Giordano Bruno Read online

  For Bruno and his contemporaries, a Divine Comedy was much harder to write. Dante’s certainties about natural philosophy were no longer certain. Astronomy had begun to split away from astrology, substituting a mechanical system of stars and planets for a system tied to the gods of Olympus. Mathematicians like Copernicus could track their movements with the help of complex equations, an activity as absorbing, in the end, as tracking their personalities had been in times past. In a whole series of applications, from cosmology to mechanics to geometry, algebra promised more exciting discoveries than numerology. At the end of the fifteenth century, Leonardo da Vinci had already confided in one of his notebooks that mathematics, combined with experimentation, provided the secret to all knowledge:

  No human investigation can be called real knowledge if it does not pass through mathematical demonstrations; and if you say that the kinds of knowledge that begin and end in the mind have any value as truth, this cannot be conceded, but rather must be denied for many reasons, and first of all because in such mental discussions there is no experimentation, without which nothing provides certainty of itself.

  Leonardo thus anticipated, by more than a century, Galileo’s famous statement about mathematics in The Assayer, his 1623 attack on the Jesuit scientist Orazio Grassi:

  Philosophy is written in this great book that stands ever open before our eyes (I mean the universe), but it cannot be understood without first learning to understand the language and recognize the characters in which it is written. It is written in mathematical language, and the characters are triangles, circles, and other geometric figures; without these tools it is impossible for a human being to understand a word; [to be] without them is to wander aimlessly through a dark labyrinth.

  Bruno’s scrutiny of the universe reflected a different kind of mind from Galileo’s. Astronomers like Copernicus, Tycho Brahe, and Galileo all had the mental habit of counting everything they saw. They could happily spend night after night watching the stars, measuring and tallying, until their individual observations added up to a larger theory. Bruno’s mind ran, more spectacularly than most, to visual imagery (although his minute account of the puppies and bedbugs of Nola suggests that he might have been a compulsive counter, too). Geometry intrigued him in a way that calculation did not. Yet he, too, was attracted by the idea of a universe run by mechanical principles: when he looked out at the stars, he saw Bernardino Telesio’s battle between heat and cold creating pinpoints of light in a vast sea of darkness.

  At the same time, with another part of his imagination, he could still look at the stars in their old role, as mythological figures, but here, too, he did so in a new way, using the stars, and their characters, to create new myths. Bruno’s versatility—part poet, part artist, part natural philosopher, part moralist, part theologian—makes him hard to fit into contemporary ideas of science, but this is not a problem unique to him: many of the best scientists today face it as well.

  There was nothing like teaching Aristotle to remind Bruno how much he resented the grand old Greek. No other thinker, not even Plato, could simply be called “the Philosopher,” but then no one else had earned such a position of authority on so many topics. In one sense, of course, the Philosopher was an ancient sage, but in another sense, as Bruno would point out, Aristotle’s thinking was younger, more immature, than that of the philosophers who came after him. In Bruno’s dialogue The Ash Wednesday Supper, the pedant Prudenzio praises the wisdom of the ancients until Bruno’s alter ego, Teofilo, turns an old proverb on its head:

  PRUDENZIO: Have it as you like, but I don’t like to depart from the opinion of the ancients, for, as the proverb says, “Wisdom lies in antiquity.”

  TEOFILO: And adds, “And prudence lies in great age.” If you really understood what you were saying, you would see that your statement implies the opposite of what you think: I mean that we are more ancient and greater in age than our predecessors; at least regarding some of the opinions we have been discussing. The judgment of [Aristotle’s student] Eudoxus (who lived just after the rebirth of astronomy, if he was not that rebirth himself) cannot have been as mature as that of Callippus, who lived 30 years after the death of Alexander the Great, for just as he added years upon years, he also added observations to observations. Hipparchus, for the same reasons, had to have known more than Callipus, because he saw the changes that had occurred up to 196 years after the death of Alexander. Menelaus Romanus the geometer understood more than Hipparchus for the simple fact that he saw what had been set in motion 432 years after the death of Alexander. Mahomet of Arak [an Arab astronomer] had to have seen still more 1,202 years afterward. Copernicus saw still more, because he lived almost up to our own time, 1,849 years after [Alexander’s death]. And if those closer to us in time have been no wiser than those who went before them, and most people today have no extra wit, it is because (what’s worse) they have lived their lives as if they were dead.

  Bruno saw no reason to cling to Aristotle’s ideas simply because Aristotle had been a great man and had lived a long time ago. Where data contradicted the Philosopher’s conjectures, he accepted the data. But he also reserved the right to conjecture as freely as the Philosopher had before him, confident that humanity had learned something in its nineteen added centuries of existence—and confident, like many an academic before and since, that his own native abilities were a good match for those of the Philosopher in any case.

  Copernicus did not invent the idea that the Earth might revolve around the sun; a Greek astronomer living in Alexandria, Aristarchus, had already made the proposal in the third century B.C. The behavior of the stars and planets fit the Earth-centered and sun-centered schemes just about equally, that is, well but not perfectly, especially because everyone from ancient Greece up to Bruno’s time took it for granted that the heavenly bodies orbited in perfect circles. The slight differences in measurement on which Copernicus based his argument were not as interesting to Bruno as the idea that all these measurements produced at best an approximation of a larger reality; in the old Platonic sense, they were as “real” as footprints in a forest. What interested Bruno was the forest itself.

  The Arab astronomers, like the Greeks, recognized that their measurements produced only approximate proof that the universe was a set of nested spheres surrounded by a realm of fixed stars and the enigmatic Milky Way. In tenth-century Cairo, the Egyptian court astronomer Ibn Yunus used extremely large instruments in hopes of making more accurate readings of heavenly motions that occurred on a gigantic scale. A fifteenth-century German cardinal, Nicholas of Cusa (in Latin, Nicolaus Cusanus), proposed the idea that the universe might be infinitely large, and that each of the fixed stars might loom as large as the sun, if only we were to come close enough. Cusanus, in addition to his temporal and religious duties, was a philosopher who loved paradoxes of all sorts; his treatise On the None Other declared, “The None Other is none other than the None Other.” In his greatest work of paradox, On Learned Ignorance, an obvious inspiration for Bruno’s preoccupation with holy asininity, Cusanus suggested that perhaps only an infinitely large universe did proper justice to God, who, as Saint Augustine had insisted, was “the measure beyond measure.”

  For his fellow cardinals of less ample imagination, Cusanus’s universe posed an immediate problem for their own role in the world: What, exactly, was the place of the human race, put on earth at the creation in order to be saved some four thousand years later by Jesus Christ, whose Church continued his work of salvation through his vicar the pope, and themselves? Fortunately for the cardinal, the Inquisition had not yet become a permanent institution, and his speculations were punished only by indifference. As for the place of Jesus Christ within an expanded cosmos, Cusanus himself simply marveled at the full scope of divine Providence.

  So did the Jewish mystics who wrote about riding on cherubs “over a cloud a thousand worlds beyond the world” with eyes that “have seen nothing but God alone.” At around the age of thirty, Giordano Bruno began
to cast his own imagination a thousand worlds beyond the world and find that the universe he had been teaching looked pitifully inadequate. More and more, he found himself agreeing with Cusanus.

  The change of mind might have come initially as a flash of insight (and Bruno’s writings suggest that it did), but it would take him years to work out its details. Among the tools he applied to the task of understanding very large numbers, almost from the beginning, was his magnificent trained memory. Within his head, the artificial memory constituted its own kind of infinite universe. Already at Toulouse he had begun to work on a book about the art of recollection that he would call Clavis magna (The Great Key). Somehow, he believed that a strictly disciplined mind would provide the necessary guidance for people who finally realized the full complexity of creation. As it did to Cusanus, the prospect of an opening, massively expanding universe seems to have filled him with awe rather than terror, “fear of God” in its most positive sense.

  Bruno described his revelation, however, as falling in love. In Greek, philosophia means “love of wisdom,” and Plato, the most voluptuous of writers, had long ago used the language of erotic love to suggest that the pleasures of philosophical love were similar, but incomparably more intense. The Platonic philosophy of Marsilio Ficino and Giles of Viterbo reconciled this eroticism with Christian faith; Giles in particular connected the most sensuous passages of Plato with the erotic poetry of the biblical Song of Songs, a book he and his contemporaries read as a series of allegorical love songs between God and the human soul, or Christ and the Church. Ficino, like Plato’s Socrates, focused both his erotic and his philosophical desire on young men, whereas Giles, by introducing the Song of Songs, transformed both divine and philosophical love into the love of male and female, variously conceived as the love of God and the soul (anima), Christ and the Church, or the philosopher and Wisdom (a feminine noun in Greek, Latin, and Hebrew).

  Bruno described his illumination in a sonnet, where the “twin lights” of truth and goodness enter through his eyes into his heart and transform him into their passionate lover:

  Against Love’s blows I built a strong redoubt;

  When his assaults struck, countless, everywhere,

  Pounding my heart within its diamond lair—

  Still, over his my own desires won out.

  At last (as was the heavens’ plan throughout)

  I chanced one day upon a holy pair

  Of lights, and through my own lights, then and there

  They found an entry to my heart laid out.

  Toward me then a double arrow sailed,

  Shot by a hand that held a warrior’s rage

  Who’d fought for thirty years and always failed.

  But now he’d marked the spot and pressed the siege;

  Planting his trophy right where he prevailed,

  And forced my wayward wings into his cage.

  On a more solemn stage

  The angers of my sweetest enemy

  Will never cease to strike my heart, and me.

  As a proper successor not only to Plato but also to Plato’s student the Philosopher, Bruno saw that his ideas would have spiritual and ethical repercussions as well as mathematical. Bernardino Telesio had already argued that the whole universe was composed of the same elements without distinction; Bruno agreed, and thus could envision the whole expanse of the stars as hot “suns” surrounded by cold, lightless “earths” invisible to the human eye.

  In an infinite expanse of space, the motions of these “suns” and “earths,” like those of the sun, moon, Earth, and planets, became a matter not of one body revolving around another but of motions within an infinite continuum. The cosmic systems of Aristotle, Ptolemy, and Copernicus were all relative—schematic expressions of one tiny part of an immeasurably larger set of motions.

  The nested wheels he had borrowed from Ramon Llull’s art of memory now served Bruno as a useful model for analyzing large numbers; each successive wheel created an exponential increase in the system’s number of possible combinations and allowed him to arrive mentally, at least, at nearly limitless magnitudes. He began to think about what kind of a mathematics could deal with infinite numbers: extremes not only of immensity but also of tininess. Arithmetic and geometry as he knew them were not enough.

  Bruno’s was the century in which European merchants and scholars definitively abandoned Roman numerals and their traditional ancient tools of abacus and counting stick for Hindu-Arabic numerals. The Arabic numerals came along with a related discipline that bore an Arabic name, algebra, and opened out the range of subjects that mathematicians could investigate—long division no longer represented the peak of their sophistication. Just before Bruno’s birth, therefore, Gerolamo Cardano provided a mathematical account of probability in his Book on Games of Chance. Even Fortune had her rational side.

  Through the development of complex equations, made possible by Hindu-Arabic notation, arithmetic could keep up at last with geometry. At the same time, however, mathematicians faced the insoluble mysteries of irrational numbers, the geometric quantities that could be drawn easily but never be calculated with arithmetical precision: square roots and the golden section, both having to do with the ratio between the side of a rectangle and its diagonals; and pi, the ratio between a circle’s radius and its circumference. Bruno’s writings reveal his own eagerness to confront one of the places where geometry and arithmetic collide most insistently with each other: the mathematics of motion. He had begun, in other words, to ask the questions to which only calculus would provide answers. Working a century before Newton and Leibniz and without their deeply arithmetical feel for numbers—as his writings show, to the end of his career he was still a numerologist at heart—Bruno simply lacked the mathematical means to answer his own questions himself.

  Often, like his contemporaries, Bruno uses the word mathematici to mean astronomers, and mathematici of the 1590s stood on the verge of revolution. Bruno heaped praise on the observational data of Tycho Brahe and the theoretical insight of Copernicus, but the real empirical breakthroughs in astronomy would come after Bruno’s death, with the invention of the telescope in 1609. In 1610, Galileo would train his own telescope on the heavens, and publish the discoveries in his Starry Messenger that same year: the moons of Jupiter, the seas and craters on the moon’s surface, and the remarkable number of the Pleiades. Bruno, by contrast, had arrived at his own idea of the infinite universe with nothing more than the naked eye. Furthermore, in one of his philosophy’s most sophisticated developments, he understood that such a universe must involve a mathematics of infinite quantities and infinitesimal quantities, numbers so inconceivably large that they were all equal and so inconceivably tiny that they were equal again.

  At the same time that the heavens began to open for the Nolan philosophy, one of Bruno’s colleagues at the University of Toulouse was exploring his own paradoxes in the spirit of Cusanus and On Learned Ignorance. The faculty’s other professor of philosophy, Francisco Sánchez, published his best-known work, Why Nothing Is Known, in Lyon in 1581. He gave Bruno a copy, which he inscribed “To the most illustrious Giordano Bruno, Keen-Witted Doctor of Philosophy, in friendship and esteem.” Bruno added his own inscription in the margin of the title page, alongside the last word in the byline, “Franciscus Sánchez, Philosopher and Physician, Doctor”: “Remarkable that this ass professes himself a doctor.” On the first page of Sánchez’s text, Bruno added another note: “Remarkable that he presumes to teach”—a barb at the teacher’s insistence, at such length, that “nothing is known.” Bruno’s keen wits were never tempered by charity toward his weaker colleagues. Other asses might be redeemed by their patience and their ability to endure, but he seemed to exempt pedant asses from any such hope of salvation.

  In Toulouse, with the rest of his life settling into place, Bruno pondered returning to the Church, and to his order. In the secrecy of a confessional, he confided his whole situation to a Jesuit priest, for Jesuits had the authority
to grant absolution to repentant heretics without involving the Inquisition. There were other advantages to consulting a Jesuit as well. Gossip traveled fast from one Dominican house to the next; that was how Bruno learned that he had been excommunicated in absentia and defrocked by the Dominican provincial of Naples, Fra Domenico Vita. Any inquiries he made among the Dominicans, however discreet, were likely to be passed back to Italy, and fast. Of the other orders, the Jesuits were among the least likely to divulge any information to the Dominicans: the two orders, one old, one new, were archrivals, for papal favor, for the best minds in the Church, and for the reputation as Catholicism’s intellectual vanguard. Some years later, that old rivalry still instinctive, Bruno would tell a Parisian bookseller that “he despised … all the philosophy of the Jesuits, which is nothing but questions about the text and intelligence of Aristotle.” Yet when Bruno entered a confessional in Lyon for the first time in years, he must have hoped to find a receptive hearing. For all its famous rigor, its spiritual exercises, and its vows of obedience, the Society of Jesus had bred some remarkably independent and flexible minds: Christoph Clavius was only one example, but an example any professor of astronomy—as Bruno was—knew as well as Sacrobosco’s On the Sphere.

  The Jesuit listened, but he could do no more than listen. As he explained through the confessional screen, he lacked the authority to perform absolution on an excommunicate—that is, to forgive the sins just confessed—unless, or until, Bruno rejoined the Church. Rejoining the Church, in turn, would require, at the very least, the approval of a bishop. In the meantime, the priest warned against participating in the Mass; to do so under excommunication was a grave sin. It was no sin, however, to pray privately, and prayer was perfectly permissible within a church at any time. The confessor could do little else to fulfill his order’s mission “to comfort souls,” and Bruno carefully respected his counsel, avoiding Mass and especially Communion, but listening to sermons and vesper services, and continuing, at least for the moment, to pray for private absolution every time he sinned. The conversation in the confessional cannot have been easy for either party.