The cultural potpourri of visual knowledge in portolan charts of the fourteenth century
The analysis of important elements of the visual language of
portolan charts produced in Genoa, Venice and at Majorca during the
fourteenth century has been slowed down by privileging the study of
coastal lines, methods of construction, toponymy, inscriptions and the
questions of origin and priority. Other objects such as rivers, rulers
or riders – to name only a few examples – were either ignored for a
long time or downplayed as fantasies. Assumptions about the movement of
people and knowledge along the shores and across the Mediterranean and
the obstacles for such movements blinded researchers for seeing the
obvious, namely that there did not exist two competing, geographically
defined traditions of portolan chart making during the fourteenth
century, one situated in the Italian towns of Genoa and Venice and the
other at Majorca, but a shared pool of visual and non-visual sources
from which all chart makers drew their knowledge about which rivers to
represent and how to do it. The same applies to representations of
human beings and animals.
I will argue this
thesis by showing that the visual language of individual
fourteenth-century portolan charts consists of elements appropriated
from Byzantine maps of Ptolemy’s Geography, medieval Latin world maps,
regional or/and world maps from Islamic societies and art works from
thirteenth-century Arabic and fourteenth-century Iranian provenance. I
will point to changes between the source material and the images
displayed on the portolan charts and reflect on possible causes for the
transformations.
The multiple translations of Ptolemy in the Middle Ages
In terms of multiple translations of individual texts into Latin in the Middle Ages, Ptolemy scores higher than any other ancient or medieval author of mathematical texts: at least 3 translations of the Almagest (2 from Arabic, one from Greek), 7 translations of the Quadri-partitum (6 from Arabic, one from Greek), and 5 of the Centiloquium (commonly understood to be by Ptolemy). What accounts for this popularity of Ptolemy, and what why were so many Latin versions made (all within the 12th and 13th centuries)? This talk will address the origins of the different translations, the variety of styles that they manifest, the relative characteristics of the Arabic and Greek contributions, and the place that these works eventually establish for themselves in the Latin West.
The Paradox of the Fides Interpres. Remarks on the transformation of Aristotelian Thought in the Middle Ages
It is a well-known fact that translators who rendered Aristotle from Greek into Latin in the twelfth and thirteenth centuries adopted a very literal translation method. Undoubtedly one of the reasons to do so was the respect for Aristotle's authority, whose text should be rendered as faithful as possible in order to preserve its 'virginity'. Yet, by adopting this method, they produced texts that were almost Greek-in-Latin-words and that, as a consequence, were hard to read and to understand. It is thus not surprising that medieval users of these translations developed strategies to deal with them, strategies that were different according to the cultural and linguistic context. In this way the fidus interpres paradoxically contributed to the transformation of Aristotelian thought in the Middle Ages. In this paper, I will discuss some aspects of this transmission and transformation process.
Students and teachers of Latin astronomy from Roman schools to the Carolingian court and cloister into the eleventh century
Astronomical knowledge in the Western Empire was preserved in the early medieval West by royalty, aristocratic landlords, and literate monks desiring basic descriptions of the patterns of stars in the heavens for very practical needs. Travel, navigation, agriculture, nocturnal time-keeping, setting feast days, and establishing an annual calendar were the standard needs through the eighth century. The era of Charlemagne and his dynasty saw the extensive recovery of Roman texts, like Martianus Capella’s, for many disciplines, including astronomy, and their study and teaching ca. 800 – 1050. This new knowledge emerged through the tradition of literary, textual commentary; it included eccentrics and epicycles. Many Carolingian commentaries emphasized diagrams. At times, diagrams could be equivalent to commentary. The improvement and understanding of Roman astronomical texts was enhanced by the new attention to diagrams, with greater comprehension of geometrical techniques and precise data.
The Transformation of Arabic Astrology in Renaissance Humanism
Arabic astrology was available in the Latin West since the twelfth century (and, partially, already in the eleventh century), but the highpoint of its influence, at least in some of its branches, came as late as in the sixteenth century. This is particularly true of general astrology. In this paper, I discuss the Renaissance reception of two originally Persian doctrines that were later developed by the Arabs: revolutions of the years of the world and great conjunctions. In the Renaissance, these doctrines were criticized by Giovanni Pico della Mirandola and be¬came the object of much controversial discussion; they were amply used in annual predictions and apocalyptic prognostications; and they were employed to construct elaborate astrological histories. The question is: in what sense did these Renaissance trends lead to a transformation of the Arabic doctrines?
Parallel Transformations: Two rules of Brahmagupta in the Islamic world and the Dutch republic
This paper concerns Brahmagupta’s rule for the computation of the diagonals and area of a cyclic quadrilateral from its sides. The area rule was stated (in sutras) by Brahmagupta, who did not make clear that it is correct for cyclic quadrilaterals only. It was transmitted from India to the Islamic world. There, the rule was restated according to the rules of Greek geometry and provided with an elegant proof in Greek style, which was attributed to Abu Abdallah al-Shanni (ca. AD 990). The diagonal rule was stated by Brahmagupta but seems to have been unknown in Islamic geometry. It was discovered in Western Europe, possibly more than once. Ludolph van Ceulen (1540-1610) stated it in arithmetical form in the 1580s. The rule was turned into an incorrect geometrical construction in Greek style by Joseph Scaliger (1540-1609), and then into a correct construction (with proof) by Francois Vieta (1540-1603). The proof was misrepresented by Ludolph van Ceulen. Concyclic quadrilaterals provide an example in which the transmissions of mathematics between two cultures (from India to Islam) can be compared to the transmission of mathematics between two communities in one culture (arithmeticians-surveyors working in the vernacular, and scholars working in Latin).
The transfer of Arabic and Hebrew onomancy into Latin: the case of the Alchandreana
The Alchandreana are of particular importance in the history of
Western science, because they represent the earliest Latin translations
and adaptations of Arabic sources (as well as Hebrew sources for that
matter). They are made of seven main texts, all of which were produced
in Catalonia around the middle or in the second half of the tenth
century. Their subject matter is astrology, but astrology of a special
kind, that requires very little astronomical expertise and where the
fundamental elements of the ‘horoscope’ are not based on the date and
time of birth of the individual, but on the numerical value of his/her
name, that is onomancy.
Onomancy supposes a
system of letter-number equivalents. In Greek and in the Semitic
languages, this system is provided by the ‘abjad’ alphabet, where the
first nine letters correspond to the units, the nine following letters
to the tens, and the remaining letters to the hundreds. Onomantic texts
survive at least in Greek, Syriac, Ethiopic, Arabic and Hebrew, and, in
all cases, these texts are accompanied by the ad hoc numerical
alphabet. Of course, the transfer of onomantic techniques between these
linguistic groups does not necessitate significant adaptation or
‘transformation’, since there is a general phonetic agreement between
‘abjad’ alphabets (most letters, i.e. sounds, have the same numerical
value in all these languages, e.g. l=30, m=40, n=50).
The situation is different when the appropriating culture is Latin,
because there is no system of letter-number equivalents in the Latin
language. As is immediately obvious, the making of a Latin ‘abjad’
(i.e. by attributing numbers to letters following the order of the
alphabet) is not a suitable solution, because such a system would bear
no phonetic correspondence with the Arabic and Hebrew ‘abjad’ (results
would be, e.g., l=20, m=30, n=40), with the result that Arabic and
Latin astrologers would calculate different horoscopes for the same
person. The translators and authors of the Alchandreana were of course
aware of this problem. The aim of this talk is to review the various
solutions they put forward to resolve it.
“Indian” and “Yavana”: foreign identity in the transmission of the exact sciences
The name “Indian” was attached to many mathematical concepts and techniques in West Asia/North Africa and Europe starting at the beginning of the medieval period, from the “Indian numbers” and “Indian calculation” adopted by Arab mathematicians to the “Hindoo method” for solving quadratic equations in nineteenth-century algebra texts. Likewise, the Sanskrit term “Yavana”, originally a transliteration of “Ionian (Greek)” but later applied to other foreigners as well, was attached to various foreign importations in the exact sciences. However, not all innovations adopted from or into the Indian tradition were labeled “Indian” or “Yavana” respectively. This paper examines the question of what characteristics marked some borrowed techniques and concepts as "foreign" and stamped them with their outlandish origin, while others were quietly assimilated into "indigenous" learning.
The Formation of the Arabic Pharmacology. Between Transmission and Innovation
Like Islamic medicine more generally, the pharmacological tradition
in Arabic heavily relied on Greek models. But the medicinal plants and
substances available, for instance, in tenth-century Baghdad differed
considerably from those found in classical Athens or imperial Rome.
Moreover, the physicians themselves innovated in a number of ways.
Therefore, the story of Islamic pharmacology is paradoxically one of
both tradition and innovation.
The two foremost
authorities on pharmacy in Greek were undoubtedly Dioscorides and
Galen. Pedianus Dioscorides of Anazarbos (in modern Turkey), who lived
in the middle of the first century AD, composed a work entitled On
Medicinal Substances in five books. He organises his material according
to the types, and attributed certain qualities to each substance. Galen
wrote a substantial monograph on the same subject with the title On the
Powers of Simple Drugs. He often takes his cue from Dioscorides, but
introduces an important innovation: he classifies the qualities,
already found in Dioscorides, according to their strength into degrees
(e.g., ‘warming in the second degree’; ‘moistening in the first
degree’). Both these works were transmitted into the Arabic-speaking
world in the ninth century through translation, and formed the basis of
Islamic pharmacology.
We do find, however, also
change and innovation is the pharmacological literature which developed
in the lands of Islam. On the theoretical level, the ninth-century
polymath al-Kindī, mostly known for his work in the area of philosophy,
refined the classification system of Galen. Galen talked about
qualities in the first, second, third, and fourth degree (one being the
lowest), but did not specify how these qualities interact with each
other in compound drugs. Al-Kindī devised a system in which the power
of the qualities grows exponentially (1, 2, 4, 8) and theorised how
these different degrees of quality interacted in specific compound
drugs. On the level of practice, we see that many new ingredients
entered the formularies written in Baghdad during the ninth and tenth
centuries. Especially ingredients from India proved particularly
popular. In this way, both new pharmacological ideas and new
ingredients were incorporated into the Greek system, thus expanded and
enhanced.
The transfer and transformation of Arabic-Islamic knowledge in mediaeval European maps
Interdisciplinary research of the last decades has shown the strong influence of Arabic-Islamic knowledge on Christian Europe. Especially in the history of medicine, the history of philosophy, and the history of astronomy the impact of Arabic scholars is well documented. The interrelations between the Arabic-Islamic maps and their European counterparts are mentioned occasionally in the research on mediaeval cartography as well. However, the conditions, methods and contents of exchange of cartographical knowledge between the cultures are still to be studied in detail. Based on a case study of Christian-Latin maps from the 12th and the early 14th century, the first purpose of my paper is to analyze the different kinds of Arabic knowledge presented in maps. Secondly the functions of these elements within the maps and within the accompanying texts are to be questioned. Why was Arabic-Islamic knowledge used and attractive for a European mapmaker? In which ways were traditional Western spatial concepts challenged and changed?
In the Wake of Bessarion's Greek Almagest: The Circulation of Ptolemy in the Fifteenth Century
This talk will survey the transformations of knowledge, meaning, and context that followed upon the arrival of Bessarion’s Greek Almagest mss. (and related works) in Italy. Landmarks include George of Trebizond’s 1451 Almagest translation and commentary; the Almagest controversy between George of Trebizond, Bessarion, and Regiomontanus (Epytoma Almagesti and Defensio Theonis contra Georgium Trapezuntium); and George of Trebizond’s astonishing attempts to dedicate his works to Mehmed II (1465-66) in Istanbul and Bessarion’s reaction to them.
Transmission Strategies in Medieval Science: the case of Abraham ibn Ezra (1089/92-1164/67)
Abraham ibn Ezra published influential scientific works in two languages—Latin and Hebrew—in which he transmitted his first-hand knowledge of Arabic science, especially mathematics, astronomy and astrology. This fact offers us the opportunity to compare and contrast the strategies he used to impart his knowledge to the different audiences. Can we detect different transmission techniques? What levels of scientific knowledge did he pre-suppose the educated Jews and Christians had whom he tried to teach? Did Ibn Ezra possibly follow different agendas in his attempt to educate both groups?
From numerical schemes to mechanical gears: a new form of the transmission of Babylonian astronomy to Greece
Abstract: The Antikythera Mechanism, a geared astronomical calculator dating to the first century BC, contains on the lower back side a dial that tracks the months of lunar and solar eclipse possibilities. In this talk I will present recent research on the dial and explore the relationship between the scheme used to generate the eclipse possibilities and similar schemes from Babylonia. The transformation of a Babylonian numerical scheme into a mechanical model provides a new perspective on our understanding of the transmission and adaptation of Babylonian astronomy within the Greek world.
What Remains of the Mathematical Sciences in Syriac – From Sergius of Resh‘aina and Severus Sebokt to Barhebraeus and Patriarch Ni‘matallah
It is known that Syriac translations and Syriac scholars played an important role in the transmission of the sciences from the Greek to the Arabic world. Relatively little, unfortu-nately, remains of the translations and original works of earlier Syriac scholars, but some materials have survived, and further glimpses of what did exist may be gained from works of later authors. The paper will provide a brief survey of the earlier materials that have survived. This will be followed by examples illustrating how further materials can be recovered from the writings of later authors, and a mention, by way of epilogue, of an instance where the Syriac scientific tradition influenced a major scientific event in the West, namely the reform of the calendar by Gregory XIII.
Success and failure of foreign astronomical tables in Byzantium
Tables of Islamic origin - Arabic or Persian - appear in two periods in the Byzantine world: initially in the 11th and 12th centuries, then in the 13th and 14th centuries, although there is no link between the two periods. Each time one can distinguish two categories:
Αt the end of the 14th and in the 15th century the horizons of the
Byzantine world were considerably enlarged. Latin tables make their
appearance (Alfonsine Tables), and a great number of Jewish tables were
introduced, which replaced the Persian Tables.
During all these periods the tables of Ptolemy never ceased to be used,
and the Almagest was more and more studied and commented. In the
manuscripts one sees a mélange of tables, tables adapted for specific
places, and new tables created by George Gemistos Plethon.
In this account we try to outline the reasons for these tendencies, and the changes due to the adaptations.
The Transformation of Algebra from Arabic to Latin to Italian
The means by which the art of algebra was transmitted from Orient to Occident through the translation and dissemination of several key texts has long been established through the publication and editing of these seminal works, but little attention has so far been given to the transformation that algebraic concepts and methods underwent during this process of transmission. Through an analysis of the key words, concepts, procedures, and problems of algebra as it passed from Arabic to Latin and then to Italian, I will show that during this process algebra was in fact transformed from an early practical and quite ancient method of problem solving, thoroughly embedded in its limited cultural context, to an incipient theory of equations that would prove to be capable of universal application to all of mathematics.
