Part 4 (2/2)

When Fludd's enemies at the court of King James I accused him of collaborating with them, he argued persuasively that the Rosicrucians were innocent of heresy. James was so impressed that he became Fludd's patron.

In his book Fludd a.s.serted that ”the true philosophy...will sufficiently explore, examine and depict Man, who is unique, by means of pictures.” In other words, he intended the sumptuous ill.u.s.trations in his books not merely as decoration but as saying something very definite about the world. Kepler, too, used diagrams, but of a scientific character-optical constructions made up of rays of light, a sphere with light emanating from its center as straight lines, or an image of planets moving in ellipses around a sun displaced from the center of the universe.

Both agreed that there was an invisible realm of qualities and powers, as well as a harmonics of nature. But while Fludd's world was one of astral powers and invisible spiritual illumination, Kepler's was of invisible magnetic forces, archetypal images, and hidden astrological meanings.

In his Harmonices, Kepler included a devastating critique of Fludd's book. Fludd immediately sprang to the defense. To start with, Kepler derided Fludd's extensive reliance on pictures; for what interested Kepler was mathematics. In reply, Fludd ranked him with ”vulgar mathematicians” who concern themselves only with ”quant.i.tative shadows.” Philosophers like himself, Fludd wrote, ”comprehend the true core of natural bodies” rather than stripping nature bare with cold mathematics. Kepler replied, ”In Fludd's method is the business of alchemists, hermetists and Paracelsians; mine is the task of the mathematician.”

In his drawings Fludd represented the text of Genesis using images based on alchemy, astrology, and the Kabbalah, with light playing a central role. To him the mundane world was the mirror image of the invisible world of the Trinitarian G.o.d. He represented this as two equilateral triangles placed together and wrote beside the upper one: ”That most divine and beautiful Object [G.o.d] seen in the murky mirror of the world drawn underneath.” The upper triangle contains the four Hebrew characters -the tetragrammaton-for the ineffable name of G.o.d, YHVH, set within another perfect triangle. The triangle beneath it is the ”reflection of the incomprehensible triangle seen in the mirror of the world,” Fludd wrote.

The divine and mundane triangles. (Fludd, Utriusque Cosmi Maioris scilicet et Minoris, Metaphysica, Physica atque technica Historices mundi [1621].) To depict the creation Fludd used an image of interpenetrating triangles. One triangle ascends from the earth. It is dark at the base and becomes brighter as it moves toward heaven. The inverted triangle, meanwhile, has its apex on the earth. The former culminates in the perfect triangle, the symbol of G.o.d, while the latter emanates from it. They mirror each other precisely and thus represent the constant struggle of polar opposites: the triangle rising from the earth represents the dark principle, or matter, while the other is the light principle, or form. Matter and form, light and darkness are the polar principles of the universe. This is reminiscent of the Kabbalah where these opposites are called antipathy and sympathy.

Interpenetration of material and formal pyramids. (Fludd, Utriusque Cosmi Maioris scilicet et Minoris, Metaphysica, Physica atque technica Historices mundi [1621].) Fludd emphasizes that the world about us results from a struggle between dark and light by placing the sun at the intersection point of the two pyramids, where the opposing principles counterbalance each other. This also signals his belief that the unity of G.o.d Himself is symbolized in the mystery of the alchemical wedding in which opposites are fused together.

Placing the apex of the light triangle on the earth symbolizes the withdrawal of light and the appearance of matter. In his a.n.a.lysis of all this, Pauli was particularly interested in the Lurianic story of Creation, as revealed by the sixteenth-century mystic and kabbalist Isaac Luria, of whom Fludd was aware. Luria reported that his soul often traveled to divine realms to study the secrets of existence and claimed that he could not write his visions down because they gushed so rapidly from his mind. Others recorded them in what became known as the Lurianic Kabbalah. Some of his disciples a.s.serted that his early death, at thirty-eight, was G.o.d's retribution on him for revealing forbidden knowledge.

Luria asked questions such as, Why everything? Why did creation occur? What is the meaning of everything? Fludd's inverted triangles contain his replies. Luria called Tsimtsum-the withdrawal of light and thus of G.o.d to create matter-one of the most important notions in kabbalistic thought. The problem is, if G.o.d is everywhere, how can there be a world? How can there be anything that is not G.o.d? To accomplish this separation G.o.d must have had to abandon a region within Himself to create a ”kind of mystical primordial s.p.a.ce from which He withdrew in order to return to it”-or so the kabbalistic scholar Gershom Scholem, a friend of Pauli's, wrote.

Once darkness, or Nothing, could be visualized, then the act of creation-Let there be light!-followed, or so Fludd believed. To express this he drew a dark square. In another image he drew rays of light emanating from a dark core and terminating at a circular periphery with darkness outside it-light, dark, and spirit, the Trinity. From this triad, according to Fludd, the four elements emerged and the struggle among them began. This cosmogony was the blueprint for all natural processes in that they were bases for all subsequent alchemical transformations among the four elements.

Thus the Pythagorean tetraktys emerged out of Fludd's version of how G.o.d created the cosmos. First comes the unity (one) culminating in darkness, followed by the duality of light and dark (two), then by the Trinity (three), culminating in the four elements and the four seasons, and all the other sets of fours that make up the world as we know it, Fludd argued. Pauli wrote appropriately, ”His goal is the coniunctio of light and darkness: not the spiritualization of matter.... This is alchemy in the best sense.”

Kepler versus Fludd.

Kepler scoffed at Fludd's attempt to seek harmonies ”from the interpenetration of his Pyramids which he privately carries around in his mind as a world drawn in pictures.” Kepler conversely claimed to have found harmonies in the motions of the planets within a scheme based on mathematics, and that fit astronomical observations and measurements. Without mathematics, he wrote, ”I am like a blind man.” While Fludd claimed to take his lead from the ”Ancients,” Kepler followed ”Nature herself.”

All the same, Kepler's Harmonices was full of astrological, alchemical, Pythagorean, and mystical concepts. Even though Kepler had fulfilled Pythagoras's dream of explaining the universe through geometry and number, he was not satisfied. He was torn between the irresistible pull of his three laws, which postulated that the sun was not at the center of the universe, and the archetypal Trinitarian view of a spherical cosmos with the sun at its center. They did not mirror each other.

He fretted over the division between inert and live matter. Mathematics seemed to apply only to the former; but surely matter had a soul? He could not derive his laws with the mathematics available to him and they did not make much sense without the concept of there being something that tied the planets to the sun.

Fludd published the full text of the Macrocosm two years after Kepler's Harmonices. ”Spurred on by the insolence of” Kepler, Fludd gave the usual Pythagorean reasons as to why the key number of the universe was four: its importance for geometry and music, its role in the ”mystery of the seven days of creation: the sun was created on the fourth day.” Four plus three, he pointed out (the quaternary plus the Trinity) adds up to the magic number seven.

He then referred to the four letters that made up the name of Yahweh--the tetragrammaton. The double ”He,” he wrote, signified the progression from the Father to the Son.

To this he added the ”hieroglyphic monad”-the four symbols representing the sun, the moon, the four elements, and fire. These are depicted as the crescent moon on the round sun, connected by the ”quaternary of the cross, four lines being arranged so as to meet in the common point” to the symbol for fire. All of these, according to ancient beliefs and also the beliefs held at the time-such as Hermeticism, alchemy, the Kabbalah, and the Rosicrucians-are responsible for the cycle of transformations that produce our world.

Kepler looked at all this and realized he was wasting his time. He decided to cease communicating with Fludd, ”I have moved mountains; it is astonis.h.i.+ng how much smoke they expel,” he wrote.

All coherence gone.

Among Kepler's last projects was the completion of Somnium, Sive Astronomia Lunaris-Dream or Astronomy of the Moon, a science fiction story about a journey to the moon. In it he imagined what the universe would look like to someone standing on the moon. It was a bold notion that had been important to his discovery of his three laws.

The Somnium in its fragmented form sparked the curiosity of many readers, including the poet John Donne. Donne visited Kepler in 1619 as part of an English delegation dispatched by King James I to Germany. He was interested also in Kepler's book on new stars, De Stella nova. Donne was struck by the implications of the new astronomy: stars no longer immutable, the earth no longer at the center of the universe and, worst of all, the universe most likely of infinite extent, making Heaven far away while h.e.l.l was just beneath our feet. ”Tis all in peeces, all cohaerence gone [sic],” he wrote.

At this point Kepler and his family were living in an apartment in the wall surrounding the city of Linz, which was constantly under siege. They often had to admit soldiers to fire their guns through their windows. When the siege was lifted in 1626, Kepler finally left. He died in Regensburg on November 15, 1630. The cemetery in which he was buried was obliterated in the Thirty Years War.

Fludd died seven years later in London. Like a lightning rod his ideas had attracted sharp controversies, most notably with Kepler. His will stated that all those at his funeral should return to the local pub and entertain themselves at his expense.

Three or four?

To Pauli, Kepler and Fludd were a study in opposites. At first he sided with Kepler but over time came to realize that Fludd's worldview included science, music, religion, and the mind. For Fludd four was ”the eternal fountainhead of nature.” For Kepler the perfect number was three. ”I hit upon Kepler as trinitarian and Fludd as quaternarian-and with their polemic, I felt an inner conflict resonate within myself. I have certain features of both,” Pauli wrote.

Like Kepler, Pauli brooded about his work, suffering over problems he couldn't solve, far removed from the world of ordinary people. In 1924, when he discovered the exclusion principle, perhaps like Kepler he felt that he had tapped into something that went beyond science. Moving from three to four quantum numbers was a momentous step. It meant a complete break with the iconic imagery of the Bohr atom as a miniscule solar system. It was a step into the unknown, into a world without any visual images. Perhaps Pauli had in mind one of Bohr's favorite sayings from the eighteenth-century German poet Friedrich Schiller: Only fullness leads to clarity.

And truth lies in the abyss.

In his day Kepler stopped short at the number three, basing this decision on the three-dimensionality of s.p.a.ce, on the one hand, and the Holy Trinity on the other. The deep mysteries of alchemy with its emphasis on the number four overwhelmed him.

Pauli, Heisenberg, and the Great Quantum Breakthrough.

EVERYONE AGREED with Pauli that there should be four not three quantum numbers. His exclusion principle had shown that no two electrons in an atom could have the same four quantum numbers. Beyond that his colleagues could see that the principle must have huge implications. But no one could yet see what they were.

By the beginning of 1925 it was clear that Bohr's theory of the atom as a miniature solar system no longer provided even an adequate basis for understanding the atom, let alone for the exclusion principle or the anomalous Zeeman effect. Bohr's theory by now was under attack from all sides.

The demise of Bohr's theory of the atom.

Pauli, despite his best intentions, had been one of the key wielders of the knife. As he had discovered, the theory had failed to produce a realistic model of either a hydrogen-molecule ion or a helium atom. Then new data appeared showing that the hydrogen atom did not respond to being hit by light as if it were a tiny solar system. This model produced spectral lines for the struck light that did not agree with those found in the laboratory.

Bohr fought back with a variation of his theory in which the invisible orbits of the invisible electrons were replaced by invisible electrons on springs, each emitting light at the frequency of an observed spectral line. To emphasize that these invisible electrons were an intermediate kind of reality, he referred to them as ”virtual oscillators.” Pauli wanted nothing to do with them. He had had enough of bizarre models and was totally discouraged.

Heisenberg, who was twenty-four, thought otherwise. Throughout spring 1925 he pushed Bohr's theory of virtual oscillators to its limits. But it failed. It seemed that Bohr's theory barely worked even for the hydrogen atom and even then no one really understood why. Atomic physics lay in ruins.

Many physicists spoke of their despair. Pauli did not respond well to crises and was becoming more and more depressed. He joked bitterly that physics was all wrong and wrote to Kronig, ”I wish I were a film comedian or something similar and had never heard of physics.” He hoped, he added, that ”Bohr will rescue us with a new idea.”

Around this time, Pauli wrote to Bohr about Heisenberg, ”I always feel strange with him. When I think about his ideas, they seem dreadful to me and inwardly I swear about them. For he is very unphilosophical, he pays no attention to expressing clearly the fundamental a.s.sumptions and their connection with existing theories. But when I talk to him he pleases me very much and I see that he has all sorts of new arguments.... I believe that some time in the future he will greatly advance science.” Pauli was to be proved right.

Unlike Pauli, Heisenberg thrived in periods of chaos. Far from despairing, he would go all out to find a solution. He welcomed the stretch of the imagination required by Bohr's virtual oscillators. He used his immense experience in every aspect of atomic physics, together with his natural audaciousness, spurred on by Pauli's critical comments-among them that he should deal only with quant.i.ties that can be measured in the laboratory, such as the energy and momentum of electrons, and avoid abstract concepts such as...o...b..ts of electrons. ”We must adjust our concepts to experience,” was the approach Pauli suggested. Heisenberg worked day and night and came up with a whole new atomic physics that was to become known as quantum mechanics. Full of excitement, Pauli wrote that Heisenberg's work gave him ”new hope and a renewed enjoyment in life.”

”We must adjust our concepts to experience”

Like every highly creative scientist of his era, Pauli was a philosophical opportunist. He picked and chose from whatever philosophy had to offer to tackle the problem at hand. Scientists use philosophy when they ask the deepest of questions, such as What const.i.tutes a scientific theory? What sort of physical objects should it consider and how should it treat them? What is physical reality?

At the beginning of the twentieth century these questions became crucial when scientists had to contend with objects-such as electrons and atoms-that they could not actually see. Cla.s.sical ways of understanding the world suddenly seemed insufficient. An intellectual tidal wave-the avant-garde-swept across Europe.

Scientific concepts, ways of thinking, and ways of knowing were all being re-examined. Einstein did so when he discovered his special theory of relativity in 1905. This upheaval in thinking pervaded the world outside science too. In 1907 Pablo Pica.s.so launched cubism with his ”Les Demoiselles d'Avignon” and in 1910 Wa.s.sily Kandinsky unveiled abstract expressionism. In 1913 Igor Stravinsky ruptured all the conventions of cla.s.sical ballet with his ”Rite of Spring.” The postwar 1920s produced the twelve-tone music of Arnold Schonberg, Bauhaus architecture, and James Joyce's extraordinary novels, which encompa.s.sed everything from relativity to cubism. Meanwhile Freud and Jung were investigating the unconscious.

Pauli first encountered this ferment of ideas through his G.o.dfather, the positivist Ernst Mach. As a boy he was spellbound by the scientific equipment in Mach's apartment. Its ultimate purpose, said Mach, was to eliminate unreliable thinking-to demonstrate that the only thing that was really out there was what you can experience with your senses. The rest was all metaphysics-quite literally beyond physics and not worth considering, mere illusion.

Atoms could not be experienced with the senses. Did that mean they were merely ”metaphysical,” in Mach's pejorative sense? Were they not part of the elaborate scientific theories which made predictions that could be proved in the laboratory? According to Einstein's theory of relativity-Pauli's first scientific love-time turned out to depend on the motion of a clock and our world was four-dimensional, not three as everyone had always thought. The message of relativity theory seemed to be that scientists should look beyond what was immediately perceptible by the senses. It was to Einstein's disappointment that he failed ever to convince Mach to accept relativity theory.

In the light of relativity theory Mach's view seemed too restrictive. A group of young philosophers with strong scientific backgrounds began to meet in the coffeehouses of Vienna to discuss how to correct this situation, how to bring positivism into line with relativity theory. They called themselves the Vienna Circle and came up with a sophisticated version of positivism that they dubbed ”logical positivism.” Then they renamed it ”logical empiricism”: the word ”empiricism” refers to experimental data (empirical data). Logical empiricism emphasized the role of mathematics in that a theory required a consistent logical or mathematical structure. Mach, on the other hand, regarded mathematics as merely an economical way to summarize experimental data.

In the view of the Vienna Circle a scientific theory had to be built on empirical data with the help of mathematics and had to generate predictions that could be tested in the laboratory. Science was a two-way street, beginning with data and ending with predictions that could be verified by data in the laboratory. Logical empiricism also insisted that every concept in a scientific theory must be measurable. Distance could be measured with a ruler, time by clocks, and so on. Thus they claimed that Einstein's discovery of relativity theory was actually in accordance with positivism.

As for atoms, this was just a name for a list of experimental results. The rays emerging from cathode-ray tubes-primitive television tubes-were a.s.sumed to be a sort of light ray with an electric charge. Actually, every scientist knew that cathode rays were made up of electrons. Both Mach and the logical empiricists declared that atoms were not real as they could not be seen or measured individually. But the logical empiricists were able to see a way around Mach's rejection of Einstein's theory of the relativity of time in that it emerged from a consistent mathematics and experiments had been done to ill.u.s.trate it in the laboratory. Mach's philosophical heirs made the important point that the criterion ”to observe something in the laboratory” had to be replaced by ”to ascertain it or measure it in the laboratory.”

Pauli was well read in philosophy and introduced himself to the then-doyen of the Vienna Circle, the German-born Moritz Schlick. Schlick was twice his age and an esteemed professor at the University of Vienna, where he had taken over Mach's position. Schlick was impressed with Pauli's philosophical ac.u.men. Pauli did not let the fact that he was a mere postdoctoral student hinder him from giving Schlick his blunt a.s.sessment of positivism. He had no objection to it, he wrote in 1922, ”But, of course, it is not the only [philosophical approach].”

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