Circling Around the Truth: Rotating Symbols in the Mechanization of Thought and Reality

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: MS. Lyell 51, Bodleian Libraries, University of Oxford. (© Bodleian Libraries, University of Oxford. Creative Commons licence: CC-BY-NC 4.0.)

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How do pre-modern theories of language and signs interact with early modern theories of semiotics and cryptography, which would later be foundational in the development of computer science? What reflections do these theories offer on writing, or more broadly language, as technology? This workshop examines these questions through the development of a technique – the combination of symbols through rotation – and its manifestation in three objects: the zā’irjah, Llull’s ars combinatoria, and Alberti’s cipher disk.

In his 1476 treatise De componendis cyfris, Leon Battista Alberti described a cipher disk, which was made up of two concentric disks attached by a common pin. The disks could be rotated in relation to one another in order create a system of polyalphabetic substitution that could be used to encode messages according a unpredictable law of correspondence. Alberti’s cipher disk revolutionised cryptography. Kahn (1997) traces the inspiration for the cipher disk back to Ramon Llull’s ars combinatoria, which he described in his Ars Magna, published in 1305. The ars combinatoria took the form of a paper machine operated by rotating three concentrically arranged circles to create combinations of a symbolic alphabet. Llull claimed that these combinations would show all possible solutions to questions concerning any discipline - from astrology, to law or medicine. Llull’s ars combinatoria not only served as a source of inspiration for Leibniz’s 1666 Dissertation on the Combinatorial Art, but also piqued the interest of Pico della Mirandola, Giordano Bruno, Agrippa von Nettesheim and John Dee. It has been suggested that Llull derived his disks from the Kabbalistic tradition, and in particular from the disks of alphabets used in the Sèfer Jetzirà. However, Link (2010) also suggests that Llull’s ars combinatoria was in fact inspired by the zā’irjah. Ibn Khaldun (d.1406) describes the zā’irjah as a diagrammatical representation of the universe used as a divinatory device. Consisting of a series of concentric circles, often enclosed in a square and divided by twelve rays, the zā’irjah enabled the diviner to derive answers to questions in rhymed verse.

At the basis of these three objects - the zā’irjah, Llull's ars combinatoria and Alberti’s cipher disk- is the production of combinations of symbols through rotation. By briefly outlining and demonstrating these three objects, and the contexts of their production and usage, we hope to open up discussion to the ‘mechanisation’ of thought and reality through systems of symbols, the potential benefits and pitfalls of attempting to trace transmission and reception, and the surprising interactions between the more ‘logical’ and the ‘esoteric’.




Arianna Dalla Costa is a PhD candidate at the Warburg Institute. Her current project explores the Latin geomantic tradition from an interdisciplinary perspective and includes the critical edition and translation into Modern English of a geomantic treatise translated by Plato of Tivoli from Arabic into Latin in 1135. Dalla Costa is interested in the transmission of Islamic astronomical and astrological doctrines in the West, in the edition of Latin medieval manuscripts and the use of diagrams in medieval scientific texts. Her current work is funded by the Gerda Henkel Foundation.

Beatrice Bottomley is a doctoral candidate at the Warburg Institute, University of London, supported by a studentship from the London Arts and Humanities Partnership. Previously, at SOAS (School of Oriental and African Studies) and l’IREMAM (l’Institut de Recherches et d’Etudes sur le Monde Arabe et Musulman), Beatrice’s research interests include translation and reception studies, philosophies of language, and histories of technology. Beatrice also teaches Islamic Philosophy at King’s College London and works as a translator from French and Arabic into English.

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