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Macmillan Childrens Publishing Group

Proof!

How the World Became Geometrical

Amir Alexander

Scientific American / Farrar, Straus and Giroux

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PART I

HOW THE WORLD BECAME GEOMETRICAL


1.

THE MIRROR IMAGE


THE GATES OF THE BAPTISTERY

By the early 1400s the Baptistery of St. John at the heart of Florence was already ancient, its origins lost in the mists of time. According to Giovanni Villani, the city’s medieval chronicler, the structure was originally a Roman temple dedicated to Mars, the god of war. This seemed entirely appropriate to the proud Florentines, who believed their city had been founded by the rugged veterans of Julius Caesar’s legions. Modern archaeology has revealed that this was almost certainly not the case, and that the Church of St. John (or San Giovanni, as it was known) was built from the ground up as a Christian house of worship. Beyond this, however, experts are divided even to this day: Was the striking octagonal edifice built in the late fifth century, when the Church sought to extend its reign as the Roman Empire crumbled around it? Was it a monument to the conversion of the Lombards, the Germanic tribe that ruled over much of Italy in the seventh century? Or was it an expression of burgeoning civic pride when, in the eleventh century, the city of Florence emerged from centuries of obscurity to become a bustling hub of commerce and culture?1

We do not know, as the thick walls of the baptistery hold tight to their secrets. For a thousand years the walls bore witness as each and every Florentine newborn passed through their gates. In a soothing rhythm of Christian life, men and women, rich and poor, commoners and aristocrats of ancient lineage, all were baptized in the shadow of those walls and joined together in a community of the faithful. Other events were far less tranquil, as, generation after generation, the walls stood silently by while the violent civic life of an Italian city-state raged around them. Beginning around the dawn of the second millennium C.E., as Florence rose in power and wealth, life in the city swung wildly between years of peace and prosperity and periods of brutal strife and civil war. The ancient families of the countryside, who ruled Florence during the Dark Ages, battled for power with the wealthy merchants and bankers who increasingly came to dominate the city’s economic life. Rival clans of magnates turned their city dwellings into fortified towers and fought pitched battles in the streets, leading to the victory of some and the banishment of others. Guelphs, or champions of the Papacy, fought Ghibelines, who defended the rights of the German emperor, until the Ghibelines were finally driven out, never to return. And members of the working class, full-blooded Florentines who labored in the service of their wealthy brethren, rose up repeatedly to assert their political and economic rights. Wise to the danger, the squabbling clans of the city’s elite would put aside differences long enough to crush the popular uprisings and ensure that the “republic” would continue to be ruled by those rich in money or land.

But on one summery day, in about the year 1413, the ancient walls of the baptistery were treated to a scene unlike any they had witnessed before.2 It began unremarkably, as a short man in his mid-thirties, with a balding head and aquiline nose, marched briskly through the chill morning air and headed to the monumental doorway of the Duomo, across the piazza from the baptistery.

Known officially as the Cattedrale di Santa Maria del Fiore (Cathedral of St. Mary of the Flower), the Duomo was the pride of Florence—its main church and one of the largest and grandest in all of Christendom. Compared to the ancient and myth-shrouded baptistery, the Duomo was then practically new, a recent addition to the Florentine skyline and as yet an incomplete one. Nearly 120 years after its first stone was laid down, in 1296, the great cathedral was still missing its distinctive giant dome, so familiar to visitors today. Although it had been envisioned by the cathedral’s architects as a key element in their design, no dome on such a scale had ever been built, and its construction had so far exceeded the capabilities of the best master craftsmen of the day.

In due time the man walking past the baptistery that morning would change all that, for he was Filippo Brunelleschi (1377–1446), who would one day make his name as the designer and builder of the great dome. But on that day in 1413 Brunelleschi had other matters on his mind: he walked directly under the great archway of the Duomo’s main doorway as if he were about to enter, then abruptly turned around to face the baptistery. In his hand he held a modest painting, about one foot square, and a mirror of roughly the same size.

Anyone standing close to Brunelleschi that day in the shadow of the archway would have noted with surprise that the painting was not, as one might expect, a religious scene of the kind favored by the artists of the period. It was, rather, a simple depiction of the precise view from the spot where Brunelleschi was standing: the Baptistery of St. John as seen from the entrance to the Duomo, except that in the place where the sky would normally be the painting was coated with burnished silver, reflecting anything passing before it. Even more surprisingly, near the center of the painting, at the precise point depicting the baptistery’s wall opposite the cathedral’s doorway, there was a small hole. Brunelleschi raised the painting to his face and peered through the hole at the octagonal walls of the baptistery across the piazza. As puzzled onlookers watched, he raised the mirror and placed it in front of the painting, so that all he could see through the hole was the painting’s own reflection. What, they must have wondered, was he doing?

While Brunelleschi in 1413 had yet to acquire the towering stature he would reach in later years, he was, nonetheless, already a well-known figure in Florence. A master goldsmith by trade, young Filippo got his first chance to make his mark in 1401, when at twenty-four he was a leading contender in a competition to design a set of giant bronze doors for the baptistery.3 Brunelleschi’s entry, depicting the sacrifice of Isaac and his rescue by God’s angel, was fiercely expressive and impressed both the judges and the Florentine public. But he nevertheless lost the competition to the even younger craftsman Lorenzo Ghiberti (1378–1455), whose design was elegant and refined rather than dramatic.

The contrast between the two rivals extended beyond their artistic sensibilities. Ghiberti was not only a brilliant craftsman but also a sociable and amiable man with a penchant for quiet diplomacy. Throughout the competition he reached out to fellow artisans, consulted them, and incorporated their suggestions in his design. Brunelleschi, in contrast, had already earned a reputation as irascible, arrogant, and suspicious, a difficult man jealous of his methods and his credit. “To disclose too much of one’s inventions and achievements is one and the same thing as to give up the fruit of one’s ingenuity,” he told the engineer Mariano di Jacopo Taccola years later, and there is no doubt he practiced what he preached.4 He spent the year allotted for the competition working alone, in secrecy, never letting anyone but his closest companions see what he was doing. As a result, when the time came to pick the winner, Ghiberti had many friends among the judges and in the community at large, whereas the taciturn Brunelleschi was just as he liked it—alone.5

What happened next is much in dispute. Ghiberti, years later, claimed that he won the competition outright: “To me was conceded the palm of victory, by all the experts and by all those who had competed with me. Universally I was conceded the glory without exception.” Yet exception there surely was: according to Brunelleschi’s contemporary and biographer Antonio Manetti (1423–1497), when the time came to choose a winner the judges were already well familiar with Ghiberti’s panels, and could not believe any of his competitors could do better. Once they saw Brunelleschi’s striking design they realized their mistake, but felt unable to go back on what they had well-nigh announced—that Ghiberti was the clear winner. They settled on a compromise, declaring both men winners and commissioning them to work together. Ghiberti agreed; Brunelleschi, characteristically, refused, and walked away from the project, leaving the design and casting of the baptistery doors in his rival’s hands.6

THE SPELL OF THE ANCIENTS

Devastated by his loss in a competition he thought he deserved to win, Brunelleschi did not linger long in the shadow of his triumphant rival. Instead, he traveled to Rome, where he spent much of the next fifteen years far from the jealousies and rivalries of his native city. And if disappointment was enough to keep him away from the city on the Arno, it was something else that drew him inexorably to Rome: an obsession with for the ancient classical civilizations, which Brunelleschi shared with many of his most distinguished contemporaries.

This passion for ancient Greece and Rome had spawned a movement known as humanism, which had begun in the previous century but was now sweeping through Italy and reshaping the intellectual landscape.7 For the medieval schoolmen, ensconced in the famous European universities, the humanists had little but contempt. For all their learning, the schoolmen, in the humanists’ opinion, relied almost exclusively on a single ancient source, the writings of Aristotle, which they had by secondary (and, according to the humanists, corrupt) translation from Arabic. Even worse, the schoolmen’s very language, medieval Latin, was but a pale shadow of the rich and flowery language of Cicero and Livy. Little wonder that the schoolmen were obsessed with abstruse Aristotelian commentary and pointless theological debate. On the questions that the humanists believed truly mattered—how to live a good, moral, and worthy life—the medieval schoolmen were silent. There was nothing for the humanists but to make a clean break with their medieval forefathers and draw directly from the ancients.8

In their quest to recover ancient learning, the humanists studied philosophers such as Plato and Seneca, scientists such as Archimedes and Ptolemy, historians such as Polybius and Tacitus, and poets including Virgil and Ovid. But of all the ancient authors none was more greatly admired than the Roman statesman Marcus Tullius Cicero (106–43 B.C.E.), who embodied the humanist ideal to perfection. Cicero was not only the greatest of Roman orators, and a moral philosopher of note, but also a man who put his teachings to the test. A lifelong participant in Rome’s cutthroat politics, he saved the state from a dangerous conspiracy while serving as consul and was hailed by the Senate as Pater Patriae (“Father of the Country”). One could ask for no finer model of linguistic purity, literary prowess, and civic engagement.

* * *

FOR THE MOST PART, HUMANISM was a literary and philosophical movement focused on books and texts. Itinerant scholars such as Poggio Bracciolini traveled far and wide in an effort to locate lost ancient works that might be hidden away in the monastic libraries of Europe. Seeking out the most authentic versions, they worked hard to restore the texts to their pristine glory in their original tongues, mostly Greek and classical Latin, but also Hebrew, Arabic, and other languages. These newly recovered texts would then circulate among the humanists, replacing existing (and allegedly corrupt) medieval versions if such existed, or adding new ancient sources if they did not.

Brunelleschi, however, was not a literary scholar. A brilliant artist, architect, and engineer, he was not a man to spend his days poring over ancient manuscripts. For his humanist friends the passion for the ancients meant recovering the writings of Plato, Cicero, and Lucretius and returning them to their original brilliance. For the practical-minded Brunelleschi it meant something else: studying the physical traces of the ancients—the buildings, aqueducts, roads, and sculptures that they left behind. The humanists traveled to far-flung corners of Europe in pursuit of their original texts. Brunelleschi, in contrast, headed straight to the capital of the ancient world and the home of its greatest monuments: Rome.9


Copyright © 2019 by Amir Alexander