is what was transmitted to us of this explanation in secrecy and hiding.”30 It sounds very much as though Duran were communicating with his students while at the same time living as a Christian. Did they meet clandestinely? Did Duran write out his explanations of ibn Ezra and pass them secretly to one of his students? Striking, too, is the fact that Duran’s students do not seem to have been particularly disturbed by the fact of his baptism. That he was concurrently pretending to be a Christian (and attending mass?) did not apparently disqualify him from providing teachings on biblical interpretation; it only seems to have made their meetings more difficult and so less frequent.
As I have mentioned, Meir Crescas also chose to add one passage not by Duran. To all appearances Crescas’s own, it is a further comment on the appearances of the number seven in the Bible and in particular two aspects of that number that he has found in Duran’s epistle on the hebdomad. The first is that seven represents rest in this harsh world, like the holiday of Shemini Atzeret on the seventh day of Sukkot; Rosh Hashanah and Yom Kippur in the seventh month; the shemittah year, which takes place every seventh year; and the Jubilee year, occurring once every forty-nine (seven times seven) years. His second point is that the square of seven is forty-nine, which represents a cycle of return. Then he offers his own opinions, gleaned from “books and his own mind.” First: seven represents the creation of the world. Second: since man is a social creature, he must devote six days to maintenance of the body, the house, or the city. The Sabbath, on the other hand, is one day set aside from the week to contemplate metaphysics and to cleave to the separate intellect. Meir Crescas would thus seem to share Duran’s philosophical rationalism, a rationalism that thinks of the Sabbath as inculcating belief in God’s creation of the world (through its association with the number seven), and the Sabbath as a time for metaphysical study.
Who were these students of Duran? Although it was common enough for parents who could afford the expense to hire tutors for their young children, it seems plain that Duran’s disciples were long past that age. Meir Crescas himself was no child: in the opening to his essay on the number seven, Duran twice addresses him as gevir, “master,” and treats him in terms of respect and flattery that one can hardly imagine a teacher employing toward a youngster (unless, perhaps, he were of a truly exalted station in life).
Aside from study circles and personal correspondence, another method of transmitting scientific knowledge was via the learned epistle. These, like the letters Duran sent to Meir Crescas, were evidently circulated among interested parties and copied into notebooks or manuscripts.31 One example is Duran’s Ḥilluf ha-yamim ve-haleilot (“The Variation of the Days and the Nights”), a brief treatment of the equation of time—that is, variations in the length of the day according to the time of year and the latitude. The text explains why and how the true solar day varies over the course of the year, and why it is necessary to define a mean solar day for astronomical measurements. Another is his letter to Shealtiel Gracian on the differences between the true and the median conjunction, which, just like the question about the equation of time, explains why astronomy, for its own computational purposes, defines the “mean” behavior of the celestial motion and how this mean relates to the actual, true motion of the earth and planets.
In both these epistles, Duran displays his understanding of the geometrical models used in medieval astronomy. Both topics may have been related to understanding the workings of astronomical tables, which could include tables for the equation of time as well as tables of eclipses (which, when they take place, do so either at conjunction or opposition). The tables of Jacob Bonjorn, for example, astronomer to Pere III, specified for an observer in Perpignan the true conjunctions and oppositions of the sun and moon for the years 1361 through 1391, including the date and time for each conjunction (and opposition), a correction for finding the time of the true conjunction in previous or later cycles, and the true positions of the sun and moon at the time of the conjunction.32
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Current scholarship has argued that in general the imprint of the court as a locus of scientific activity was less important in early modern Spain than it was in Renaissance Italy, Spanish science being more strongly shaped by the needs of a specifically maritime empire.33 In the case of the Jews, however, the court seems to have been the primary factor. Although the flourishing of an important family of Jewish cartographers in fourteenth-century Majorca would seem to offers a prime example of Jewish science shaped by the needs of a maritime kingdom, the Jews in question, as Gabriel Llompart and Jaume Riera have shown, were not cartographers but rather illuminators of maps of the world and nautical charts.34 In this particular case, many of their maps (and elaborately painted compass cases) seem to have been produced as courtly gifts or fashionable luxuries rather than as practical charts used for actual navigation.
Of course, that the Aragonese kingdom drew much of its wealth and prestige from maritime trade and exploration was clearly a factor in the courtly interest in such maps and charts. But in the case of late medieval Iberian Jews, the role of the court in shaping scientific activity seems to have been more direct. Jewish astronomers, physicians, astrologers, instrument makers, clockmakers, and more were all employed by the Iberian monarchs, and royal interest in their skills was precisely what enabled their scientific activity. Jacob Bonjorn, though we know relatively little about him other than his astronomical tables, seems himself to have been a beneficiary of such royal patronage at the Aragonese court in Perpignan.
Joan I’s court was particularly open to the occult and to astrological divination. Profayt Duran’s appointment as astrologer reflects that openness. The skills needed for the practice of astrology—namely, knowledge of the principles of astronomy, the use of observational instruments, and the reading of astronomical tables—are precisely what some of Duran’s students were interested in.35 In the medieval Islamic world, too, scientific work was done for “rulers whose primary interests lay in the practical benefits promised by the practitioners of medicine and astronomy and astrology and applied mathematics.”36 Reflected very clearly in the class notes discussed above are both the technical nature of the science being imparted and the pragmatic nature of what appear to be the students’ scientific ambitions, as well as the fact that they were engaged in using and understanding astronomical tables. Duran’s teaching activities in these documents are thus emblematic of the kind of extrauniversity transmission of knowledge, court patronage, and utilitarian focus that seems to have characterized Iberian science (both Jewish and non-Jewish) at this period. Yet as we will see in Chapter 5, Duran’s scientific correspondence with peers also reflects a nonpragmatic preoccupation—for example, with the relation between the mathematical models of the heavens and sensible reality—that seems to stem from more theoretical and possibly theological concerns. In fact, Duran engaged in scientific activity at many levels, reflecting the interplay of social and economic factors with theological rationalizations and issues of Jewish identity.
One commonly recognized characteristic of the sciences in the Iberian Peninsula is their continued reliance on Arabic astronomy well into the sixteenth century, a conservatism usually attributed to the area’s geographical proximity to North Africa and to what has been called “indelible Arabic cultural influences.”37 In the case of Duran, it is important to point out that Catalonia had no history of Muslim domination, or significant Muslim population. Still, the same conservative impulse has also been associated with Jewish and converso prominence in these fields, since, wherever in Iberia they lived, Jews were presumably the custodians of Arabic science. Indeed, recent quantitative studies confirm a decided preference among Jewish scholars for Arabic over Latin sources when it came to translating philosophical and scientific texts into Hebrew, a preference holding steady in Iberia up to the fifteenth century, when there appears a flurry of Hebrew translations of Latin philosophical texts.38
On this point, what Duran and his students were studying is entirely congruent with the common perception. Apart from the obvious Ptolemy, their sources can be categorized as primarily ninth- through twelfth-century Arabic writers: al-Farghānī, al-Farabi, ibn Sina,
