A Cautious Scientific Spirit
The appetite for scientific inquiry was no greater among scholars and pretenders to learning than among ordinary people. The spirit of the age leaned toward classical Greek and Latin literature, and even the revival of Greek studies tended to overlook Greek science. In arithmetic Roman numerals stood in the way of progress, since they seemed inseparable from Latin culture. The Hindu-Arabic numerals were counted as Islamic, so using them was taken as a sign of irreligion, and they were coldly received in the Christian world, especially north of the Alps. The French auditing office kept using the clumsy Roman figures until the eighteenth century.
Mathematics: From Bradwardine to Oresme
Even so, Thomas Bradwardine, who died of plague in 1349 within months of becoming archbishop of Canterbury (the book's wording here is garbled and has been reconstructed), introduced a number of Arabic trigonometric rules and theorems to English mathematicians. His pupil Richard of Wallingford, abbot of St. Albans, was one of the outstanding mathematicians of the fourteenth century, and his book was the first important work on trigonometry written in western Europe. At forty-three, weeping over a life spent on science instead of theology, he died of leprosy.
Nicole Oresme, despite a busy career in the Church, won distinguished results in several sciences. By developing the use of coordinates and of geometric figures to represent the increase of a function, he paved the way for analytic geometry. His thought touched on a fourth dimension, which he rejected. Like some of his contemporaries he hinted at the law, later Galileo's, that the speed of a falling body increases regularly with the time of its fall. In a commentary on a work of Aristotle he wrote that no experiment can prove that the heavens turn daily and the earth does not; rather, there are arguments that show well that it is the earth that moves daily, not the heavens. He then returned to the Ptolemaic system, but he gave considerable help in opening the road for Copernicus.
Astronomers and Observers
When we remember that the Middle Ages had neither the telescope nor photography for observing and recording the heavenly bodies, we may be proud of the accuracy and intelligence of the astronomers of this age, Muslim, Jewish and Christian alike. After years of personal observation Jean de Lignières fixed the positions of forty-eight stars with an accuracy comparable only to that of Muslim observers, and calculated the obliquity of the ecliptic to within seven seconds of the latest estimates. In 1344 Jean de Murs and Firmin de Beauvais proposed to correct the Julian calendar, which had fallen behind the sun, by omitting one leap day every four years for forty years; but reform was not carried out until 1582, and still needs understanding among religions and nations. William Merle of Oxford recorded the weather on 2,556 days and made meteorology independent of astrology. Unnamed observers and sailors of the fifteenth century discovered the declination of the magnetic needle: it does not point exactly north but leans by a small yet important angle from the true meridian, and this angle varies from place to place, as Columbus found.
Regiomontanus
The greatest figure in the mathematical and astronomical sciences of the age was Johannes Müller, born in 1436 near Königsberg in Lower Franconia and known to history as Regiomontanus. He entered the University of Vienna at fourteen, where Georg von Peurbach introduced German society to humanism and to the latest advances of Italian mathematics and astronomy. Both men matured early and died young: Peurbach at thirty-eight, Müller at forty.
Determined to read Ptolemy's Almagest in the original, Müller went to Italy, studied Greek under Guarino da Verona, and read all the available Greek and Latin texts on astronomy and mathematics. Back in Vienna he taught these subjects with such success that Matthias Corvinus invited him to the University of Buda; he was then called to Nuremberg, where a wealthy patron built him the first European observatory. Müller equipped it with instruments he had made or improved himself. A letter of 1464 to a mathematician friend has the clean fragrance of science: he did not know where his pen would lead him, and if he did not rein it in it would cover all his paper; problems came to his mind one after another, some so alluring that he did not know which to tell his friend first. In 1475 Pope Sixtus IV called him to Rome to reform the calendar, where he lived barely a year.
His short life did not allow more. He had planned treatises on mathematics, physics and astrology and wanted to print the classics of those sciences, but only a part was published. He completed Peurbach's epitome of the Almagest and wrote On Triangles, the first independent book on trigonometry. He seems to have been the first to recommend the tangent in astronomical calculation, and his tables of sines and tangents made Copernicus's calculations easier. His ephemerides were more accurate than any made before, and his method of finding longitude and latitude was a great gift to navigators. In 1474 he published an astronomical almanac giving the daily positions of the stars for the next thirty-two years.
From this book Columbus predicted the lunar eclipse of February 29, 1504 (as the book says) and filled the hungry stomachs of his sailors. Regiomontanus's observations of a comet laid the foundation of modern comet studies. His personal influence in life exceeded his books: his attractive lectures contributed to the intellectual spirit of Nuremberg and made the city famous for charts and nautical instruments. One of his pupils, Martin Behaim, painted on calfskin the oldest surviving terrestrial globe (1492), still kept in the German National Museum at Nuremberg.
The New Geography
The new geography was created by sailors, merchants, missionaries, ambassadors, soldiers and pilgrims, not by geographers. Catalan merchant ships used excellent charts, probably of their own making. Their Mediterranean harbor guides of the fourteenth century were as accurate as the navigational charts of our own time. Since the old trade routes between East and West had fallen into Ottoman hands, European exporters opened new ones through Mongol lands. The Franciscan friar Odoric of Pordenone spent three years in Peking (1323–1326) and recorded his journey to China by way of India and Sumatra and his return by way of Tibet and Persia. Clavijo, as we shall see, left an interesting account of his embassy to the court of Tamerlane. Johann Schiltberger of Bavaria, captured by the Ottomans at Nicopolis in 1396, wandered thirty years through Turkey, Armenia, Georgia, Russia and Siberia and described Siberia in his Travels, the first account of it by a western European. In 1500 Juan de la Cosa, one of Columbus's captains, published a large map of the whole world and for the first time charted the voyages and discoveries of his master, Vasco da Gama and others. In the fifteenth century geography was a drama in motion.
In one respect the most influential geographical treatise of the Middle Ages was the Imago Mundi (1410) of Cardinal Pierre d'Ailly, which stated that the Atlantic could be crossed in a few days if the wind were favorable, and so urged Columbus to his great voyage. It was only one of many treatises this shrewd cleric wrote on astronomy, geography, meteorology, mathematics, logic, metaphysics, psychology and the reform of the calendar and the Church. Reproached for spending much of his time on secular studies, he replied that theologians must keep in step with the advance of science. He half-regarded astrology as a science and, on its basis, predicted great changes for Christendom over the next hundred years and startling events for the world in 1789 (the book's claim).
Physics: Dietrich, Buridan and Albert
The best scientific ideas of the fourteenth century appeared in physics. Dietrich of Freiburg (died about 1311) stated the basis of our modern theory of the rainbow, explaining it as the result of two refractions and one reflection of sunlight in raindrops. Jean Buridan reached great results in physics, and it is a pity he is known only for the story of his ass, which may not be his. Born near Arras before 1300, he studied and taught at the University of Paris. He not only argued for the daily rotation of the earth but rejected, in astronomy, the theory of angelic intelligences by which Aristotle and Aquinas explained the motion and guidance of the heavenly bodies. Buridan said that to account for their motion nothing was needed except the impetus God gave them at the start and the law of motion, that a moving body continues to move until some force stops it. Here Buridan anticipated Galileo, Descartes and Newton. He also said that the same mechanical laws governing the earth govern the motions of planets and stars. These propositions, which seem so easy and obvious today, struck devastating blows at the foundations of medieval belief, and they almost mark the beginning of astrophysics.
Buridan's pupils carried his views to Germany and Italy, and Leonardo da Vinci, Copernicus, Bruno and Galileo were influenced by them. Albert of Saxony took these ideas to the University of Vienna, which he founded (1364), and Marsilius of Inghen to Heidelberg, which he helped found (1386). Albert was the first to reject Aristotle's view that a vacuum is impossible. He helped advance the theory that all bodies have a center of gravity, and anticipated the principles of equilibrium of bodies at rest and of uniformly accelerated fall, which are Galileo's. He also held that the gradual wearing down of mountains by running water and the gradual uplift of the earth's surface by volcanic action form two balancing forces, a geological idea that deeply interested Leonardo.
Practical Mechanics
Moderate advances were made in practical mechanics. The principles of windmill construction were used for pumping water, draining land, pounding grain and other daily tasks. Water power served in refining metals and sawing, in driving furnace bellows and mechanical hammers, and in turning silk-spinning machines. Cannon barrels were cast and bored. Steel was made in notable quantities. In the fourteenth century large tall furnaces were built in northern Europe. Digging wells by machine is mentioned in 1373; in the fifteenth century wire-drawing was common at Nuremberg; and a manuscript of 1348 shows a pump made of several buckets fixed to an endless chain.
In a design by an engineer, Konrad Kyeser (about 1405; the book calls him a Hussite), we find the oldest diagram of the conversion of reciprocating straight motion into circular motion and the reverse: two moving arms alternately turn a cylinder, exactly as pistons turn the crankshaft of a car.
The Mechanical Clock
As industry and trade advanced, better instruments for measuring time became more necessary. Monks and peasants had divided the day into equal parts in every season, so hours were longer in summer than in winter. City life needed uniform divisions, and in the thirteenth and fourteenth centuries clocks were invented that divided the day into equal parts all year round. In some places the hours were numbered from one to twenty-four, as in the military time of our day, and in 1370 some clocks, such as that of San Gottardo in Milan, struck at each hour the total number of hours since the previous day, which was a dizzying excess. In 1375 the day was divided into two halves of twelve hours each.
The mechanical clock worked from a weight that slowly turned a wheel; its turning was regulated by the teeth of an escapement wheel, resistant enough to let the first wheel advance only one tooth in a set time. The first mechanical clocks were placed in bell towers or church towers visible from most of the town. One of the oldest was installed by Richard of Wallingford at St. Albans (1326–1335); it showed not only hours and minutes but the tides and the motions of moon and sun. Later clocks added other arts. The clock of Strasbourg Cathedral (1352) showed a crowing cock, the three Magi, and a human figure marking the proper times for bleeding each part of the body. In the clock of Wells Cathedral a moving sun showed the hours, a small star moving on an inner circle showed the minutes, and another circle showed the days of the month; when the clock struck, four horsemen appeared on a platform above the dial and charged at each other. On a fifteenth-century clock at Jena a buffalo's head opened its fearsome mouth to take a golden apple from a pilgrim's hand, and as it was about to swallow, the man pulled his hand back; this comedy ran hourly for hundreds of years, and the clock still exists. A similar clock installed at Nuremberg in 1506 was badly damaged in the Second World War and resumed its comic show in 1953.
For watches and pocket timepieces the coiled spring replaced the pendulum weight (about 1450): a thin strip of steel wound into a circle or cylinder, which by gradual unwinding did the work the weight did in turning the gears. By the end of the fifteenth century timepieces of every shape were to be found, some as big as a palm and some as small as an almond, and many, like the "Nuremberg eggs" of Peter Henlein (1510), oval. The principles used in the clock, the weight, the escapement and the gear train, were applied to other purposes, and so the mechanical clock became the father of tens of thousands of other machine inventions.
From Alchemy to Chemistry
As the physical sciences thus announced the coming industrial revolution, alchemy gradually turned into chemistry. By the end of the age alchemists had discovered and described bismuth, zinc, sulfur compounds, antimony compounds, volatile alkali and other substances. They distilled alcohol and vaporized mercury. By sublimating sulfur they made sulfuric acid. They prepared ether, aqua regia and a red substance better than the colors now in use. They bequeathed to chemistry the experimental method, the greatest gift of medieval science to the modern world.
Botany, Zoology and the Dead Body
Botany was still limited to farm calendars and herbals describing medicinal plants. Henry of Hesse (1325–1397) thought that new species, especially among plants, arise by natural development from older species, five hundred years before Darwin. The menageries of kings and popes, animal-breeding places, veterinary clinics, treatises on hunting, fishing, bee colonies and silkworms, bestiaries with moral and religious overtones, and books on keeping and training hawks, like the Mirror of Phoebus (1387) by Gaston III, count of Foix, supplied more or less the material needed for zoology.
Anatomy and biology necessarily advanced mostly from the dissection of animals and the wounds of soldiers and, now and then, when the law required it, from a human corpse. Pious Christians had reasonable grounds for opposing the dissection of the human body, even a dead one, for they believed the body must rise whole and intact from the grave on the Day of Judgment. Throughout the fourteenth century getting bodies for anatomical study was difficult; north of the Alps, before 1450, only a very few physicians had seen human dissection. Even so, about 1360 Guy de Chauliac urged the authorities of Avignon, then under the papal court, to hand criminals' bodies over to the medical schools for dissection. Dissections were performed before students at Venice in 1368, Montpellier in 1377, Florence in 1388, Lérida in 1391 and Vienna in 1404, and in 1445 the first dissecting hall was built at the University of Padua. The consequences for medicine were incalculable.