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L'arithmétique divinatoire: De Leibniz à l'Oulipo

Abstract : This forthcoming book proposes a journey, or rather a walk, in time, space and also in some regions of the mind. It is first, indeed, to explore some activities of the mind seeming at first glance to have no connection with each other, but between which some authors (and not the least: Leibniz, Simone Weil, Italo Calvino ...) thought they spotted as a family resemblance. These activities are: divination (or at least some geomantic procedures using arithmetic operations, such as Chinese geomancy, but also Arabic and Tuareg geomancies); some games (examples used will be chess, go, and also an African game known as awélé); mathematics; literary writing (such as it was at least practiced by some authors like Italo Calvino, members of the Oulipo, and some German poets of the Baroque period). The whole may seem heterogeneous, and it is, the challenge that the author has set himself being precisely to show that this heterogeneity is only apparent. The book will therefore go from one to the other of these activities, gradually putting before the reader's eyes reasons for admitting that they are, in a way, related. It is not because of a taste for paradox that this walk is proposed, but because, as has been said, great minds have not been far from proposing it. Leibniz, for example, thought he could affirm in 1703 that the 64 hexagrams of Chinese geomancy were nothing more than the writing of the numbers 0 to 63 in the binary system. He was wrong, but his initial intuition was correct. The arithmetic underlying Chinese geomancy does have something to do with binary numeration (but the state of mathematics in 1703 did not allow Leibniz to perceive exactly what was at stake; only Gauss' discoveries a century later could have allowed this). As for the relationship between divination and writing, Italo Calvino said he used a "combinatorial narrative machine" running on tarot cards to write his Castle of Crossed Fates. Divination by cards is a priori very different from geomancy, but it so happens that Tuareg geomancers use a kind of combinatorial narrative machine very comparable to that of Italo Calvino. Not to mention the role that the Yi-King played in the plot and even in the writing of Philip K. Dick's Master of the High Castle. And as for mathematics, in addition to seeing it present in divination and in certain writing practices, we will sketch, from the confidences of some illustrious names of the profession (Laurent Schwartz, Alexandre Grothendieck, Cédric Villani...) an ideal portrait of the mathematician that we will place alongside an ideal portrait of the player, composed according to some game theorists (Leibniz there again, Fontenelle, Colas Duflo). The reader will be able to judge the resemblance. The "machines" I am talking about here after Calvino are mental machines rather than machines in the ordinary sense of the word, but we will also encounter real machines, technically very modest but very tangible in other writing enterprises. The most notorious is the wheeled machine of the Catalan Ramón Lull (end of the 13th century) that Luis Borges called, to make fun of it, Ramón Lull's máquina de pensar. And a plastic artist linked to the Oulipo made a very comparable machine designed to make Queneau's One Hundred Thousand Billion Poems simultaneously visible. In addition to this, there were other machines that appeared in Baroque Germany. In short, a journey in space (from the Sahel to China, via Baroque Germany), in time (from the 12th century, when the earliest treatises on Arab geomancy date back to the present day, with the authors of Oulipo) and in spirit (since the reader will be invited to reflect on what goes through his mind when he engages in such mundane activities as flipping a coin or stripping a daisy, for example). Finally, it will come as no surprise to learn that this trip will bring us face to face with an illustrious traveller: Gulliver had the opportunity to observe a machine on the island of Lagado that is very similar - albeit a little more extravagant - to the ones discussed in this book.
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Contributor : Dominique Casajus <>
Submitted on : Friday, May 29, 2020 - 1:24:33 PM
Last modification on : Tuesday, July 21, 2020 - 3:52:01 AM


  • HAL Id : halshs-02650180, version 1


Dominique Casajus. L'arithmétique divinatoire: De Leibniz à l'Oulipo. A paraître. ⟨halshs-02650180⟩



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