left a large sore." At twenty-one he was "offered union with a virgin; on New Year's Eve I achieved this with the greatest possible difficulty, experiencing the most acute pains of the bladder."

Given his poor health, interest in religion, and excellent record in the elementary Latin school, the obvious choice of career was to join the clergy. In 1589 he entered the theology school at the University of Tubingen. The professor of mathematics and astronomy there, Michael Maestlin, invited him to join his private study group.

Copernicus's sun-centered universe.

In his public lectures Maestlin taught Ptolemy's model of the universe with the sun and stars circling the earth, which agreed with Christian theology. But in private he was intrigued by the world-picture proposed by the Polish priest Nicholas Copernicus in his book of 1543, De Revolutionibus (On the Revolutions), which put the sun, not the earth, at the center of the planetary orbits.

In Copernicus's model, the six planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) make circular orbits around the sun, all enclosed by the sphere of the fixed stars. But Copernicus was perfectly aware that planets do not move in this way. A planet moving from west to east might cut back to the west, then resume an easterly orbit (known as retrograde motion). To explain these more complicated motions, Copernicus set planets moving on circles whose centers were on the surfaces of other circles that were also in circular motion, making the motions of planets the sum total of many circular motions. When more precise observations resulted in one of these planetary systems falling out of line, he added yet more circles. Thus he was able to explain the observed motion of the planets.

Copernicus's 1543 model of the universe. The sun (sol) is at the center with the six planets moving around in circular orbits. All this occurs within the seventh sphere-the sphere of the fixed stars (Stellarum fixarum). (Copernicus, De Revolutionibus [1543].) Church authorities condemned Copernicus's system as heresy, in that even though his system offered the best available mathematical basis for a twelve-month calendar, it did not place the earth at the center of the universe. (By "universe," Copernicus and his contemporaries meant what we now know as the solar system.) Church scientists expurgated De Revolutionibus, declaring that a.s.sertions made with certainty were in fact merely hypothetical. But Maestlin believed otherwise: that this was the way things actually were.

Kepler, too, read Copernicus's book. Two pa.s.sages fired his imagination. In one Copernicus wrote, "In the middle of all sits the Sun enthroned. In his beautiful temple could we place this luminary in any better position from which he can illuminate the whole at once? He is rightly called the Lamp, the Mind, the Ruler of the Universe; Hermes Trismegistus names him the Visible G.o.d, Sophocles' Electra calls him the All-seeing. So the sun sits as upon a royal throne ruling his children, the planets which circle around him."

In the other Copernicus wrote of his model of the sun-centered universe: "We find in this arrangement a marvelous symmetry of the world and a harmony in the relationship of the motion and size of the orbits, such as one cannot find elsewhere." These words struck Kepler like a bolt of lightning. He was gripped by the notions of order and harmony.

More than two hundred years were to pa.s.s before scientists were able to give incontrovertible proof that the earth circled the sun by measuring stellar parallax-the change in a star's position caused by the earth's movement around the sun. The only proof Copernicus had was his sense of aesthetics and harmony phrased in the language of mysticism. But that was good enough for Kepler.

"Geometry is the archetype of the beauty of the world"

Kepler believed in a reality beyond appearances. To him the three-dimensional sphere was the most beautiful image because it symbolized the Holy Trinity, the Triune G.o.d, with G.o.d the Father at the center, the Son at the circ.u.mference, and the Holy Ghost emanating from the center, as the radius. Thus there was an unchanging relationship between the circ.u.mference, the radius, and the center point. As he put it, "Although Center, Surface, and Distance are manifestly Three, yet are they One." The curved surface of the sphere with no beginning and no end represented the eternal Being of G.o.d.

The universe, with the sun at the center and the planets revolving around it in three-dimensional s.p.a.ce, was the perfect sphere and thus the very image of the Holy Trinity. Kepler saw it as a triumph of geometry, the discipline which to him ranked highest among the sciences. Pauli quotes from Kepler three different a.s.sertions of this: The traces of geometry are expressed in the world so that geometry is, so to speak, a kind of archetype of the world.

The geometrical-that is to say, quant.i.tative-figures are rational ent.i.ties. Reason is eternal. Therefore the geometrical figures are eternal; and in the Mind of G.o.d it has been true from eternity that, for example, the square of the side of a square equals half the square of the diagonal. Therefore, the quant.i.ties are the archetype of the world.

The Mind of G.o.d, whose copy is here [on earth] the human mind, from its archetype retains the imprint of the geometrical data from the very beginnings of mankind.

Writing in 1952, many years after he began his a.s.sociation with Jung, Pauli could not have failed to notice the appearance again and again of the word "archetype." The axioms of geometry, Kepler believed, are imprinted in our minds from birth by the Supreme Geometer. "Geometry is the archetype of the beauty of the world," he wrote.

In his thinking Kepler was influenced by the philosopher Proclus, who lived in the fifth century A.D. Proclus believed that mathematics-to be specific, whole numbers-held the key to understanding the nature of G.o.d, the soul, and the world-soul-the ethereal order and beauty of the cosmos. He wrote of an eternal unchanging universe, governed by laws of mathematical order and different from the imperfect world in which we live. His universe emanated from the One. Later commentators interpreted this One as a fecund Deity who gives light, warmth, and fertility.

Echoing Proclus, Kepler argued that it made sense to a.s.sume that the sun, not the earth, was at the center of the universe. Only thus could it "diffuse itself perpetually and uniformly throughout the universe. All other beings that share in light imitate the sun." The sun, its light, and the sphere of the fixed stars reveal the Holy Trinity before our very eyes. As Pauli put it: "because [Kepler] looks at the sun and the planets with this archetypal image in the background he believes with religious fervour in the heliocentric [sun-centred] system.... [It is his religious belief that impels] him to search for the true laws of planetary motion."

Thus the discovery of the sun-centered universe and the mathematical concepts that went along with it, including three-dimensional s.p.a.ce, could be traced to the visual image of the abstract sphere representing G.o.d the Trinity-an archetype from deep in the collective unconscious. This was a product of a geometry, wrote Kepler, that "supplied G.o.d with the models for the creation of the universe." The sun-centered universe reflected G.o.d's glory and this was why Kepler was impelled to search out its laws.

Pythagoras, apostle of fourness.

Pauli traced the origins of Kepler's thinking back to the Greek scientist and priest Pythagoras, who lived around 500 B.C.