Towards the EIDA corpus for the history of astronomical diagrams
Tuesday, 28 – Thursday, 30 March 2023
Observatoire de Paris, Salle du Conseil
Organisation: Scott Trigg, Divna Manolova, Samuel Gessner, Matthieu Husson
Rationale
Recent scholarship in the history of the sciences has gradually and increasingly focused on the methodological possibilities afforded by the study of images, the study of diagrams being just one possible area of research. This research has produced a variety of methods and approaches for analysing the epistemic and documentary aspects of different visual practices, their circulation and transmission within and across cultures, and their relationship to other means of communicating knowledge.
EIDA (Editing and analysing hIstorical astronomical Diagrams with Artificial intelligence) aims to build on these developments to study astronomical diagrams on a cross-cultural Afro-Asiatic-European scale. Our specific focus is on astronomical diagrams as historical sources in a great variety of types and functions. Two aspects of astronomical diagrams will be jointly examined: the documentary aspect (diagrams as written artefacts in specific manuscripts) and the epistemic aspect (diagrams as scientific tools for historical actors). EIDA’s activities will be carried out in close connection with the development of DH and AI tools for both conducting research and communicating research. In particular, EIDA will develop new computer vision algorithms capable of decomposing astronomical diagrams into components that are meaningful for analysis and edition without relying on human annotation. Moreover, online DH tools will be set up that allow researchers to explore and visualise the corpus of diagrams and communicate their findings. This online platform will lead to a new standard for producing ‘natively digital’ critical editions of diagrams (i.e. editions primarily conceived as digital objects).
The initial stage of EIDA is dedicated to constituting a corpus of astronomical diagrams and works containing them. Even when restricted to mathematical astronomy, there is a vast and complex history of visual representation. There are diagrams for different types of instruments or instrument parts, mathematical diagrams which support various kinds of mathematical reasoning, diagrams of cosmological models, diagrams exemplifying a nomenclature of technical terms, diagrams of phenomena like eclipses, and so forth. These diagrams may fulfil diverse functions as is the case with visualisations in other areas: from reasoning tool to mnemotechnics, from heuristic method to construction plan, to name just a few. Some diagrams are closely connected to works by specific authors, others are more loosely attached and circulate between works on similar topics, some appear in consistent series while others are unicums, some are executed with much care and accuracy, even artistic virtuosity, while others are mere sketches executed in haste as annotation by a reader. Many additional features can be considered to describe and understand the diversity of visual means used by historical actors.
The goal of this first conference is therefore to address these multiple layers of complexity and define the essential features and the scope of the EIDA corpus. This need not be done in terms of strict boundaries and formal definitions, it shall be achieved rather more organically as a core surrounded by concentric circles. We seek a historiographic cohesiveness so that processes of development, circulation and transmission on both local scales and in a temporally and geographically broader scope can be analysed.
At the same time, given the diversity of types and uses of astronomical diagrams, we seek for the EIDA corpus a semiotic cohesion that affords the possibility to trace relationships between the documentary and epistemic aspects of diagrams. This could mean that we consider a range of ‘visual idioms’ including: the use of points, lines and circles, that of different labelling conventions and graduated scales, the representations of full and empty, light and shadow with, for instance, the use of colour or gold, and even some pictorial elements. The corpus will also be influenced by the project’s goal of developing specific DH tools (a data structure, an interface for consulting and visualising the corpus, and new AI algorithms). These may imply different constraints on the diagrams that can be included (or not) depending on the availability of the sources.
This conference addresses these issues by bringing together scholars who will present and reflect on specific diagram case studies. These discussions are paired with presentations from DH and AI experts on the current state of advancement of computer vision tools and annotation methods. Scholars and experts together will explore the approaches we seek to develop for the study of astronomical diagrams.
Participants
Ségolène Albouy, Mathieu Aubry, Hamid Bolhoul, Ji Chen, Christopher Cullen, Samuel Gessner, Catherine Jami, Stephen Johnston, Richard Kremer, Guillaume Loizelet, Divna Manolova, Anuj Misra, Clemency Montelle, Ioanna Skoura, Scott Trigg, Stefan Zieme
In Italic, expected in visio-conference
Program
Tuesday 28 March
Chair: Matthieu Husson
9:30 – 10.00 Welcome – Introduction
10:00 – 11:00 Anuj Misra (Gerda Henkel Research Fellow at the Department of Cross-Cultural and Regional Studies, University of Copenhagen) Decision and Dilemmas: transcreations of astronomical diagrams in and from Sanskrit manuscripts
11:00 – 12:00 Clemency Montelle (University of Canterbury) Eclipse diagrams in the Parvadvayasādhana of Mallāri: A sixteenth-century Sanskrit table text to compute eclipses
12:00 – 13:00 Stefan Zieme (Humboldt-Universität zu Berlin) Mapping the transmission of the Almagest from its diagrams
Lunch (90 min)
Chair: Scott Trigg
14:30 – 15:30 Ioanna Skoura (Independent Scholar) An enriched Ptolemaic diagram drawn by Theon of Alexandria and used in his commentary on Almagest VI.7
15:30 – 16:30 Divna Manolova (SYRTE, Observatoire de Paris-PSL) The Diagrams in Cleomedes’ The Heavens in the Medieval Greek Manuscript Tradition
Break (20 min)
16:50 – 17:50 Ségolène Albouy (SYRTE, Observatoire de Paris-PSL) Building a platform for diagram edition
Wednesday 29 March
Chair: Divna Manolova
9:30 – 10:30 Scott Trigg (SYRTE, Observatoire de Paris-PSL) Diagrams for Structure and Motion in Islamicate Astronomy : The Case of the Moon
10:30 – 11:30 Guillaume Loizelet (Université de Toulouse) Diagrams for the computation of planet’s diameter in Kūshyār and al-Bīrūnī
Break (15min)
11:45 – 12:45 Hamid Bohloul (Independent Researcher) Diagrams and textual ambiguities: Planets in or on the epicycles?
Lunch (105 min)
Chair: Sophie Serra
14:30 – 15:30 Samuel Gessner (CIUHCT, Universidade de Lisboa) Diagramming the eighth sphere: a genealogy of Comitibus and Peurbach
Break (15min)
15:45 – 16:45 Mathieu Aubry (École des Ponts ParisTech) Computer Vision for Historical Diagrams analysis
18:30 – 19:30 (Optional Visit) Bibliothèque Sainte-Geneviève, 10 place du Panthéon – Brief introduction to the manuscript collection and viewing of selected manuscripts.
20:15 Dinner
Thursday, 30 March
Chair: Richard Kremer
10:30 – 11:30 Ji Chen (Department for the History of Science and Scientific Archeology, University of Science and Technology of China) The adoption and evolution of eclipse diagrams in the official forecast reports during the late Ming and early Qing period
Break (15min)
11:45 – 12:45 Christopher Cullen (NRI, Cambridge, and CCJ, Paris) & Catherine Jami (CNRS, CCJ) Circulation, global and local: the case for including 17th and 18th century Chinese astronomical diagrams in the EIDA corpus
Lunch (105 min)
Chair: Samuel Gessner
14:30 – 15:30 Richard Kremer (Dartmouth College) When do diagrams “work”? Enabling construction in astrolabe texts
15:30 – 16:30 Stephen Johnston (History of Science Museum, University of Oxford) Between diagram and device: motion, structure and materiality in astrological astrolabes
Break (20min)
16:50 – 17:50 General discussion and conclusion
Abstracts
Building a platform for diagram edition
Ségolène Albouy
SYRTE, Observatoire de Paris-PSL
At the same time as defining the scientific stakes of the study of the diagrams, the digital team of the EIDA project must focus on laying the first bricks of an online platform that can help researchers to carry out their research questions. More than building a database of diagrams and offering navigation and visualisation of the corpus, it is also a question of anticipating future research practices and opening the way to tools not yet conceived. Based on a data structure that distinguishes historical aspects from their modern digital retranscription, the information system will offer the means to order, group and analyse diagrams. With the help of artificial intelligence algorithms, different steps of the research process can be accelerated (visual elements extraction, clustering, vectorization) which will open new perspectives for the study of astronomical diagrams.
Computer Vision for Historical Diagrams analysis
Mathieu Aubry
École des Ponts ParisTech
This presentation will first introduce the basics of supervised Machine Learning and Neural Networks architectures and training. It will then focus on use cases and research direction in the context of the EIDA project. It will include a review of existing methods we plan to fine-tune to our needs for automatic diagram detection and visual similarity search. It will finish with the main options we will consider to extract geometric primitives from the diagram: classical edge detection coupled with robust estimation, supervised learning approaches, and unsupervised learning approaches.
Diagrams and textual ambiguities: Planets in or on the epicycles?
Hamid Bohloul
Independent Researcher
In the Islamicate astronomical texts, the position of a planet in relation to its epicycle is primarily specified by two distinct prepositions: on (ʿalā) or in (fī) (al-kawkab ʿalā (fī) al-tadwīr [the planet on (in) the epicycle]). In this presentation, I explain that these two ways of imagining planets and epicycles, which originate from Ptolemy’s Almagest and Planetary Hypotheses, are associated with the concepts of solid spheres and imaginary circles. This investigation primarily aims to explore how each group is drawn in the planetary diagrams. According to the results of my ongoing study on approximately a hundred manuscripts of astronomical books, predominantly hayʾa (configuration of the universe), the following types of epicycle diagrams can be identified: 1) Epicycle circle without a graphical indication of its planet; 2) Planet is represented by a small dot on the epicycle; 3) Planet is displayed by a small circle whose centre lies on the epicycle; 4) Planet is displayed by a tiny full circle (or a small empty circle) which is tangent to the inner surface of the epicycle; 5) Planet is illustrated by a small empty circle that touches the inner surface of the epicycle while the centre of the planet lies on a small concentric circle with epicycle, almost always in red. These diagrams will be discussed with various examples from astronomical manuscripts and then I attempt to reveal which diagrams are accurately based on their descriptions in the text, and when possible, I aim to identify whose fault is if the diagram is not correct: author, scribe or diagram maker and to speculate about the potential reasons.
The adoption and evolution of eclipse diagrams in the official forecast reports during the late Ming and early Qing period
JI Chen
Department for the History of Science and Scientific Archeology, University of Science and Technology of China
With European astronomy introduced into China, eclipse diagrams that were commonly used in European works began to appear in the official forecast reports occasionally during the Chongzhen 崇禎 calendar reform, and eventually became required content of the official reports in the early Qing 清 dynasty. By analysing the eclipses diagrams in the official forecast reports during the period, this paper reveals the evolution process of them, during which the changes were made to adapt to Chinese tradition and situation. Among the changes, there was a contribution of the determination of beginning and ending positions of eclipses contributed by Chinese unofficial astronomers Wang Xichan 王錫闡 and Mei Wending 梅文鼎. A further comparison of the attitudes towards European diagrams of these two typical representatives indicates how European astronomy was gradually accepted by Chinese unofficial astronomers
Circulation, global and local: the case for including 17th and 18th century Chinese astronomical diagrams in the EIDA corpus
Christopher Cullen NRI, Cambridge, and CCJ, Paris
Catherine Jami CNRS, CCJ
Starting in 1629, the Jesuit missionaries who worked on an astronomical reform in Beijing produced a number of treatises, known collectively as the Chongzhen lishu 崇禎曆書 (Astronomical Writings of the Chongzhen Reign). These treatises presented the knowledge that underlay the new calendrical system that they proposed to provide for the Ming 明dynasty (1368-1644), and that they ended up producing for the Qing 清dynasty (1644-1911) after the Manchus took Beijing in 1644. For about a century after this date, further astronomical treatises were produced under state patronage, while a number of Chinese scholars versed in astronomy also wrote books discussing the Jesuits’ “new methods” (xin fa 新法) and earlier Chinese astronomical systems. It is the astronomical diagrams produced in this vast body of literature that we propose should be included into the EIDA corpus.
In this presentation, we will focus on the Chongzhen lishu. The study of the diagrams it contains is a necessary first step to understanding the history of diagrams within China in the century that followed. While the European sources of the astronomical techniques and data of the Chongzhen lishu have in great part already been identified, there is as yet no systematic study of the extent to which the diagrams in the Chongzhen lishu were borrowed from European works, or were specially created by its Jesuit authors.
A first inventory of the diagrams found in the Chongzhen lishu will enable us to assess the magnitude of the task. We will also discuss a few examples to bring out some issues that the EIDA project might fruitfully address to shed light on the circulation of astronomical diagrams between Europe and China and within China in the 17th and 18th centuries.
Diagramming the eighth sphere: a genealogy of Comitibus and Peurbach
Samuel Gessner
CIUHCT, Universidade de Lisboa
This case study proposes to look at the phenomena that affected the long-term propagation of diagrams associated with a given astronomical topic: the motion of the eighth sphere. The aim is to examine the diagrams in works of the same topic but of more or less diverging content, paying particular attention to diagrammatic dependencies. A chronologically extended corpus is considered. It starts with a mediaeval treatise on the eighth sphere of obscure Arabic origin De motu octave spere. While the work is usually ascribed to Thabit ibn Qurra it possibly originated in the eleventh century. Only Latin versions of it are known and they are illustrated by diagrams. This work explains the geometry and quantities of the motion called ‘access and recess’ intended to account for both changes of the longitudes of the fixed stars and of the obliquity. The tables that are often included in the copies correspond to those found with the Toledan Tables. Its typical diagrams depict the two small circles surrounding the mean equinoctial points, presenting a 3D configuration in the paper plane.
Samso (2020) recalled that a different type of motion which combined linear and oscillating motions for precession is mentioned in a range of other astronomical works. These include al-Battani, al-Zarqalluh and al-Bitruji, some of which include diagrams. In particular, references to this two-component precession are to be found in the early fourteenth century, in the context of Parisian Alfonsine astronomy, where the corresponding tables were available. As far as we know today, these works did not include diagrams, however.
Later works coping with the topic and using diagrams are known from ca. 1450. They are authored by Niccolò Conti (Nicolaus Comes de Comitibus) and Georg Aunpekh of Peurbach. As Nothaft (2019) has shown, some of the diagrams used in both works are similar. What went unnoticed is that, notwithstanding the visual similarity of the diagrams, the two works propound different geometries of the motions. What is even more striking is that the similarity of the diagrams seems to derive from their common attempt to use the same ‘visual idiom’ as transmitted in the copies of the abovementioned De motu octave spere. Moreover, both fifteenth-century authors added diagrams of a new type.
Systematically harvesting diagrams from sources associated with the works known to mention the eighth sphere might even expand the corpus. From what we already know, the accompanying diagrams offer instances of inertia due to inheritance as well as variation and accretion when diagrams propagate. Studying diagrams from the entire corpus on the eighth sphere shall contribute to identifying a variety of processes that underlie the choices of authors and copyists in shaping diagrams by tracing their genealogy.
Between diagram and device: motion, structure and materiality in astrological astrolabes
Stephen Johnston
History of Science Museum, University of Oxford
When the Jardines père et fils reviewed the critical editing of astronomical diagrams in 2010 their primary concern was with the final appearance of historical images on the printed page: how do scholarly conventions and intended audiences affect editorial decisions? They noted in passing the dizzying potential of digital media and how this might reshape editorial practices and possibilities in the future. While that day had not yet come in 2010, it has now definitely arrived. How can digital technology be used to deliver maximum scholarly impact for the EIDA project?
An area ripe for digital transformation is surely the treatment of motion. Historically, static diagrams were used to represent or trace astronomical motion, for example by adapting the techniques of Ptolemy’s analemma constructions. However, studying these in terms of the “intelligent eye” (Crowther and Barker, 2013) tends to point inwards, to inaccessible psychological states of understanding.
A more immediate way to “mobilise” digital technology is by reproducing diagrams with moving parts. Volvelles or rotulae are the most familiar examples of this technology. Here the diagram consists of independent but connected parts, at least one of which can rotate over another. There are classic examples in print from Regiomontanus’ Kalendarium to the many complex examples in Apian’s Astronomicum Caesareum, but the genre was already well-established in mediaeval Latin manuscripts, and was freely mixed with other diagrammatic material in the corpus astronomicum. Because they have a layered structure but can nevertheless be accommodated within the physical bounds of a codex, volvelles appear intermediate between 2D and 3D. They are, to borrow a term from contemporary digital imaging, 2.5D.
Could EIDA provide a platform that enabled the manipulation of such diagram-devices? My case study explores the intellectual and practical benefits of such a development. I look at astrological astrolabes as a particular variety of volvelle. They drastically simplify the standard planispheric instrument, and usually lack the latter’s time telling functions, instead prioritising the casting of the houses for horoscopes. Following the trail of these items – from 15th-century manuscript examples on parchment to 16th-century versions printed on paper or engraved on brass – forces us to ask if (and where) we should now recognise a boundary between diagrams and devices. Examples in these diverse media are typically housed in different institutions (archive, library, museum) but digital technology can allow us to recognise and recover their “semiotic cohesion”. The close comparison of astronomical diagrams drawn by compass, rule and square with engraved brass instruments reveals that they are far more closely aligned as mobile and dimensionally structured “manuscripts” than our traditional vocabulary allows.
When do diagrams “work”? Enabling construction in astrolabe texts
Richard Kremer
Dartmouth College
Most of the vast literature on the functions of diagrams, on the epistemic work they perform, considers them as static artefacts that, like texts, are designed to be “viewed” by “readers” either once or repeatedly into the indefinite future. As such, a diagram carries “meaning” as long as the visual and epistemic cultures in which it is embedded continue to carry their meanings. However, a particular type of diagrams, found in mediaeval astronomical traditions, perform their work on a different time scale. Rather than being “viewed” they are intended to be reconstructed by the “user” (not “reader”). Only as they are directing this reconstruction are these diagrams actively performing their intended function. Such diagrams appear in a widespread mediaeval and early modern astronomical genre, the “making and using” (fabrica ususque) texts on instruments.
In this paper, I will consider examples of “making” diagrams found in astrolabe texts. The text-plus-diagram delivers sequential instructions as the maker inscribes lines on the brass or paper instrument being constructed. The diagram functions in a process of making, a real-time visual, haptic and epistemic experience of the maker. I will explore the graphical clues, the unrecorded tacit knowledge, and the materiality of the 3-d working tools (compass, protractor, rule, metal punch) that together enable the process of “making” an astrolabe.
Diagrams for the computation of planet’s diameter in Kūshyār and al-Bīrūnī
Guillaume Loizelet
Université de Toulouse
I will start with an example: the diagrams used respectively by Kūshyār ibn Labbān (al-zīj al-jāmiʿ, Ms. Leiden Or. 8 f.101r) and by Abū Rayḥan al-Bīrūnī (al-Qānūn al-Masʿūdī, Ms. British Library Or. 1997 f.235r) to explain their method of calculating the diameter of the five planets. Whereas Kūshyār’s diagram is an idealisation derived from an observational situation that allows the reader to carry out the calculation algorithmically for each of the planets, the diagram produced by al-Bīrūnī is a schematisation of the three situations that can be encountered, depending on whether the apparent diameter of the planet under consideration is less than, equal to or greater than the apparent diameter of the Sun, which is used as a reference for the quantification of this angle. Thus, while Kūshyār’s diagram makes the procedure obvious, but obliterates its genesis, al-Bīrūnī’s diagram makes the genesis of the calculations clear and allows him to produce a very simple formulation. I will then proceed to a comparative analysis of the genesis of both Kūshyār’s and al-Bīrūnī’s diagrams, their use and the consequences of their use. The next step would be to identify other pairs of diagrams in the manuscripts of the zīj al-jāmiʿ and al-Qānūn al-Masʿūdī and to carry out the same type of analysis in order to see whether any epistemological characteristics emerge.
The Diagrams in Cleomedes’ The Heavens in the Medieval Greek Manuscript Tradition
Divna Manolova
SYRTE, Observatoire de Paris-PSL
The manuscript tradition of Cleomedes’ The Heavens in Greek, between the tenth and the sixteenth centuries includes ca. 83 manuscripts. The four manuscripts predating the thirteenth century either do not include any diagrams or very few and the same is valid for the early thirteenth century copies which, though more numerous, nevertheless are not heavily diagrammatic. From the late thirteenth century onwards, however, and possibly influenced by a new ‘edition’ (ca. 1290) by Maximos Planudes and the composition of the first known medieval commentary to The Heavens by John Pothos Pediasimos (during the last decade of the thirteenth century), the scholars and scribes copying The Heavens introduced an ever increasing number of diagrams, some of their own design.
This paper will offer a diachronic survey of the diagrammatic corpus of The Heavens in the Greek medieval manuscripts and discuss the set of cosmological and astronomical diagrams, which become canonical, as it were, and how they relate to the drafting instructions given by Cleomedes in his text. Taking my cue from scholarship on Macrobian diagrams, I define as canonical those diagrams whose presence and design are prescribed by the main narrative and which are consistently included in its copies. The presentation will also include a case study of one of the canonical diagrams and the subtle changes it undergoes – in terms of design, labelling, colouring and layout – as it is copied throughout the centuries.
Decision and Dilemmas: transcreations of astronomical diagrams in and from Sanskrit manuscripts
Anuj Misra
Gerda Henkel Research Fellow at the Department of Cross-Cultural and Regional Studies, University of Copenhagen
Understanding astronomical diagrams in mediaeval sources is a novel programme inasmuch as it offers new insights into the complex of its role as computational, representational, or demonstrational aids. In Sanskrit mathematical astronomy – as with other traditions – the ontological basis of diagrams and its purported epistemological use remains an open topic of investigation. In this talk, I present a few examples of astronomical diagrams from early-modern Sanskrit manuscripts to discuss their historical presentations and technical purposes, and to add to our discussions on modern-day dilemmas in transcreating these diagrams from mediaeval manuscripts to modern machines.
Eclipse diagrams in the Parvadvayasādhana of Mallāri: A sixteenth-century Sanskrit table text to compute eclipses
Clemency Montelle
University of Canterbury
The Parvadvayasādhana (“Computation of the two syzygies”) of Mallāri (fl. late sixteenth century) is a short Sanskrit treatise dedicated to the computation of lunar and solar eclipses. What is particularly significant about this composition is that Mallāri belonged to the prominent kin-school, an influential family of astronomer-mathematicians working in central and northern In- dian in the mid-second millennium, following the compositions of Gaṇeśa A key part of this work includes the parilekha ‘diagram’ section which presents instructions for constructing a graphical representation of an individual eclipse. While the Parvadvayasādhana itself only includes prose descriptions, commentaries on this work often present rendered diagrams for particular eclipses which follow these prose instructions. We will explore these diagrams and their features and high- light how they document various technical details, and consider the uniformity of practice among commentator-scribes, and their broader epistemic scope.
An enriched Ptolemaic diagram drawn by Theon of Alexandria and used in his commentary on Almagest VI.7
Ioanna Skoura
Independent Scholar
One of the cases where Ptolemy in the Almagest uses a schematic diagram is when representing the phases of the lunar obscurations in a total eclipse (Almagest, VI.7). Theon, when commenting on this part of the Almagest, enriches, following his common practice throughout his Commentary, Ptolemy’s diagram with elements which he considers useful for his reader. The main subject of the present paper is a documentary aspect of this diagram of Theon. Firstly, I will present both Ptolemy’s schematic diagram and Theon’s enriched diagram and I will discuss the elements used by Theon to enrich the Ptolemaic one. In the following, I will consider the structure of the Theonian diagram as a written artefact and its formal relation with Theon’s text and the organisation of certain manuscripts transmitting this diagram. Concerning its manuscript transmission, I will first examine six manuscripts carrying Theon’s commentary on Almagest VI.7. The earliest to be considered is the 9th-century codex Firenze, Biblioteca Medicea Laurenziana, Plut. 28.18, while the latest is the 16th-century Vatican City, Biblioteca Apostolica Vaticana, Ott. gr. 26. Apart from the manuscripts transmitting Theon’s Commentary, the diagram in question is found in certain manuscripts transmitting the Almagest and it is drawn in the margins of Ptolemy’s text. In most cases, along with the diagram we see written Theon’s relative text as well. In this context, I will also consider six manuscripts of the Almagest spanning from the ninth to the fourteenth century. The presence of the Theonian diagram next to the Ptolemaic text shows that it was used for the study of the Almagest.
Diagrams for Structure and Motion in Islamicate Astronomy : The Case of the Moon
Scott Trigg
SYRTE, Observatoire de Paris-PSL
Theoretical astronomy (ʿilm al-hayʾa) in the post-Classical Islamicate world was both a continuation of, and a break with, Hellenistic astronomy. In particular, rather than two-dimensional circles it was now physical, three-dimensional spheres that were seen as the appropriate “building blocks” for astronomical models. Previous research has highlighted Islamicate astronomers’ critiques of Ptolemaic models and their innovative solutions, but little attention has been paid to the function of diagrams as more than an adjunct to the text. This paper takes manuscript diagrams for the lunar theory as a case study, for the lunar theory is the first application of the famous Ṭūsī-Couple device to produce a non-Ptolemaic model in Naṣīr al-Dīn al-Ṭūsī’s (d. 1274) al-Tadhkira fī ʿilm al-hayʾa. I argue that diagrams fulfil a vital function as tools of reasoning. In analysing the Almagest and its diagrams within a different cosmological framework, Ṭūsī and other authors of hayʾa texts produced new types of diagrams. These diagrams, unlike the mathematical, geometric figures of the Almagest, represented a shift from images intended to support geometric reasoning to images that adapted and transformed the visual vocabulary and conventions of the existing tradition in the service of expressing different concepts. Diagrams not only helped to illustrate celestial phenomena associated with the motion of the Moon, but served as a crucial means by which astronomers could visualise problems associated with the three-dimensional structure of complex astronomical models, propose new solutions, and analyse and critique the work of their predecessors. In particular, this paper demonstrates how manuscript diagrams serve to develop and communicate knowledge about physical bodies in motion, and also highlights significant features of the visual practice of Islamicate astronomy.
Mapping the transmission of the Almagest from its diagrams
Stefan Zieme
Humboldt-Universität zu Berlin
As one of the most important sources of mathematical astronomy Ptolemy’s Almagest was copied, translated, discussed, and taught for one and a half millennia. Originally written in Greek and referred to as Syntaxis mathematica, nowadays it is better known by its mediaeval Arabic name Almagest. It was translated several times before the sixteenth century. Today, beyond Greek and Byzantine sources, six different translations are still extant in their entirety that comprise translations from Greek into Arabic, Arabic into Latin, Greek into Latin, and Arabic into Hebrew. In total there are about 150 manuscripts still extant through which knowledge about the Almagest was transmitted in different cultures, languages, and times. Over centuries owners and scribes of these manuscripts compared, annotated, or corrected their manuscripts. Especially the geometrical diagrams, numerous within the Almagest, feature manifold variations among different manuscript witnesses. In this talk, I will systematically analyse variations of a specific set of diagrams across all extant manuscript witnesses of the Almagest. Based on transcribing these diagrams into a machine-readable framework, with respect to their intended mathematical function, I will perform a network analysis of diagrammatic variations. My aim is to visualise the transmission and translation of the Almagest across space, time, and culture from its diagrams.