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Accueil > Archives > Séminaires des années précédentes > Séminaires 2020-2021 : archives > History of Science, History of Text 2020–2021

Axis Interdisciplinary Research in History and Philosophy of Science

History of Science, History of Text 2020–2021



The seminar examines the various types of documents produced in the context of scholarly practices in order to understand how the shaping of textual forms and inscriptions is part of the scientific activity. The seminar also aims to understand how these works make it possible to better interpret the sources on which historians of science draw to conduct their research. We will focus this year on the following topics :
  • how are layouts instruments that scientists put into play in their work and do they need to be interpreted as such ?
  • How to read diagrams ?
  • how do the writings and inscriptions produced in one environment circulate and how are they taken up in other milieux ?
  • How can we document the genesis of texts, calculations, textual forms, and what does it tell us about the modes of writing practiced in various contexts ?
  • How do the sources document what they do not talk about ?
  • What does the organization of the writings of the actors tell us about their scholarly activities ?


Organizers : Karine Chemla (SPHere, CNRS-University of Paris & Radcliffe Institute, Harvard University) & the HSHT Group.


SCHEDULE 2020-2021

IMPORTANT : Due to the current health situation, the sessions will take place by webconference, on Thursdays. Access to links and abstracts by clicking on dates

2020/10/15, !!! 10:15am–4:30pm !!! : Working with and Interpreting Columns
C. Proust Sémantique des colonnes dans quelques textes mathématiques cunéiformes
E. Haffner Mise en page des brouillons mathématiques : colonnes, colonnes et colonnes
K. Chemla Elements of a History of the Reading of ancient sources

2020/11/19, 10:15am–4:30pm : Texts in pieces
S. Schmitt Les encyclopédies spécialisées au 18e siècle. L’exemple de l’histoire naturelle
M. C. Bustamante Géométries non archimédiennes selon un procédé d’écriture du physicien Jacques Solomon
F. Bretelle-Establet Notes marginales, commentaires et ajouts : les multiples interventions dans les textes de médecine en Chine à la fin de l’empire (17e-19e siècles)

2020/12/17, 10:15am–4:30pm : Diagrams 1
J. Lefebvre Quelques remarques sur l’articulation d’un diagramme à une ligne écrite : typologie et enjeux interprétatifs
M. Decorps Sur la relation entre texte et figure dans les traités mathématiques et techniques grecs : étude de quelques exemples
A. Trouillot Production of an archive and production of a calculation text in the Saharan West

2021/01/14, 10:15am–4:30pm : Organizing texts
A. Costa De la taxinomie à l’encyclopédie : les plans d’ouvrages dans la production de G.W. Leibniz
T. Morel Writing, Drawing and Preaching Mathematical Practices
 in Early Modern Mines
A. Keller La colonne comme outil de calcul dans les commentaires mathématiques en Sanskrit : avec ou sans sens ?

2021/02/04, 10:15am–4:30pm : Diagrams 2
S. Gessner Between astronomical diagrams and instruments : spatializing numerical data of astronomical tables
N. Jacobson The Role of Planetary Diagrams in Fourteenth-Century Procedure Texts to the Alfonsine Tables

2021/03/04, 10:15am–4:30pm : Drafts
A. Remaki Choix des variables dans les brouillons d’algèbre de Leibniz (1)
Edgar Lejeune How did historians scholarly edit for IBM punched cards ? A comparison between two case-studies (France, 1970-1980)
M. Grote Synthesis and systematization – Modern European Encyclopedisms

2021/04/08
A. Remaki Choix des variables dans les brouillons d’algèbre de Leibniz (2)
A. Bréard Numbers beyond discourse : disruptive or heuristic diagrammatic patterns in Chinese mathematical texts ?
A. Volkov Mathematical texts from Dunhuang : The problem of filiation

2021/05/06
10am–1pm
M. Geller The Cuneiform Conundrum : how do you ‘alphabetise’ without an alphabet ?
M. Friedman Medieval Hebrew mathematical manuscripts left in mediis rebus : The case study of “A treatise on measurement of areas and volumes” of Bar Hiyya
2021/06/10
A. Keel Steensen
 ! postponed !
Working with inscriptions : making and breaking formal rules as computational practice
Discussion on next year program

ABSTRACTS

October 15, 2020, !!! 10:15am–4:30pm !!!, Room Mondrian, 646A

: : Working with and Interpreting Columns

10:15am–11:45am

  • Christine Proust (SPHERE, CNRS & University of Paris (Diderot))
    Sémantique des colonnes dans quelques textes mathématiques cunéiformes
    Certain textes mathématiques cunéiformes se présentent sous la forme de listes ou de tables sans autre forme d’explication qui nous renseignerait sur leur signification ou leur mode d’emploi. Cependant, ces textes comportent des alignements verticaux qui semblent intentionnels. Dans quelle mesure ces éléments de mise en page suppléent-ils à l’absence d’explication ? Peut-on déceler une sémantique des alignements dans ces textes ?

11:45am–12am : break

12am–1:30pm

  • Emmylou Haffner (University Paris Saclay)
    Mise en page des brouillons mathématiques : colonnes, colonnes et colonnes
    Dans les brouillons de mathématiciens, les organisations spatiales des écritures se démarquent souvent du texte imprimé rectangulaire et propre que l’on a coutume de lire. Une récurrence de ces organisations spatiales est l’utilisation de colonnes. Nous verrons, sur une sélection d’exemples, que plusieurs manières d’utiliser les colonnes cohabitent dans de tels textes, chacune donnant des indications différentes sur les pratiques mathématiques au brouillon et sur certaines temporalités de la recherche.

1:30pm–2:30pm : picnic together

2:45pm–4:15pm

  • Karine Chemla (SPHERE, CNRS-University of Paris & Radcliffe Institute, Harvard University)
    Elements of a History of the Reading of ancient sources
    In contrast with the majority of other mathematical classics, the work completed in the first century CE under the title The Nine Chapters on Mathematical Procedures is characterized by the fact that throughout history it was the subject of commentaries. I will compare the reading of a single paragraph that various commentators carry out to highlight how different commentators expect different types of knowledge from their readers and what these differences reveal on the text commented upon.

November 19, 10:15am–4:30pm

: : Texts in pieces

  • Stéphane Schmitt (Archives Henri Poincaré)
    Les encyclopédies spécialisées au XVIIIe siècle. L’exemple de l’histoire naturelle
    Il est bien connu que le 18e siècle a vu l’essor d’une grande tradition encyclopédique, représentée notamment par l’Encyclopédie de Diderot et d’Alembert, mais aussi par de nombreuses autres (Cyclopaedia de Chambers, Dictionnaire de Trévoux, etc.). Plusieurs de ces ouvrages, qui ont en commun d’être généralistes, ont été soigneusement étudiés par les historiens. Mais parallèlement, un très grand nombre d’encyclopédies spécialisées, c’est-à-dire restreintes à un champ particulier, ont été publiées au cours de la même époque. Cette littérature, qui a été très largement diffusée, a joué un rôle important dans l’histoire de chaque discipline concernée. Je présenterai ici quelques exemples dans le domaine de l’histoire naturelle et de la médecine.
  • Martha Cecilia Bustamante (SPHERE & University of Paris (Diderot))
    Géométries non archimédiennes selon un procédé d’écriture du physicien Jacques Solomon
    Entre 1939 et 1941, Jacques Solomon (1908-1942) a porté un regard aigu sur les géométries non archimédiennes. Nous nous intéresserons aux documents qui sont restés dans la perspective de la génétique des textes et des procédés d’écriture mis en jeu par le scripteur. Nous montrerons comment Solomon rassemble des travaux publiés depuis la fin du XIXe siècle, et, sur cette base, met en place une écriture par fragments impliquant des auteurs et des sources très diverses. Dans le regard que Solomon porte sur le sujet, le travail du mathématicien italien Veronese a une place de premier plan. Enfin, l’analyse que nous faisons des documents en question montre que comprendre les implications épistémologiques du type d’écriture que Solomon met en œuvre est un enjeu essentiel.
  • Florence Bretelle-Establet (CNRS, SPHERE, & University of Paris (Diderot))
    Notes marginales, commentaires et ajouts : les multiples interventions dans les textes de médecine en Chine à la fin de l’empire (XVIIe-XIXe siècles)
    Augmentés de notes marginales manuscrites, de notes marginales imprimées, de commentaires, de nouveaux morceaux ou de nouvelles préfaces, les textes médicaux en Chine, à la fin de l’empire, attestent de multiples interventions non auctoriales. Nous mettrons en lumière les différents types d’interventions qui accompagnent les textes de médecine, dès leur première édition, et celles qui s’ajoutent lors de nouvelles éditions et nous tenterons d’en saisir les enjeux.

December 17, 10:15am–4:30pm

: : Diagrams 1

  • Julie Lefebvre (University Paris-Ouest-Nanterre, MoDyCo, UMR 7114)
    Quelques remarques sur l’articulation d’un diagramme à une ligne écrite : typologie et enjeux interprétatifs
    Nous reviendrons tout d’abord sur l’appellation de « diagramme » en convoquant des éléments lexicographiques et étymologiques, mais également en la confrontant à d’autres dénominations telles que « figure », « schéma » ou encore « illustration » qui désignent couramment, dans un texte donné, des entités à dimension iconique articulées à une chaîne de signes graphiques —une linéarité écrite. Sur la base d’un corpus de textes contemporains relevant de genres discursifs variés, nous proposerons ensuite de poser les bases d’une typologie linguistique de l’articulation entre un diagramme et la ligne écrite à laquelle il est relié. On s’interrogera ainsi sur la nature des éléments associés dans cette mise en relation et sur les ressources, notamment syntaxiques, référentielles et ponctuationnelles, qu’elle met en jeu. Ce faisant, nous essaierons de montrer comment les différentes modalités de l’articulation entre une ligne graphique et un diagramme conditionnent l’interprétation du texte que, dans leur association, ils constituent.
  • Micheline Decorps (University Blaise Pascal, Clermont II)
    Sur la relation entre texte et figure dans les traités mathématiques et techniques grecs : étude de quelques exemples
    À la lumière des études menées sur les diagrammes et les problèmes posés par leur interprétation, on apportera ici quelques éléments concrets empruntés à certains textes mathématiques et techniques de l¹Antiquité grecque. Dans cette approche on donnera une importance particulière aux différents aspects à la fois matériels et intellectuels de la relation entre le texte et la figure.
  • Alexis Trouillot (University of Paris (Diderot), SPHERE)
    Production of an archive and production of a calculation text in the Saharan West
    This talk aims to present a source for Saharan intellectual history : the Harūn Sīdiyyā library, a collection of 2051 works from a Mauritanian family library. By recreating a short history of this particular archival entity we will first show what it can tell us on the status of erudition in the region in the 19th and 20th centuries but also what was omitted.
    We will then place the library in the wider context of the Saharan West. On the one hand, the manuscript culture of the region has received considerable attention by different actors ranging from the French colonial government to an informal association of American researchers to Mauritanians scholars and government officials leading to an explosive growth in cataloguing efforts. On the other hand, they all had different ideas on how to catalog and preserve texts, or on how to divide them into genres and subjects while operating under the same impression that only manuscripts should be preserved and not printed texts. This, added to the fact that the texts were seldom read once catalogued, leads to blind spots in our access to the history of local erudition, some of which can be mended by working on texts of the Sīdiyyā library. Finally, we will demonstrate the kind of inquiries into local intellectual history that the library allows us to produce by looking at the production of a text on inheritance calculations written by his founder, the Sharḥ bāb al-tarikā min Mukhtaṣar Khalīl b. Ishāq.

January 14, 2021, 10:15am–4:30pm

: : Organizing texts

  • 10:15–11:45 Andrea Costa (CNRS, Centre Jean-Pépin UMR 8230)
    De la taxinomie à l’encyclopédie : les plans d’ouvrages dans la production de G.W. Leibniz
    Les pages des volumes de l’édition nationale allemande des œuvres de G.W. Leibniz s’avèrent parsemées d’inventaires, catalogues, taxinomies, énumérations et répertoires bibliographiques à travers lesquels se définit la cartographie globale de l’énorme projet encyclopédique que le philosophe d’Hanovre poursuivit tout au long de sa vie. Condensée dans la dimension minimale de la « liste » ou développée jusqu’à atteindre l’ampleur d’un ouvrage autonome et articulé, la pratique de l’inventaire se révèle ainsi comme le noyau originaire structurant le dispositif de la réflexion leibnizienne ainsi que sa pratique d’écriture. La communication se propose d’étudier l’évolution des lignes directrices du projet encyclopédique leibnizien à partir de ses ébauches taxinomiques, à travers l’analyse d’une série d’exemples tirés des œuvres publiées et des manuscrits inédits.
  • 11:45am–12am Break
  • 12am–1:30pm Thomas Morel
    Writing, Drawing and Preaching Mathematical Practices
 in Early Modern Mines
    Subterranean geometry developed during the early modern period around a set of concrete technical problems, in specific cultural and religious settings. In the second half of the sixteenth century, scholars published their view on this craft, most famously Georg Agricola (1494–1555) with this De Re Metallica. However, one can dig up other sources to understand these geometrical practices : mining laws and customs, sketches and technical documents used by practitioners. Mining sermons, which developed with the rise of protestantism, offer another – and diverging – conception of underground surveying. Which methodology can be used to cross-reference sources that can tend to be contradictory ? How to cope with the heterogeneity between a scholarly approach and traces of concrete practices, an acute problem concerning mathematics ? Can we then reach more general conclusions about the scope and role of early modern practical mathematics ?
  • 1:30pm–3pm pause déjeuner
  • 3pm–4:15pm Agathe Keller (CNRS, SPHERE, & University of Paris (Diderot))
    The columns as a computational tool in Sanskrit mathematical commentaries : with or without meaning ?
    In the representations of working surfaces that Sanskrit mathematical commentaries include in their texts, as well as in the names given to certain algorithms and to configurations in an algorithm, columns (vallī lit. creeper) appear. In two case studies I would like to observe how the column works as a formal tool in the execution of procedures : it is a configuration that has a meaning at the beginning of the computation and in the end, but in its intermediary steps it works seemingly like an algebraic symbolism, enabling one to execute computations without having to worry about their meanings. Or is it so ? My presentation will take examples from Pṛthūdhaka (fl. 860)’s commentary on the mathematical chapter of the Theoretical astronomical treatise of the true Brāhma School (Brāhmasphuṭasiddhānta-628) dealing with fractions and combinatorics mirroring them with other uses of columns in the same context..

February 4, 2021, 10:15am–4:30pm

: : Diagrams 2

  • Alexei Volkov (Institute of Advanced Studies (Paris) and National Tsing-Hua University (Taiwan)
    Mathematical texts from Dunhuang : The problem of filiation !! postponed until April 8, 2020 !!
  • Samuel Gessner (SYRTE, Observatoire de Paris)
    Between astronomical diagrams and instruments : spatializing numerical data of astronomical tables
    Astronomers have connected their computational methods with geometrical representations in various ways. The ways these connections were elaborated on are not universal, but historically contingent of the local astronomical practice. Parchment instruments to graphically determine (approximate) positions of the planets, i.e. the family of planetary “equatoria” instruments, saw renewed developments in the 15th century. We will start with a European case study about a particular type of instrument that emerged in manuscripts from Erfurt and Leipzig termed “Theorice novelle”. In discussing this material the talk proposes to look into possible connections between the representation of computed data in tables and corresponding diagrammatic representations on the “Theorice novelle” and similar instruments. More generally, it raises the question of how the use of tables was preparing the minds for experimenting with new types of instruments and whether this trait can be used to characterise a specific astronomical practice.
  • -* Nick Jacobson (SYRTE, Observatoire de Paris)
    The Role of Planetary Diagrams in Fourteenth-Century Procedure Texts to the Alfonsine Tables
    Medieval Latin manuscript witnesses from the fourteenth and fifteenth centuries that contain instructions for using astronomical tables are remarkably free of geometrical diagrams. This has led some scholars to conclude that the texts are concerned principally with the basic arithmetic operations for manipulating the tables, rather than the theoretical models that were used to calculate the tabular values. This conclusion is partly belied by the fact that many procedure texts within the Alfonsine tradition allude to diagrams in some way or another, and engage in verbal forms of geometrical reasoning even if there are no diagrams to be found directly accompanying the procedures. In collaboration with the ALFA research team, I have been collecting witnesses to procedure texts that do, in fact, have diagrams constructed in the margins to passages containing diagrammatic and geometrical language. In this presentation I will treat two such sources : Erfurt UFB, Amplon. Q. 366 and Oxford, Bodleian Library, Digby 97. By close textual and material analysis, I will consider whether these should be strictly defined as procedure texts or classified under a separate genre. I will suggest that there are variations in language that correlate to different registers of the texts’ instructions. These registers draw from different sources and make use of the diagrams in different ways. Ultimately I hope this analysis might help us to understand what epistemic role(s) the diagrams play – specifically in terms of the mathematical practices of the historical actors. At times they serve to clarify tabular procedures ; at other times they seem to justify these procedures. What results is an interesting interplay between arithmetic and geometric reasoning in parallel passages.

March 4, 2021, Room Mondrian, 646A

: : Brouillons

  • Arilès Remaki (University of Paris (Diderot), SPHERE, & ANR Mathesis)
    Choix des variables dans les brouillons d’algèbre de Leibniz
    L’algèbre constitue un domaine absolument central des mathématiques du XVIIe siècle occidental, considérée par beaucoup d’acteurs de l’époque comme le modèle à suivre pour diriger le progrès des sciences. L’un des aspects qui touche le plus le jeune Leibniz, lorsqu’il découvre cette discipline durant son séjour parisien, se trouve dans la spécieuse, c’est-à-dire l’utilisation de caractères spécialisés pour incarner les objets du calcul algébrique. Au travers des nombreux brouillons que Leibniz nous a laissés, nous pouvons donc porter notre attention sur le choix des variables opéré par l’apprenti géomètre. Cette étude porte doublement ses fruits. D’abord, elle permet de mettre en évidence des nouveaux indices quant à la datation des manuscrits. Mais elle permet également d’interroger les conceptions d’inconnus, connus ou d’indéfinis faites par Leibniz et de les confronter à ses discours méthodologiques.
  • Edgar Lejeune (University of Paris (Diderot),SPHERE, et Paris Sorbonne Nouvelle, LATTICE)
    How did historians scholarly edit for IBM punched cards ? A comparison between two case-studies (France, 1970-1980)
    Between 1961 and 1989, numerous computer-assisted historical studies were conducted in France. Historians involved in these projects were members of various historiographical programs (history of the mentalities, social history, economic history). They also adopted a wide range of computational methods, used by other social sciences (demography, linguistic, sociology) and they dealt with several types of historical sources (political tracts, charters, censuses, etc.). Moreover, these studies took place in different types of institutions (universities, CNRS, EHESS, laboratories, etc…), which shaped the way in which these historians had access to computers and to computer scientists. However, in these diverse configurations, one element appears to be shared by a large number of these scholars : the storage device used for the recording of the data, IBM punched cards.
    My communication aims at comparing two computer-assisted projects on the basis of the text editing methods they developed in relation to that storage device technology. The first one is an international cooperation conducted by Christiane Klapisch-Zuber and David Herlihy between 1966 and 1978. It aimed at creating an edition for the computer of a gigantic late medieval Italian archive : the catasto fiorentino of 1427. The second one is a project conducted at the university Paris 1 Panthéon-Sorbonne by a small group of medievalists, who focused on English political texts from the 13th to the early 16th century. I will show how four different types of elements took shape in the conception of these text editing practices : 1) the collective organization of these groups ; 2) the type of documents on which the study relied and 3) the research goals that these medievalists pursued.
  • Mathias Grote (Humboldt-Universität zu Berlin)
    Synthesis and systematization – Modern European Encyclopedisms
    In order to understand which factors beyond the recent effects of digitization have influenced transformation processes of scientific literature, this talk will investigate the history of scientific writing, publishing and reading in a short 20th century. More specifically, my aim is to analyze the strategies and practices employed by scientists, research institutes, libraries or publishers to systematize and synthesize, critically evaluate, document and communicate knowledge. In other words, this talk looks for answers to the historical as well as political question of which "knowledge infrastructures" have been formed and maintained in a largely pre-digital, but nevertheless technologically advancing century in order to put reliable knowledge into circulation. One case in point is the coming into existence and transformation of an influential book for philosophy of science, the International Encyclopedia of Unified Science (1938-1945), edited by Otto Neurath et al. My future goal is to work comparatively on Francophone cases.

April 8, 2021, webconference

  • 10:15am–11:45am
  • Arilès Remaki (Université de Paris–ED 623, SPHere, & ANR Mathesis)
    Choix des variables dans les brouillons d’algèbre de Leibniz (2)
    L’algèbre constitue un domaine absolument central des mathématiques du XVIIe siècle occidental, considérée par beaucoup d’acteurs de l’époque comme le modèle à suivre pour diriger le progrès des sciences. L’un des aspects qui touche le plus le jeune Leibniz, lorsqu’il découvre cette discipline durant son séjour parisien, se trouve dans la spécieuse, c’est-à-dire l’utilisation de caractères spécialisés pour incarner les objets du calcul algébrique. Au travers des nombreux brouillons que Leibniz nous a laissés, nous pouvons donc porter notre attention sur le choix des variables opéré par l’apprenti géomètre. Cette étude porte doublement ses fruits. D’abord, elle permet de mettre en évidence des nouveaux indices quant à la datation des manuscrits. Mais elle permet également d’interroger les conceptions d’inconnus, connus ou d’indéfinis faites par Leibniz et de les confronter à ses discours méthodologiques.
  • 11:45am–12am Break
  • 12am–1:30pm
    Andrea Bréard (University of Erlangen & University Paris-Sud)
    Numbers beyond discourse : disruptive or heuristic diagrammatic patterns in Chinese mathematical texts ?
    In mathematics, questions concerning the relation between text and image and the intermediary space between them have been addressed mainly for the history and epistemology of geometric diagrams, but figured numbers, which bear the property to be simultaneously a matrix of arithmetical routine and of geometric configuration, have so far not been the object of study.
    In my talk I will address such questions, focusing on numbers in certain geometric shapes. By focusing upon late imperial Chinese representations of numbers in Li Shanlan’s Comparable Categories of Discrete Accumulations from 1867, I will show how number diagrams were typographically set apart from text yet epistemologically entangled with it. This discussion is based on the challenges posed by my personal work as an editor and translator of this text filled with diagrams and figured numbers. I will look at ways in which historical actors have “read” Li’s diagrams and generated a symbiotic meaning of the text that lies between the editorial and their interpretative work. Following (McGann 1991), I do not consider editorial and interpretative work as separate textual practices but rather see them as resulting in a symbiotic textual – or here rather paratextual – condition, a situation of symbolic exchange between reader and paratext.
  • 1:30pm–3pm Lunchbreak
  • 3pm–4:30pm
  • Alexei Volkov (National Tsing-Hua University, Taiwan)
    Mathematical texts from Dunhuang : The problem of filiation
    In 1900, a large collection of old manuscripts was discovered in the Buddhist monastery in Dunhuang (Gansu Province, West China) in a cave sealed between 1006 and 1035. The majority of the manuscripts were copies of Buddhist scriptures, yet the collection also included numerous non-Buddhist texts related to traditional sciences, such as astronomy, astrology, medicine, divination, and mathematics. These mathematical manuscripts are representative samples of the texts used for mathematics instruction in China in the late first millennium AD.
    In my presentation I will discuss the works devoted to the mathematical manuscripts authored by Chinese and Western authors, and offer analysis of several mathematical problems found in them. I will also attempt at restoring connections between these problems and those found in other Chinese mathematical texts of first and early second millennium AD.

May 6, 2021, 10am–1pm

  • Mark Geller (University College London & IRA Paris)
    The Cuneiform Conundrum : how do you ‘alphabetise’ without an alphabet ?
    My talk is based on an interesting tablet which is a long list of materia medica, which I have been studying for a long time. It is a very complex text, 3 columns on each side with lots of ‘paragraph’ rulings, giving the circumstances in which the drugs are to be applied. The problem is trying to determine why the drugs and diseases are listed in the particular order in which they appear, since there is good reason to argue that the drugs were listed according to the drugs in column one, or the diseases in column two, or the applications in column three. All are possible ! What I would like to explore further is whether the entire text can be a kind of theoretical ‘model’, similar to mathematical or astronomical models, which no one has as yet suggested.
  • Michael Friedman (Humboldt Universität zu Berlin)
    Medieval Hebrew mathematical manuscripts left in mediis rebus : The case study of “A treatise on measurement of areas and volumes” of Bar Hiyya
    As Israel Ta-Shema noted in 1993, the “medieval Hebrew book […] often seems perplexingly left in mediis rebus and intrinsically incomplete”. By this he points out the phenomenon of fluidity and flexibility in medieval Hebrew manuscripts, being in a state of an ‘open book’ and never reaching a final edition – emphasizing the dynamic state of the text and its transformational character. The question that stands at the center of my talk is whether these insights apply to medieval Hebrew mathematical texts, and whether these texts form a special sub-class, with its own characteristics, within the set of in medieval Hebrew manuscripts. In order to examine this question, I will look into the history of copying, transmission and reception of one of the first mathematical manuscripts in Hebrew written in the 12th century by Abraham bar Hiyya : “A treatise on measurement of areas and volumes” (“Ḥibbur ha-Meshiḥa ve-ha- Tishboret”), which was later translated into Latin in 1145 as “Liber embadorum”.

June 10, 2021, 11:00am–1:00pm, videoconference and Room Mondrian, 646A

  • Discussion on the program for next year
  • Anna Keel Steensen (ETHZ) (postponed)
    Working with inscriptions : making and breaking formal rules as computational practice
    A mathematician doing a computation may be considered to do the computation formally if following certain rules for transforming expressions without taking into account any meaning that the rules and expressions may have. In this view, ‘formal’ expresses a special relationship between a rule and its meaning : a ‘formal’ computation operates according to a rule independently of its interpretation.
    This presentation is about on-going work on the formal computation as a historical dynamic phenomenon exploring the idea that ‘formal’ computation as operation without interpretation emerges together with the development of new mathematical, logical and computational practices.
    I address the question from a semiotic perspective : I apply an analytical approach building on e.g. Herreman, Hjelmslev and Lévi-Strauss. This approach gives ‘the formal rule’ as an effect of the mathematical text by describing the creation and following of computational rules in terms of relations between the written expressions. From this perspective, my question becomes : what makes us interpret the expressions of a specific passage of text as formal ?
    I apply this framework to combinatorial analysis papers by Carl Friedrich Hindenburg (1741-1808) and Heinrich August Rothe (1773 – 1842) (both associated with the ‘Combinatorial School’). The analysis does not reproduce the intentions or interpretations of the historical actors (such as the historical writer or their typical reader). Instead, it seeks to describe the surface phenomena of signs and their relations and give a contemporarily relevant interpretation. This provides (hopefully) a useful analytical perspective on formal computation that complements (rather than replaces) historical, philosophical and cognitive analyses.
    In the case of Hindenburg and Rothe, the analysis generates a marked historical contrast separating an 18-19th c. formal computational practice from later (post-19th c.) ones.







VENUE



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