The Music of Pythagoras

by Kitty Ferguson

  In 1799, Sylvain Maréchal wrote a six-volume biography titled Voyages of Pythagoras that raised its protagonist above the level of an ideal for this one revolutionary period. Kepler had dubbed Pythagoras “the grandfather of all Copernicans,” but the family became considerably larger when Maréchal insisted that all revolutionaries of all times were “heirs of Pythagoras.” The Pythagoras of Maréchal’s biography was a great geometer who was driven from the island of Samos by the tyrant Polykrates and fled to Croton, where he founded a philosophical-religious brotherhood with the goal of transforming society. The story went on, reimagined from the point of view of those who felt themselves part of a noble, centuries-old tradition devoted to that same goal: Neo-Pythagoreans who were radical intellectual reformers had flourished in Alexandria in the second century B.C. . . . the Pythagorean Apollonius of Tyana, the itinerant wonder-worker, was not a rather ridiculous cult figure but a legitimate and important rival to Christ, since discredited by Christian writers. . . . in the Middle Ages, those attracted to Pythagorean ideas recognized that Pythagoras was a secret Jewish link between Moses and Plato. . . . Pythagoreanism had never ceased to fascinate thinkers of the Renaissance and Enlightenment but had remained only an undercurrent until the time for its new awakening had come, in the revolution that would transform France and the rest of Europe. Maréchal wrote of “the equality of nature” and a Pythagorean “republic of equals,” and echoed Weishaupt and Buonarroti in advising his readers to “own everything in common, nothing for yourself.” Volume VI of the Voyages included no fewer than 3,506 supposed “Laws of Pythagoras.”

  Masons, Illuminists, and intellectual revolutionaries associated Pythagoras with prime numbers, though there had been no suggestion in antiquity of such a link. Great significance was attached to what were believed to have been the central prime numbers of Pythagorean mysticism: 1, 3, 5, and 7. The most extreme uses of “Pythagorean principles” were efforts to find paths, by means of mystical numbers and numerology, to the deep truths of nature, different from the use of numbers by early Pythagoreans, and even more different from their use by scientists to reach a mathematical understanding of nature and the cosmos. In a moment of leftist paranoia about a possible Jesuit plot for a secret takeover of Masonry, there was a suggestion that 17 was the number needed to understand the Jesuit plan. A rightist pamphleteer turned that idea around and proceeded, ingeniously, to show how all of revolutionary history derived from the number 17. Other opponents on the right picked up on this same type of pseudo-Pythagorean number mysticism and produced pamphlets suggesting that the prime numbers were a code for the organization of revolution.

  The obsession with Pythagoras did have something to do with the way revolutionary activities were organized, though this involved triangles and circles rather than prime numbers. The link revolutionary intellectuals made between Pythagoreans and the circle and sphere was not far-fetched. The Pythagoreans (as reflected, for instance, in the fragments of Philolaus) had been among the earliest to think in terms of a system in which the Earth and the universe were both spherical. Furthermore, Newton’s laws of gravity, which Newton himself had linked with Pythagoras, revealed a “circular harmony.” Another Pythagorean doctrine, the transmigration of souls, also suggested a circular movement, forever returning to begin again. Illuminist “Pythagoreans” were fond of the idea that a purification process took place within the framework of this “circular” transmigration of souls, beginning with the lowest forms of life, spiraling upward through the level of humanity to the divine spheres of pure rationality. The “rules of geometry,” as they called the laws behind such schemes, were appropriate for those who thought of themselves as the “mason-architects” of a new society. The architect Pierre Patte argued that there was a superior morality about circular shapes because they were essentially more egalitarian and communal.

  Accordingly, one way of organizing Illuminist groups was in a hierarchy of concentric circles. A flame “at the center” represented the central fire around which Earth, Sun, and planets moved in the Pythagorean ten-body system. As one advanced in Illuminism, one progressed from the outer circles inward, freeing oneself from physical limitations to join, or rejoin, life in the inner circle or most heavenly sphere. The same symbolism applied to societies, connecting the circles to the idea of “revolution.” Like individuals, societies could revolve inward through concentric circles, freeing themselves from the limitations of old traditions and beliefs to join the inner circle of freedom and rational simplicity. According to the report of a young collaborator of Buonarroti’s, Gioacchino Prati, the first organization that Buonarroti instituted, in the 1790s, the Sublime Perfect Masters, was composed of concentric circles each of which had its own secret creed. The inner circle was absolutely egalitarian and so secret that the outer circles were unaware of its existence. If the writings of some critics of the Illuminists are to be trusted, Illuminist groups organized also in another way into “circles,” a code name for nine-man cells of conspiracy. Weishaupt, the Bavarian Illuminist, was particularly fond of circles as symbols and considered it symbolic to speak of “circulating” his ideas by means of “circulars.”

  The triangle used in revolutionary symbolism was the equilateral triangle, the tetractus, which had also previously been an important symbol in Masonry. On seals, stamps, placards, and banners, Liberty, Equality, and Fraternity made up sides of a triangle, colored in red, white, and blue. Hats were tricornered. In 1798 Franz Xavier von Baader wrote a book called On the Pythagorean Square in Nature, a strange title for a book that celebrated triangles. Three elements—fire, water, and earth (air seemed not to interest von Baader)—were given life by an “all-animating principle,” a “point of sunrise,” represented by a dot in the center of an equilateral triangle. This image became hugely popular. Maréchal saw triangular harmonies in the three roles of a man as father, son, and husband, three persons in one, replacing the Christian Trinity with a trinity centered in each individual.

  The triangle showed up in a triangular organization of revolutionary groups. An individual from an inner group recruited two apprentices from an outer group, and eventually each of those recruited two more to form his own triangle. As Weishaupt described it,

  I have two directly under me into which I breathe my entire soul, and these two each have two others, and so forth. In this manner I am able, in the simplest way, to set thousands of people into movement and flames. In this manner the Order must be organized and operate politically.

  This meant that each man knew the name and identity of only one from the inner group above him. It was a relatively secure form of organization, an interlocking system that was difficult to infiltrate effectively. The Spanish Triangle Conspiracy of 1816, a plot to kill King Ferdinand VII, was appropriately named.*

  In a less potentially deadly usage, the mystic Louis-Claude de Saint-Martin wildly mixed images and cultures in his hope that Pythagorean forms and numbers could be employed to transform Paris into a new Jerusalem, with revolutionary democracy becoming a “deocracy.” Others made related plans for an innovative Parisian architecture, based on the circle, triangle, pyramid, and sphere—an idea that was remarkably realized in the 1980s in I. M. Pei’s controversial modern entrance to the Louvre, a glass pyramid.

  The “Pythagoreans” who idealized their role model as an intellectual turned revolutionary also celebrated his association with music and were particularly fond of “songs without words.” These seemed a link with the music of the spheres, expressing “the harmony of creation, or rather of the world as it should be.” Antoine Fabre d’Olivet, who composed music for Napoleon’s coronation, also set to music the Golden Verses of Pythagoras, the pseudo-Pythagorean work that had been popular in the Roman/Hellenistic era, and wrote that music was “the science of harmonic relationships of the universe.”

  In 1804, Napoleon, who five years earlier had installed a military dictatorship in France with himself as “First Consul”—the event usually identified
as the end of the French Revolution—declared France a hereditary empire and crowned himself emperor. Thus, with the beginning of the new century, European revolutionary hopes waned seriously, but the iconic Pythagoras became important in a new way to those who opposed Napoleon. As France followed the Roman example and transformed herself from a republic to an empire, Pythagoras was viewed nostalgically as an ancient, nobler alternative to Napoleonic images of conquest, expansion, and domination. Both Paine and Maréchal envisioned themselves as still following in the footsteps of Pythagoras, as intellectuals temporarily unable to act effectively (“in exile”) but devoted to constructing a brotherhood that would eventually free human society. In the words of Billington, two labels—Pythagoras and “Philadelphia” (signifying brotherly love)—“recur like leitmotifs amidst the cacophony of shifting ideals and groups during the recession of revolutionary hopes. . . . Pythagoras became a kind of patron saint for romantic revolutionaries,” who more than ever were in need of “symbols of secular sanctity.”

  Pythagorean inspiration and iconography reached Russia the same year Napoleon became emperor in Paris, when Maréchal’s biography of Pythagoras began to appear in official Russian government journals, a volume each year, and parts of it were excerpted in other Russian periodicals. A kruzhkovshchina (mania for circles) began in Russia and would last into the twentieth century. In 1818, in the western Ukraine, young men organized a “society of Pythagoras” with its own collection of “rules of the Pythagorean sect.” A series of groups calling themselves free Pythagoreans were soon forming in other areas of the Russian empire. Groups of radicals frequently debated one another about rival sets of “laws of Pythagoras.” Some preferred those that banned private ownership of property; others, those (whose Pythagorean origin was dubious) stressing that weapons and friendship could conquer all. Still others insisted that Pythagorean teachings regarding moral perfection had to be given priority over legal reform. Billington also tells of one student group in Vilnius that met at night in locations of great natural beauty to hear occult wisdom of an “arch-illuminated visitor” from an “inner circle.”

  A brief new tide of insurrections against monarchs in Europe that started with the Spanish Triangle Conspiracy of 1816 ebbed dramatically in 1823. The pope condemned Masonry, and several of the monarchies outlawed it. Throughout Europe, civil liberties were curtailed and organized discussions came under suspicion. Vestiges of republicanism, including Pythagorean symbols, fell out of official and public favor. The rector of the University of Kazan decreed that the Pythagorean theorem should not be taught.

  The Russian revolution of December 1825 was a failed echo of the fervor that had inspired intellectuals in Europe for more than half a century. Young officers who had helped defeat Napoleon and marched into Paris in 1814 had experienced there a freer, more enlightened world. They, rather than the lower classes in Russia, had begun to organize with the hope of bringing reform to Russia—in the words of one of the Turgenev brothers, to resist being turned “back into gingerbread soldiers! And by whom? Political pygmies.”

  Among those whose thinking and work led up to that brief, doomed Revolution of 1825, Pythagoras was again an inspiration. F. N. Glinka, who founded a group called the Union of Salvation, one of many secret societies formed at this time, was strongly moved by a French work that he read in translation about “the institute of Pythagoras.” A leading Russian periodical featured an article about the Sect of Pythagoreans that included a series of questions and answers like those favored by the acusmatici (“What is universal? Order. What is friendship? Equality”) and a description: “not having any private property, not knowing false pride and vain praise, far from petty things that often divide, they competed with one another only in doing good . . . and learned to use things in common and forget about ownership.” One of the leaders of a “circle” that helped foment the revolt, called the Green Lamp, wrote a piece that imagined St. Petersburg three hundred years in the future. In his vision, the tsar and all Orthodoxy would have given way to Pythagorean forms represented by a circular temple, music, and a phoenix with an olive branch.

  When the 1825 revolution failed, five leaders were hanged and the others exiled to Siberia. Perhaps there was consolation in recalling that Pythagoras, their iconic ancient model, had—at least in the mythology they thought they knew—been forced to flee in ignominy from a city he had tried to introduce to a better way of life.

  BEYOND REVOLUTIONARY CIRCLES, other literature of the nineteenth century remembered Pythagoras. The poet Percy Bysshe Shelley wrote a piece praising the vegetarian “Pythagorean Diet,” and Leo Tolstoy chose to follow it. Louisa May Alcott knew her readers would need no explanation when she wrote in Jo’s Boys that “Grandpa March cultivated the little mind with the tender wisdom of a modern Pythagoras, not tasking it with long, hard lessons, parrot-learned, but helping it to unfold as naturally and beautifully as sun and dew help roses bloom.” Honoré de Balzac attributed the saying “no man is known until he dies” to Pythagoras. Pythagoras was one of the ghosts present in Charles Dickens’ The Haunted House and also made an appearance in The Pickwick Papers.

  Also in the nineteenth century, the belief continued that the concept of the mathematical structure of the universe had originated with the Pythagoreans. The economist William Stanley Jevons wrote: “Not without reason did Pythagoras represent the world as ruled by number. Into almost all our acts of thought number enters, and in proportion as we can define numerically we enjoy exact and useful knowledge of the universe.”11

  One Pythagorean ideal began to come into its own in a way it could not have done earlier. The assumption that there was unity to the universe had already become one of the pillars on which science rested, but not until the nineteenth century did the knowledge and the instruments begin to be available that would allow scientists to explore the question whether this assumption was valid, or whether, like the music of the spheres, it was best relegated to the realm of poetic metaphor. The idea that there is unity to nature emerged strongly in the work of three men who had a particularly significant impact on the future of science.

  When the Danish physicist and chemist Hans Christian Oersted wrote his doctoral thesis about a book by Immanuel Kant called The Metaphysical Foundations of Knowledge, he was already convinced that all experience could be accounted for by a correct understanding of the forces of nature, and that the forces of nature were actually not many forces but one. Kant had suggested there were two basic forces, but Oersted decided to push forward with the certainty that light, heat, chemical affinity, electricity, and magnetism were all different faces of “one primordial power.” In 1820 he discovered electromagnetism, having “adhered to the opinion, that the magnetical effects are produced by the same powers as the electrical . . . not so much led to this by the reasons commonly alleged for this opinion, as by the philosophical principle, that all phenomena are produced by the same original power.”

  Michael Faraday was another early-nineteenth-century scientist who undertook a lifelong search for ways in which the forces of nature are unified. He began his professional life as a chemist and discovered several new organic compounds. As had been true of Linnaeus’ numerous previously unknown species, those discoveries might have been taken to indicate a lack of unity, but instead they expanded awareness of what was out there to be unified. A tally of Faraday’s most notable contributions included producing an electric current from a magnetic field, showing the relationship between chemical bonding and electricity, and discovering the effect of magnetism on light.

  Michael Faraday

  Faraday’s work was the experimental foundation—and also a large part of the theoretical foundation—for the work of James Clerk Maxwell later in the century. Maxwell’s electromagnetic field theory achieved the full unification of electricity and magnetism. The “electromagnetic force” would enter the twentieth century as one of four basic forces of nature. Maxwell’s equations, based in turn on Faraday’s study of el
ectric and magnetic lines of force, would also be instrumental in setting a scientific trajectory toward the linking of mass and energy in Einstein’s special theory of relativity. Science at the turn of the twentieth century was well on the way to finding the unity of nature that Pythagoreans had so fervently believed in. Paradoxically, Maxwell’s work also provided a vision of reality with problems that would be resolved in the twentieth century by quantum theory. And quantum theory, in its turn, would cause a crisis of faith in the rationality of the universe, a crisis on a scale with that perhaps caused by the ancient Pythagorean discovery of incommensurability.

  CHAPTER 18

  Janus Face

  Twentieth Century

  IN THE TWENTIETH CENTURY, two major books appeared that highlighted humanity’s debt to Pythagoras and the Pythagoreans. “Debt to Pythagoras” might seem to imply that there is something positive for which to thank Pythagoras and his followers, and one of the authors, Arthur Koestler, certainly believed there was. Bertrand Russell, on the other hand, insisted that most of Pythagoras’ influence had been negative. Their two accounts constitute an excellent example of how taking off one pair of glasses and putting on another can change the view in astounding ways.1