The Music of Pythagoras (43 page)

Two decades later, the younger Galileo, though largely oblivious to the work Kepler was doing, had become personally convinced that the
Copernican system was correct, and he was looking for physical evidence to support that opinion and convince other scholars. Copernicus had mentioned in
De revolutionibus
that the planet Venus might supply important evidence in the case against an Earth-centered cosmos. Venus, reflecting the Sun’s light, waxes and wanes as the Moon does, but if the Ptolemaic arrangement of the cosmos were correct, Earth dwellers would never be positioned in such a way as to see the face of Venus anywhere near fully lit (the equivalent of a full Moon). As the first decade of the seventeenth century drew to a close, the newly invented telescope (Galileo did not invent it but was putting it to better use than anyone else) made it possible to observe the phases of Venus as never before, and in 1610 Galileo followed up on Copernicus’ suggestion. He found that Venus had a full range of phases. How could any scholar fail to see that this was irrefutable evidence in favor of Copernicus? But Galileo’s Catholic colleagues included a group of recalcitrant scholars who remind one of an unusually virulent strain of
acusmatici
.

Except in the case of Giordano Bruno, whose offenses by church standards were so flagrant and numerous that he would almost surely have been burned at the stake no matter where he thought the center of the universe was, the Catholic church hierarchy had for centuries been rather sluggishly tolerant of new astronomical theories. Not a murmur was heard when Nicholas of Cusa, in the early fifteenth century, put the Earth in motion and removed it from the center of the universe, nor when Copernicus published
De revolutionibus
in 1543. Two of Copernicus’ strongest supporters were prominent Catholic clergy. But in 1616, when both Galileo and his opponents were pushing the church for a ruling on the Copernican question, a decree was issued condemning the “new” astronomy, though not actually calling it heresy—a technicality perhaps, but a victory for Galileo and the cardinals who supported him. In this decree, the Pythagoreans took an unfair hit:

And whereas it has also come to the knowledge of the said Congregation that the Pythagorean doctrine—which is false and altogether opposed to the Holy Scripture—of the motion of the Earth and the immobility of the Sun, which is also taught by Nicolaus Copernicus . . . is now being spread abroad and accepted by many, as may be seen from a certain letter of a Carmelite Father.

The Carmelite father who had put the Pythagoreans in the range of fire was the Reverend Father Paolo Antonio Foscarini. His letter, dated the year before the decree, was titled “On the Opinion of the Pythagoreans and of Copernicus Concerning the Motion of the Earth, and the Stability of the Sun, and the New Pythagorean System of the World.” Foscarini insisted this doctrine was “consonant with truth and not opposed to Holy Scripture.” The church’s “General Congregation of the Index,” which made official judgments on such matters, felt differently. Copernicus’ book
De revolutionibus
—seventy-three years after its publication—was “suspended until corrected,” and Foscarini’s work was “altogether prohibited and condemned.” It took seventeen more years of on-and-off sparring, and Galileo’s book
Dialogo
, for matters to come to a truly dangerous head in his famous trial. The Catholic church, for centuries the guardian and bastion of learning, had turned foolish to the point of malign senility and condemned herself and Italy—the ancient home of Pythagoras—to what was virtually a new scientific dark age. The center of scientific endeavor and achievement moved, irretrievably, to northern Europe and England.

As the scientific revolution continued north of the Alps in the mid-seventeenth century, Kepler’s three laws of planetary motion and his Rudolfine Tables, based on Tycho Brahe’s observations, rightly gave him his earthly immortality, but his polyhedral theory and most of
Harmonice mundi
were consigned to the cabinet of curiosities. No one took nested polyhedrons or cosmic chords and scales seriously or followed up on them as science. They had been the odd and unlikely midwives to Kepler’s “new astronomy,” helping birth the future, but in doing so had relegated themselves to the past. However, the conviction that numbers and harmony and symmetry were guides to truth because the universe was created according to a rational, orderly plan began to be treated as a given, trustworthy enough to underpin what would later be called the scientific method.

No one was using the words “science” or “scientific” yet in their modern sense, but the process for determining what was and was not true about nature and the universe was continuing to evolve, and people were discussing and beginning to agree about how this process should work. The French scientist and philosopher René Descartes, one of the first to try to establish a solid foundation for human understanding of the world, chose mathematics as the only trustworthy road
to sure knowledge.
³
He tried to show that a single, united system of logical mathematical theory could account for everything that happens in the physical universe. Christiaan Huygens, Edmond Halley, and Isaac Newton all shared the conviction that when observations were inadequate, one could even with some confidence go out on a limb on the assumption that the universe is orderly, and discovering new examples of “order” was beginning to be regarded as a sign that one was on the right track. Robert Hooke, in the field of biology, suggested that crystals like those that may have alerted the Pythagoreans to the existence of the five regular solids occurred because their atoms had an orderly arrangement.
⁴
Robert Boyle wrote his book
The Sceptical Chymist
, which many identify as marking the beginning of modern chemistry, and cited Pythagoras, asserting that the final decisions of science must be made on the basis of both the evidence of the senses and the operation of reason. This balance, on which Kepler had performed such prodigious acrobatics as he struggled to write his
Astronomia nova
—without thinking of it as a “scientific method”—was becoming the balance of science.

Newton, born mid-century, capped off the Copernican revolution with his discovery of the laws of gravity and his 1687 book
Philosophiae Naturalis Principia Mathematica
(“Mathematical Principles of Natural Philosophy”), known as his
Principia
. A fervent believer in the harmony and order of the universe, he was convinced that the observable patterns in the cosmos were the visible manifestation of a profound, mysterious, underlying order. His theories of gravitation admirably supported the Pythagorean ideal of unity and simplicity. The same force, gravity, that kept the planets in orbit also dictated the trajectory of a ball thrown on Earth and kept human beings’ feet on the ground, and its laws could be stated in a simple formula. Though he was notoriously miserly about giving credit where credit was clearly due among his contemporaries, Newton, in an extraordinary gesture, wrote that his own famous law of universal gravitation could be found in Pythagoras. Nor was this the extent of Newton’s unusual attributions. He sought examples among the Greeks, the Hebrews, and other ancient thinkers, of ideas and discoveries that seemed—sometimes it was quite a stretch—to foreshadow his own. This was not modesty. Newton was by no means a modest man. It was more a way of elevating himself to the company of the greatest sages. Better than discovering something new was rediscovering knowledge that God had previously revealed only to extraordinary
men of legendary wisdom. Newton thought of another link with Pythagoras when he used a prism and split the light of the Sun into seven colors. There were seven notes in the Pythagorean scale.
⁵

Gottfried Leibniz, Newton’s arch-rival and one of those contemporaries to whom Newton should have given considerably more credit, wrote in Pythagorean tones that “music is the pleasure the human soul experiences from counting without being aware that it is counting.”
⁶
Leibniz tried to construct a universal language which had no words, that could express all human statements and resolve arguments in a completely unambiguous way, even, he hoped, bring into agreement all versions of Christian faith. His attempts to make good on this scheme included a use of numbers that would have pleased the Pythagoreans and annoyed Aristotle: “For example, if the term for an ‘animate being’ should be imagined as expressed by the number 2, and the term for ‘rational’ by the number 3, the term for ‘man’ will be expressed by the number 2×3, that is 6.”
⁷

N
EWTON’S DISCOVERIES ABOUT
gravity showed the cosmos seeming to operate like a stupendous, dependable mechanism, and, in the eighteenth century, scholars and amateur science aficionados picked up on that idea and became obsessed with mechanisms and machines. The demonstration of a new apparatus to explain or test a scientific principle was likely to cause more excitement than a lecture or a new theory at meetings of the Royal Society of London for Improving Natural Knowledge, or of the Birmingham “Lunar Men” of Charles Darwin’s grandfather. It was the age of the “clockmaker’s universe” and of England’s industrial revolution. Careful observation and experiment became the hallmark of science, but cautious generalization was also encouraged, especially if it led to practical applications.

In other ways, in the eighteenth century, the universe was failing to live up to its promise of simplicity. The Swedish botanist Carl Linnaeus was applying two-word Latin names to more and more species that travelers and voyagers to all corners of the world were discovering. There were a greater number than anyone had ever imagined. Linnaeus saw new plants in his garden, too, and began to suspect, a century before Darwin’s
Origin of Species
, that new species were emerging all the time. He decided that these had always existed in the mind of God but
were just now coming into material existence, a very Platonic way of assuaging his religious scruples.

Carl Linnaeus

No one’s faith in the completeness of universal harmony and the power of numbers surpassed that of the French mathematician Pierre Simon de Laplace, whose lifetime spanned the turn of the eighteenth to the nineteenth century. For him, numbers and mathematics were an unshakably trustworthy bridge to the past and future—if one could know the exact state of everything in the universe at a given moment. His contention was that an omniscient being with that knowledge, with unlimited powers of memory and mental calculation, and with knowledge of the laws of nature, could extrapolate from that the exact state of everything in the universe at any other given moment.

Meanwhile, Pythagorean themes appeared in other than scientific settings. The Whig party praised the governmental structure which brought together king and Parliament by means of “natural” laws, with these words:

What made the planets in such Order move
,

He said, was harmony and mutual Love
.

The Musick of his Spheres did represent

That ancient Harmony of Government
.

That was by no means an isolated allusion. The harmony of the heavens had become a beloved poetic image. William Shakespeare, a contemporary of Galileo and Kepler, had given it beautiful expression in
The Merchant of Venice
, where he had Lorenzo tell Jessica,

. . . soft stillness and the night

Become the touches of sweet harmony . . .

Look how the floor of heaven

Is thick inlaid with patines of bright gold;

There’s not the smallest orb which thou behold’st

But in his motion like an angel sings
.

Such harmony is in immortal souls;

But, whilst this muddy vesture of decay

Doth grossly close it in, we cannot hear it
.

Shakespeare’s contemporary John Davies had written a “justification of dance” titled “Orchestra” that was full of such allusions—not only to the celestial music but also to the four elements. Davies was not making a scientific or philosophical statement. He was correcting one lady’s disparagement of dancing by pointing to its ancient, primordial origins.

Dancing, bright lady, then began to be

When the first seeds whereof the world did spring
,

The fire, air, earth and water did agree
,

By Love’s persuasion, nature’s mighty king
,

To leave their first disordered combating

And in a dance such measure to observe

As all the world their motion should preserve
.

. . . . .

The turning vault of heaven formed was
,

Whose starry wheels he hath so made to pass

As that their movings do a music frame

And they themselves still dance unto the same
.