Is God a Mathematician? (12 page)

As the dark clouds were gathering on the horizon, Galileo continued to believe that reason would prevail—a huge mistake when it comes to challenging faith. Galileo published his
Dialogue Concerning the Two Chief World Systems
in February of 1632 (figure 20 shows the frontispiece of the first edition). This polemical text was Galileo’s most detailed exposition of his Copernican ideas. Moreover, Galileo argued that by pursuing science using the language of mechanical equilibrium and mathematics, humans could understand the divine mind. Put differently, when a person finds a solution to a problem using proportional geometry, the insights and understanding gained are godlike. The church’s reaction was swift and decisive. The circulation of the
Dialogue
was forbidden as early as August of the year of its publication. In the following month, Galileo was summoned to Rome to defend himself against the charges of heresy. Galileo was brought to trial on April 12, 1633, and he was found “vehemently suspect of heresy” on June 22, 1633. The judges accused Galileo “of having believed and held the doctrine—which is false and contrary to the sacred and divine Scriptures—that the Sun is the center of the world and does not move from east to west and that the Earth moves and is not the center of the world.” The sentence was harsh:

The devastated seventy-year-old Galileo could not withstand the pressure. His spirit broken, Galileo submitted his letter of abjuration, in which he committed to “abandon completely the false opinion that the Sun is at the center of the world and does not move and that the Earth is not the center of the world and moves.” He concluded:

Figure 20

Galileo’s last book,
Discourses and Mathematical Demonstrations Concerning Two New Sciences,
was published in July 1638. The manuscript was smuggled out of Italy and was published in Leiden in Holland. The content of this book truly and powerfully expressed the sentiment embodied in the legendary words “
Eppur si muove
” (“And yet it moves”). That defiant phrase, commonly put in Galileo’s mouth at the end of his trial, was probably never uttered.

On October 31, 1992, the Catholic Church finally decided to “rehabilitate” Galileo. Recognizing that Galileo was right all along, but still avoiding direct criticism of the Inquisition, Pope John Paul II said:

Newspapers around the world had a feast. The
Los Angeles Times
declared: “It’s Official: The Earth Revolves Around the Sun, Even for the Vatican.”

Many were not amused. Some saw this
mea culpa
by the church as far too little, far too late. The Spanish Galileo scholar Antonio Beltrán Marí noted:

To be fair, the Pope found himself in a no-win situation. Any decision on his part, whether to ignore the issue and keep Galileo’s condemnation on the books, or to finally acknowledge the church’s error, was likely to be criticized. Still, at a time when there are attempts to introduce biblical creationism as an alternative “scientific” theory (under the thinly veiled title of “intelligent design”), it is good to remember that Galileo already fought this battle almost four hundred years ago—and won!

In one of the seven skits in the movie
Everything You Always Wanted to Know About Sex* (*But Were Afraid to Ask),
Woody Allen plays a court jester who does comic routines for a medieval king and his entourage. The jester has the hots for the queen, so he gives her an aphrodisiac, hoping to seduce her. The queen does become attracted to the jester, but alas, she has a huge padlock on her chastity belt. Faced with this frustrating situation in the queen’s bedroom, the jester utters nervously: “I must think of something quickly, before the Renaissance will be here and we will
all
be painting.”

Jokes aside, this exaggeration is an understandable description of the events in Europe during the fifteenth and sixteenth centuries. The Renaissance has indeed produced such a wealth of masterpieces in painting, sculpture, and architecture that to this very day, these astonishing works of art form a major part of our culture. In science, the Renaissance witnessed the heliocentric revolution in astronomy, led by Copernicus, Kepler, and especially Galileo. The new view of the universe afforded by Galileo’s observations with the telescope, and the insights gained from his experiments in mechanics, perhaps more than anything else motivated the mathematical developments of the following century. Amidst the first signs of crumbling of the Aristotelian philosophy and the challenges to the Church’s theological ideology, philosophers started to search for a new foundation on
which to erect human knowledge. Mathematics, with its seemingly certain body of truths, provided what appeared to be the soundest base for a new start.

The man who embarked on the rather ambitious task of discovering a formula that would somehow discipline all rational thought and unify all knowledge, science, and ethics was a young French officer and gentleman named René Descartes.

A Dreamer

Many regard Descartes (figure 21) as both the first great modern philosopher and the first modern biologist. When you add to these impressive credentials the fact that the English empiricist philosopher John Stuart Mill (1806–73) characterized one of Descartes’ achievements in mathematics as “the greatest single step ever made in the progress of the exact sciences,” you begin to realize the immensity of Descartes’ power of intellect.

René Descartes was born on March 31, 1596, at La Haye, France. In honor of its most celebrated resident, the town was renamed La Haye–Descartes in 1801, and since 1967 it is known simply as Descartes. At the age of eight, Descartes entered the Jesuit College of La Flèche, where he studied Latin, mathematics, classics, science, and scholastic philosophy until 1612. Because of his relatively fragile health, Descartes was excused from having to get up at the brutal hour of five a.m., and he was allowed to spend the morning hours in bed. Later in life, he continued to use the early part of the day for contemplation, and he once told the French mathematician Blaise Pascal that the only way for him to stay healthy and be productive was to never get up before he felt comfortable doing so. As we shall soon see, this statement turned out to be tragically prophetic.

After La Flèche, Descartes graduated from the University of Poitiers as a lawyer, but he never actually practiced law. Restless and eager to see the world, Descartes decided to join the army of Prince Maurice of Orange, which was then stationed at Breda in the United Provinces (The Netherlands). An accidental encounter in Breda was to become very significant in Descartes’ intellectual development.
According to the traditional story, while wandering in the streets, he suddenly saw a billboard that appeared to present a challenging problem in mathematics. Descartes asked the first passer-by to translate the text for him from Dutch into either Latin or French. A few hours later, Descartes succeeded in solving the problem, thus convincing himself that he really had an aptitude for mathematics. The translator turned out to be none other than the Dutch mathematician and scientist Isaac Beeckman (1588–1637), whose influence on Descartes’ physico-mathematical investigations continued for years. The next nine years saw Descartes alternating between the hurly-burly of Paris and service in the military corps of several armies. In a Europe in the throes of religious and political struggle and the commencement of the Thirty Years’ War, it was relatively easy for Descartes to find battles or marching battalions to join, be it in Prague, Germany, or Transylvania. Nevertheless, throughout this period he continued, as he put it, “over head and ears in the study of mathematics.”

Figure 21

On November 10, 1619, Descartes experienced three dreams that not only had a dramatic effect on the rest of
his
life, but which also marked perhaps the beginning of the modern world. When later describing the event, Descartes says in one of his notes: “I was filled
with enthusiasm and discovered the foundations of a wonderful science.” What were these influential dreams about?

Actually, two were nightmares. In the first dream, Descartes found himself caught in a turbulent whirlwind that revolved him violently on his left heel. He was also terrified by an endless sensation of falling down at each step. An old man appeared and attempted to present him with a melon from a foreign land. The second dream was yet another vision of horror. He was trapped in a room with ominous thunderclaps and sparks flying all around. In sharp contrast to the first two, the third dream was a picture of calm and meditation. As his eyes scanned the room, Descartes saw books appearing and disappearing on a table. They included an anthology of poems entitled
Corpus Poetarum
and an encyclopedia. He opened the anthology at random and caught a glimpse of the opening line of a poem by the fourth century Roman poet Ausonius. It read:
“Quod vitae sectabor iter?”
(“What road shall I pursue in life?”). A man miraculously appeared out of thin air and cited another verse:
“Est et non”
(“Yes and no” or “It is and it is not”). Descartes wanted to show him the Ausonius verse, but the entire vision disappeared into nothingness.

As is usually the case with dreams, their significance lies not so much in their actual content, which is often perplexing and bizarre, but in the interpretation the dreamer chooses to give them. In Descartes’ case, the effect of these three enigmatic dreams was astounding. He took the encyclopedia to signify the collective scientific knowledge and the anthology of poetry to portray philosophy, revelation, and enthusiasm. The “Yes and no”—the famous opposites of Pythagoras—he understood as representing truth and falsehood. (Not surprisingly, some psychoanalytical interpretations suggested sexual connotations in relation to the melon.) Descartes was absolutely convinced that the dreams pointed him in the direction of the unification of the whole of human knowledge by the means of reason. He resigned from the army in 1621 but continued to travel and study mathematics for the next five years. All of those who met Descartes during that time, including the influential spiritual leader Cardinal Pierre de Bérulle (1575–1629), were deeply impressed with his
sharpness and clarity of thought. Many encouraged him to publish his ideas. With any other young man, such fatherly words of wisdom might have had the same counterproductive effect that the one-word career advice “Plastics!” had on Dustin Hoffman’s character in the movie
The Graduate,
but Descartes was different. Since he had already committed to the goal of searching for the truth, he was easily persuaded. He moved to Holland, which at the time seemed to offer a more tranquil intellectual milieu, and for the next twenty years produced one tour de force after another.

Descartes published his first masterpiece on the foundations of science,
Discourse on the Method of Properly Guiding the Reason and Seeking for Truth in the Sciences,
in 1637 (figure 22 shows the frontispiece of the first edition). Three outstanding appendices—on optics,
meteorology, and geometry—accompanied this treatise. Next came his philosophical work,
Meditations on First Philosophy,
in 1641, and his work on physics,
Principles of Philosophy,
in 1644. Descartes was by then famous all over Europe, counting among his admirers and correspondents the exiled Princess Elisabeth of Bohemia (1618–80). In 1649 Descartes was invited to instruct the colorful Queen Christina of Sweden (1626–89) in philosophy. Having always had a soft spot for royalty, Descartes agreed. In fact, his letter to the queen was so full of expressions of courtly seventeenth century awe, that today it looks utterly ridiculous: “I dare to protest here to Your Majesty that she could command nothing to me so difficult that I would not always be ready to do everything possible to execute it, and that even if I had been born a Swede or a Finn, I could not be more zealous nor more perfectly [for you] than I am.” The iron-willed twenty-three-year-old queen insisted on Descartes giving her the lessons at the ungodly hour of five o’clock in the morning. In a land that was so cold that, as Descartes wrote to his friend, even thoughts froze there, this proved to be deadly. “I am out of my element here,” Descartes wrote, “and I desire only tranquility and repose, which are goods the most powerful kings on earth cannot give to those who cannot obtain them for themselves.” After only a few months of braving the brutal Swedish winter in those dark morning hours that he had managed to avoid throughout his entire life, Descartes contracted pneumonia. He died at age fifty-three on February 11, 1650, at four o’clock in the morning, as if trying to avoid another wake-up call. The man whose works announced the modern era fell victim to his own snobbish tendencies and the caprices of a young queen.

Figure 22

Descartes was buried in Sweden, but his remains, or at least part of them, were transferred to France in 1667. There, the remains were displaced multiple times, until they were eventually buried on February 26, 1819, in one of the chapels of the Saint-Germain-des-Prés cathedral. Figure 23 shows me next to the simple black plaque celebrating Descartes. A skull claimed to be that of Descartes was passed from hand to hand in Sweden until it was bought by a chemist named Berzelius, who transported it to France. That skull is currently at the Natural Science Museum, which is part of the Musée de l’Homme
(the Museum of Man) in Paris. The skull is often on display opposite the skull of a Neanderthal man.

Figure 23

A Modern

The label “modern,” when attached to a person, usually refers to those individuals who can converse comfortably with their twentieth (or by now, twenty-first) century professional peers. What makes Descartes a true modern is the fact that he dared
to question
all the philosophical and scientific assertions that were made before his time. He once noted that his education served only to advance his perplexity and to make him aware of his own ignorance. In his celebrated
Discourse
he wrote: “I observed with regard to philosophy, that despite being cultivated for many centuries by the best minds, it contained no point which was not disputed and hence doubtful.” While the fate of many of Descartes’ own philosophical ideas was not going to be much different in that significant shortcomings in his propositions have been pointed out by later philosophers, his fresh skepticism of even the
most basic concepts certainly makes him modern to the core. More important from the perspective of the present book, Descartes recognized that the methods and reasoning process of mathematics produced precisely the kind of
certainty
that the scholastic philosophy before his time lacked. He pronounced clearly: