The Medieval Philosopher Who Outlined the Basics of the Universe
Seb Falk on the Work of John of Sacrobosco
It is hard to recapture the revelation that Aristotle represented for medieval scholars. He had answers to all the questions they had been asking—and many others they had never thought of posing. It wasn’t just the breadth of his studies—from the placement of a crocodile’s tongue to the most fundamental structure of knowledge: it was the analytical clarity with which he laid out the thought processes that would lead to a satisfying answer. Medieval scholars were so awestruck at his achievements that they couldn’t even name him. They simply called him the Philosopher.
To be sure, it was not easy to read Aristotle. Medieval natural philosophers were used to the Timaeus, by Aristotle’s teacher, Plato. The first half of this beautifully written description of the divinely ordered cosmos was translated into Latin in the fourth century, and the translator added a detailed commentary. Although the Timaeus departs slightly from the entertaining dialogue form of Plato’s other works, it is still an absorbing read, as the legend of the lost city of Atlantis leads into analysis of subjects like the four elements (fire, air, water and earth), the nature of time, the relation between the human body and the soul, and how our vision works. Aristotle’s works were more voluminous, and more obscure. In part this was because, unlike Plato’s dialogues, they were not written and refined for publication but were more like rough lecture notes. In part, too, it was a result of the translation process. The ancient Greek works had changed as they were translated through Arabic, and sometimes Spanish too. And many translators, including Gerard of Cremona, preferred to translate word by word, producing texts which, while faithful to the originals, were hardly written in flowing classical Latin.
If students—who could often join the foundational Arts Faculty aged as young as fourteen—struggled to know where to start with shelves of impenetrable Aristotelian prose, help was at hand. Like today’s undergraduates, they had textbooks. Pithy summaries of the great philosophers made their ideas accessible, and the clearest of these became bestsellers. Even as the curriculum of the Arts Faculty was completely remodeled in the image of Aristotle’s works—accommodating the “three philosophies” of natural and moral philosophy and the more fundamental metaphysics alongside the old trivium and quadrivium—these summaries became the set texts for the masters’ lecture series.
So before the students dived into Aristotle’s Physics, On the Heavens, On Generation and Corruption, Meteorology, On the Soul, On Animals, and his shorter works on psychology, respiration and ageing, all required as part of the natural philosophy course, they could warm up with the two introductory manuals of astronomy and cosmology: De Sphera (On the Sphere ) and Computus. Each of these was allotted eight days by the Oxford timetablers. The Computus covered all the calendrical calculation we tried in the last chapter. It came in various versions, each adopted and updated as the science of the cycles developed. There were multiple texts called The Sphere too, but one was head and shoulders above the others for its accessibility and popularity. It was written in about 1230 by John of Sacrobosco.
Nothing much is known about this John. Forty years after his time, Robertus Anglicus, whom we last met chronicling the inventions of clockmakers, wrote an extensive commentary on Sacrobosco’s Sphere for his students at the university of Montpellier. Near the beginning he asserted that Sacrobosco was, like him, English, but his claim has not been proved. The wandering antiquary John Leland (who, on his scholarly travels in the 1530s, was the last person to describe the St Albans clock before its destruction) tried to pin down the name—”Sacrobosco”—holy wood—to a location. Failing to find settlements named Holywood on the map of England (though they existed in Northern Ireland and south-west Scotland), Leland opted to claim Sacrobosco for the Yorkshire town of Halifax—rather implausibly, since Halifax actually means “holy hair.”
While we cannot know where Sacrobosco was born, we do know where he was buried: in the de facto University church of Paris, in a tomb adorned with an astrolabe. Evidently, by his death he was an established university master. He wrote a brief introduction to algorismus, drawing on the Arithmetic of Boethius, and his Computus was a commonly set text on that subject. But his Sphere was by far his best-known work, and still survives in hundreds of handwritten medieval copies. Monk-students, who arrived at university rather older and better educated than other undergraduates, were often exempted from the initial arts course. But it is clear from the number of monastic manuscripts which include the Sphere that canons and monks like John Westwyk were keen to work through this carefully arranged primer anyway.
In a beautifully simple text, whose four chapters together are about the length of one chapter of this book, Sacrobosco set out the basics of medieval knowledge of the universe. He drew on a range of sources, especially Ptolemy and al-Farghani (Alfraganus)—another Abbasid astronomer whose work Gerard of Cremona had translated—but also quoted classical poets like Ovid and Virgil. He began with Euclid’s geometry, defining what a sphere is, and then described the spheres of the heavens and Earth. A consummate teacher, he built up layer on layer of complexity, explaining the varied motions of the stars and planets, the ways that day-lengths and stellar visibility depended on your location and the season, and how eclipses work.
Students and masters read Sacrobosco’s Sphere avidly for hundreds of years after his time. In Oxford’s oak-panelled halls lecturers worked through it systematically, expounding Sacrobosco’s succinct prose for the benefit of their fascinated pupils. Some wrote up their lectures as extended written commentaries on the core text, so we have a good idea of the ground they covered. Let us take a moment to imitate those scholars and have a closer look at one part of the treatise. We shall focus on Sacrobosco’s explanation that the Earth is round.
Today it is widely assumed that medieval scholars thought the world was flat, but that is a myth largely invented in the 19th century. It was popularized in a work by Washington Irving that can be charitably called “imaginative history,” The Life and Voyages of Christopher Columbus, published in 1828. Irving pictured his hero, inspired by “natural genius,” arguing that it was possible to sail westward to the Indies, against fierce objections from ignorant churchmen at the Spanish court. Irving’s story was picked up by anti-religious writers and used as an emblem of a general conflict that they imagined was being waged between science and religion, in which a few brave individuals struggled against the suffocating power of the Church. No such simplistic conflict existed. In fact, Columbus’ geographical assumptions were based on the work of a contemporary of John Westwyk, the Paris master and later cardinal Pierre d’Ailly, who himself drew heavily on Sacrobosco’s Sphere.
Sacrobosco explains that the heavens are a huge sphere, with the planets set in smaller spheres nested one inside another (like a Russian doll). Beyond the seven planets—which, you will recall, included the Sun and the Moon—were two outer spheres: the fixed stars and the “first moved,” the engine of the daily rotation of the heavens. The innermost planetary sphere, with the shortest cycle, was the Moon. Citing Aristotle’s Meteorology, Sacrobosco placed four more spheres within the sphere of the Moon, for the four elements: first fire, then air, then water, and finally, the heaviest element, earth, at the centre of everything.
As evidence for the earth’s roundness, Sacrobosco pointed out that the stars rise and eclipses occur at different times as you travel east or west. And as you travel north or south, he added, you see different stars altogether. If the earth was flat, he explained, the same stars would rise at the same time for all observers. It only seems flat, he said, “because of its great size.” Yet compared to the firmament, it must be infinitesimally small, since exactly half of the sky and stars are always above the horizon. The seas, like the earth, must also be round, since a lookout stationed at the top of a ship’s mast can see further than someone standing on deck. Also, Sacrobosco suggested logically, just as water droplets form beads on leaves, so the seas “naturally seek a round shape.” Aristotle had one more argument, which Sacrobosco did not use: whenever we watch a lunar eclipse, the Earth’s shadow on the Moon is always round.
The next question, for a consummate geometer like Sacrobosco, was obvious: if the Earth is a sphere, we can easily work out its size. The oldest estimate of the Earth’s size appears in Aristotle’s treatise On the Heavens, written in the fourth century bce. There the Philosopher notes that “those mathematicians who try to calculate the size of the Earth’s circumference arrive at the figure 400,000 stades.” Aristotle only mentions this to support his arguments that the Earth must be round—otherwise it would not have a circumference at all—and that it is small relative to the stars. A stadion was the length of a stadium—rather like journalists’ habit of estimating areas in terms of today’s football fields—but that length could vary, between about an eighth and a tenth of a mile. Aristotle’s estimate thus came to 40,000 or 50,000 modern miles. The true circumference is about 25,000 miles, so Aristotle’s figure was of the right order of magnitude, albeit not particularly close.
Aristotle was rarely interested in numbers—his specialism was explaining causes, answering “how” and “why” questions. So it is hardly surprising that he didn’t explain the methods “those mathematicians” had used. Towards the end of the following century, however, another Greek philosopher named Eratosthenes did explain how he had found the Earth’s size. When Sacrobosco described, with his characteristic pithy clarity, how any student could carry out the calculation on a clear starry night, he cited Eratosthenes as an authority for his own estimate: 252,000 stades.
Those 252,000 stades are extremely close to the correct value. Where did they come from? Not from precise measurement, but by a chain of educated guesses—that was all the Greek astronomers wanted. Eratosthenes observed that at the ancient city of Syene, on the Nile in southern Egypt, the Sun was directly overhead at noon on the summer solstice. In other words, Syene lay on the tropic of Cancer. At the same time in Alexandria, the Sun was not quite overhead. If, looking up at the sky, he imagined a vertical circle which ran down from that zenith to the southern horizon, kept descending to a point directly below his feet, and came back up the other side to rise above the northern horizon and reach all the way to the zenith once more, the Sun was just a fiftieth of the way round that circle.
So, since the Earth was a sphere, the distance from Syene to Alexandria must be a fiftieth of the way round the Earth. Here Eratosthenes assumed that Alexandria, where the winding River Nile fanned out into the Mediterranean Sea, was due north of Syene. He took the distance between the two cities to be 5,000 stades. If one fiftieth of the Earth’s circumference was 5,000 stades, the full circumference must be about 250,000. Later astronomers adjusted it to 252,000 stades, simply because that number is easily divisible by 60 and 360. With that convenient rounding, Sacrobosco could say that, for every degree of the Earth’s circumference, the distance is 252,000 ÷ 360 = 700 stades. (A rather smaller—and less accurate—estimate of 500 stades per degree, reported by Ptolemy and Alfraganus, was seized on by Columbus to boost the feasibility of his proposed voyage west to the Indies.)
Neither Eratosthenes nor Sacrobosco saw any need to measure these distances. Eratosthenes’ figures of a fiftieth of a circle for the Sun’s zenith distance at Alexandria, and 5,000 stades to Syene, are clearly just round numbers. He certainly did not hire someone to pace out the distance step by step, as some fanciful retellings have claimed. His point—echoed by Sacrobosco—is simply that the Earth could be measured, with knowledge of its sphericity and the basic techniques of geometry.
From The Light Ages: The Surprising Story of Medieval Science by Seb Falk. Used with the permission of W.W. Norton & Company. Copyright © 2020 by Seb Falk. All rights reserved.
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