Doctor Profundus

I have written about the Oxford Calculators, four men at Oxford University in the second quarter of the 14th century who made great strides in science and philosophy by treating things like heat and light as if they were quantifiable, even though they did not have ways to measure them. They engaged in "thought experiments" and used mathematics to determine the validity of their points. They were not always right in the end, but they were meticulous in their approach. One of the four was so esteemed that he was called Doctor Profundus, the "Profound Doctor."

Thomas Bradwardine (c.1290-1349) had a reputation as a precocious student at Balliol College. We know he was there by 1321, and later took a doctor of divinity degree. A gifted scholar and theologian, he wrote theories on the Liar Paradox and other logical "insolubles." The Liar Paradox is the statement "I am a liar." For it to be true, the speaker must be a liar; but if it is a true statement then the speaker is not lying. Resolving with logic how such statements can be understood had been tackled for centuries. Bradwardine's work Insolubilia presented complex solutions for puzzles/statements like this.

Like many university men of his day, Bradwardine followed an ecclesiastical career path. After serving as chancellor of the university, he became chancellor of the diocese of London and Dean of St.Paul's. He was also chosen to be chaplain and confessor to Edward III (mentioned in this blog numerous times), celebrating victory masses after campaigns of the Hundred Years War and being entrusted with diplomatic missions. The only time he did not have Edward's support was when John Stratford, Archbishop of Canterbury, died. Bradwardine was elected archbishop by the canons of Canterbury, but Edward opposed the choice, preferring his own chancellor at the time, John de Ufford. When de Ufford died of the Black Death (this was in 1349), Edward allowed Bradwardine to assume the position. Bradwardine had to travel to Pope Clement VI in Avignon for confirmation. but on his return, he succumbed to the Black Death on 26 August. He had been archbishop for 40 days.

That career would not have secured his place in history, however, even with his work attacking the Pelagian heresy. As one of the Oxford Calculators, he developed the "mean speed" theorem and the Law of Falling Bodies before Galileo. He studied "star polygons" (how regular polygons "tile" or fit together in patterns) before Kepler. He developed mnemonic techniques to improve mental abilities, explaining them in De Memoria Artificiali (On Artificial Memory).

One of his theories involved the vacuum of space. Aristotle felt that a vacuum needed a container, because an open space would automatically become filled by matter outside that space flowing into it. Therefore, according to Aristotle, no vacuum could exist above the world, because there was no container beyond the world to maintain the vacuum. Bradwardine was not satisfied with this. The infinity of space was a hot topic in the Middle Ages and Renaissance. His De causa Dei (On the Causes of God) argued that God Himself was infinite, and therefore space beyond our world extended infinitely. (This was different from suggesting that God created separately a space that was infinite.) He also suggested that this infinity could include other worlds that God could create and rule over.

How far are the stars?

Rabbi Levi ben Gerson, also known as Gersonides, lived from 1288-c.1344. He was from a family of scholars: his father, Gerson ben Solomon of Arles, was the author of the Sha'ar ha-Shamayim, an encyclopedia of natural science, astronomy, and metaphysics.* Levi is credited with first mentioning, and possibility inventing, Jacob's Staff. (He references Genesis 32:10 when he describes the device; this is likely the origin of the name.)

At a time when religion, philosophy, astronomy, astrology and science were overlapping (and in some cases, interchangeable), Gersonides' greatest work, which was philosophical, contained his greatest contribution to astronomy. He put twelve years (1317-28) of effort into the Milhamot Adonai ("Wars of the Lord"), whose six books dealt with 1) the soul, 2) prophecy, 3) & 4) god's knowledge of facts and providence, 5) astronomy/astrology, and 6) creation and miracles. Gersonides firmly accepted astrology and the celestial hierarchy of powers inherited from neo-Platonists and pseudo-Dionysius (far too complex to go into here), but he also brought mathematics and observation to his work with extraordinary results for the time.

Postage stamp honoring Gersonides.

Gersonides rejected the Ptolemaic system of epicycles to explain the erratic motion of planets affixed to their crystal spheres surrounding the Earth. According to Ptolemy, epicycles explained the changing size of planets; he said, however, that Mars varies by a factor of six; Gersonides' observations told him that Mars's apparent size varies only two-fold. Gersonides used the Jacob Staff and a camera obscura (pinhole camera) to make careful observations over several years. For Gersonides, 48 crystalline spheres were needed to explain the apparent motion of various heavenly bodies. This expansion of the "physics" of the Ptolemaic model was nothing, however, compared to the actual physical expansion he proposed.

Careful observation with the Jacob Staff, the camera obscura, and math made Gersonides declare heavenly objects to be much farther away than previously calculated. Ptolemy claimed the distance to Venus was 1079 Earth radii; Gersonides estimated it to be 8,971,112 Earth radii away. Ptolemy said the fixed stars were 20,000 Earth radii away; Gersonides estimated them to be at a distance 10 billion times greater.

Pope Clement VI had the "Wars of the Lord" translated into Latin in 1344, making it available to the west. Its impact was minimal, however; we know of a few scholars who were influenced by it, and Kepler asked a friend to send him a copy in the 17th century. But it took Copernicus two centuries later to "confirm" to Western civilization's satisfaction that Gersonides was on the right track.

*As I have mentioned about medieval encyclopediæ before, they were often compilations of previous works; this one drew from Claudius Ptolemy's Almagest and the Morah Nebukim, or "Guide for the Perplexed" of Maimonides. A 1547 edition of ben Solomon's work can be had from Kestenbaum & Company.

Reasoning Wrong

Nicholas of Cusa (c.1400-1464) believed in using reason to determine how the universe worked. He did not exactly take a "scientific" approach: he argued from his understanding of metaphysics and, in some cases, numerology. His guesses, however, were better than some early scholars' observations.

Because he could not accept that God was finite, and since God is not separate from the entirety of the universe, he argued that the universe must by necessity be infinite. Also, because God must provide the center for His own totality, the Earth cannot be at the center of the universe—that would mean Earth was the center of God. Not being at the center of the universe, the Earth cannot be immovable, and it, along with the Sun, must be in motion just like every other observable heavenly body. This idea influenced Giordano Bruno.

Again, denying perfection for anything but God, he would not accept planetary orbits as perfectly circular, paving the way for Kepler (who referred to Nicholas as "divinely inspired") to design elliptical orbits in his planetary theory.

Cusa's thoughts on what we now call infinitesimals in his De Circuli Quadratura (On Squaring the Circle) helped Kepler out when trying to calculate the area of a circle, by picturing it as an infinite series of triangles. Cusa's reasoning for this was that the circle encompassed all other forms. Cusa's and Kepler's work was later important to  Leibniz' Law of Continuity.

Tomorrow: his views on bringing religions together.