Madhusudhan Raman

“I started out on burgundy,
but soon hit the harder stuff.”

Borges refers to the work of Ramon Llull (or Raymond Lully, or even Raimundo Lulio) at least thrice in his oeuvre. My earliest encounter with this medieval ecclesiastic was in Pierre Menard, Author of the Quixote, where Borges, after presenting us with the endorsements he has obtained from the Baroness de Bacourt and the Countess de Bagnoregio, proceeds to enumerate the “visible” work left behind by the titular novelist.1 Among these, we find:

…
f) A monograph on Raymond Lully’s Ars magna generalis (Nîmes, 1906).
…

This reference, one of nineteen, is of no great significance; the list serves to orient us, to help better understand the peculiarities of Menard’s thought by illuminating his intellectual milieu. A more substantive reference to Llull appears in A Note on (toward) Bernard Shaw, where Borges writes:2

At the end of the thirteenth century, Raymond Lully (Raimundo Lulio) was prepared to solve all arcana by means of an apparatus of concentric, revolving discs of different sizes, subdivided into sectors with Latin words…

He discusses this apparatus in more detail in a short essay titled Ramon Llull’s Thinking Machine, at first admitting freely its intricate futility and unperturbed by it.3

[M]easured against its objective, judged by its inventor’s illustrious goal, the thinking machine does not work. For us, that fact is of secondary importance. The perpetual motion machines depicted in sketches that confer their mystery upon the pages of the most effusive encyclopedias don’t work either, nor do the metaphysical and theological theories that customarily declare who we are and what manner of thing the world is. Their public and well-known futility does not diminish their interest.

Borges goes on to offer us an anemic defense of Llull’s Ars. After acknowledging the poverty of its revelations and the undeserving locus of its laborious construction, Borges corrects himself: “I said that the thinking machine does not work. I have slandered it: elle ne fonctionne que trop, it works all too well.” The mechanism produces an embarrassment of possible truths, each undifferentiated from the next, a “torrential ambiguity.” He concludes (rather weakly) that Llull’s thinking machine may enjoy some utility as a “literary and poetic device.”

The circumstances of Llull’s own life are of not so much contemporary interest, but briefly, Llull is moved by a vision of Christ to:4

… accept the possibility of martyrdom in an attempt to missionize; to try “to write a book, the best in the world, against the errors of the unbelievers”; and “to go to the pope, to kings, and to Christian princes to incite them” to establish language monasteries for missionaries.

After nearly a decade of study and solitude, another divine revelation presented to him the “form and method” of the Ars, a combinatorial system for asking and answering questions that he would continually develop, refine, streamline, and explicate in over 250 works written between 1274-1316. The nebulous power Llull’s Ars exerted over the nascent sciences would persist for five centuries; Agrippa, Bruno, and Leibniz were all influenced by him. Where the Ars formed the bedrock of Llull’s Christian apologetics, it also functioned more generally (not unlike the dialectic) as a universal methodology, a practical art of investigation for all subjects.

Returning now to A Note on (toward) Bernard Shaw, Borges identifies a pathology more severe underlying the logic of the Ars:

Lully’s machine… can be the subject of jokes, but [it] exaggerate[s] a propension which is common: making metaphysics and the arts into a kind of play with combinations.

It is (regrettably, dismally) in vogue these days to suggest that the discovery of truths in the mathematical and natural sciences are more amenable to this approach. (A discussion of whether this future is a desirable one appears to be beyond us at the moment. For now, we are focused too much on its inevitability.) We read on:

Those who practice this game forget that a book is more than a verbal structure or series of verbal structures; it is the dialogue it establishes with its reader and the intonation it imposes upon his voice and the changing and durable images it leaves in his memory. This dialogue is infinite… Literature is not exhaustible, for the sufficient and simple reason that no single book is. A book is not an isolated being: it is a relationship, an axis of innumerable relationships.

I feel there is an argument here that the same applies to mathematics and the natural sciences, but it is not clear to me yet.

  1. Collected in Labyrinths (1962). The translation quoted here is by James E. Irby. ↩

  2. Ibid. ↩

  3. Collected in Selected Non-Fictions (1999). The translation quoted here is by Esther Allen. ↩

  4. For a brief biography of Llull and a detailed discussion of the Ars, see The Art and Logic of Ramon Llull: A User’s Guide by Anthony Bonner (2007), where the quote below is also drawn from. ↩