Inter-studia humanitatis, 16, 2014, ISSN 1822-1114, p. 43-60 MOCKInG THE MATHS. a PRELImINARY STUDY ON THREE CENTURIES oF PARODIES oF THE MATHEMATICAL LANGUAGe moreno Bonda Vytautas Magnus University E-mail [email protected] SummaRy While mathematics has always been considered a serious subject, the histo- ry of ideas reveals a number of satirical reinterpretations of the mathemati- cal language, processes and principles. In Early Modern Europe, mathemat- ics was the object of satires, critics and mockery. Rereading three famous satirical works – Alice in Wonderland, Gulliver’s Travels, and Rabelais’ Fifth Book – in which the maths are openly ridiculed, we investigate the reasons for these parodies and define them as reactions to reforms of this discipline. Alice is caricaturing negative and symbolical al- gebra; Swift lampoons Athanasius Kircher and his followers’ computational logic; Rabelais satirizes Ramon Llull’s thinking machines. However, we suggest that the debate was much broader and not limited to the reform of mathematics. As a matter of fact, a number of theologians understood mathematics as the language able to express in symbols the in- expressibility of the Creation’s infiniteness. The parodies of the mathematics are clearly a contestation of this epistemological system. Key words: Alice in Wonderland, Gulliver’s Travels, mathematical theology, parodies of mathematics, Rabelais, ramism, Ramon Llull, thinking machine. MOCKING THE MATHS. A PRELIMINARY STUDY ON THREE CENTURIES OF ON THREE CENTURIES STUDY A PRELIMINARY MOCKING THE MATHS. LANGUAGE OF THE MATHEMATICAL PARODIES 42 43 IntroductIon While mathematics is almost always considered a very serious subject and, possibly, the most respectable scientific discipline, the histories of literature and philosophy reveal a number of satirical reinterpretations of the mathemat- ical language, its processes and its principles. At least for three centuries – from Rabelais’ desecrating critic of the Scholastic education (1564) to Lewis Carroll’s veiled parody (1865) of algebra – mathematics has been the subject of satires, critics and mockery. This paper is intended as a preliminary study on the reasons, methods, meanings and objectives of these parodies of the mathematics and the math- ematical language. More precisely, we aim at defining the extent and charac- teristics of this phenomenon in Early Modern Europe. Specifically, it will firstly define the chronological limits of this attitude toward mathematics. Secondly, it provides a contextualization of these satires in the coeval epistemological debates. The ultimate ambition of the research is to understand whether these parodies were just elaborate jokes and, thus an end in itself, or rather coherent assertions of alternative definitions of knowledge meanings and processes. The paper portrays just the broader problem aiming at framing it. Herein, concrete circumstances and specific cases cannot be analysed in depth in these pages. Accordingly, it will touch on specific theories and personalities just in passing. Rather to provide references to specific studies or lay the foundations for fur- ther investigations. 1. the ParodY oF mathematIcs: a deBate on Formal logic The idea of parodies being a reaction to reforms or redefinitions of the pro- cesses of knowledge had been formulated in the past by Helena M. Pycior’s in her study on the intersection of mathematics and humour(Pycior, 1984). Focus- ing on the parody of symbolic algebra in Lewis Carroll’s Alice in Wonderland, the scholar investigates the reasons for such an irreverent attitude during the second half of the 19th century. This study has, first of all, the merit to contextu- alize the parody of algebra in the coeval intellectual debate about knowledge. Secondly, it makes evident 19th century scholars’ interest for the relation be- tween worlds, the deductive processes of the human mind and the language onda B used to express them. Similar considerations emerge in Melanie Bayley’s Alice’s Adventures in Al- gebra (2009), where the relation between the early 19th century reform of the oreno M discipline and its parody is clearly expressed: ‘it becomes clear that Dodgson 44 45 [the real name of Lewis Carroll], a stubbornly conservative mathematician, used some scenes to satirise these radical new ideas’ (Bayley, 2009). Interest- ingly, Bayley indicates not only Carrol’s evident intent to satirize the mathemat- ics, but illustrates also the technique used to achieve this goal: the recourse to the reductio ad absurdum – a very common logical process adopted by math- ematicians devoted to Euclid. Moreover, in this article emerges, once again, the connection between the logical processes, the mathematical language and the meaning (or nonsense) of single terms. Every investigation of the comical-ironical use of the mathematical language seems a necessarily conduct to the study of the relation between formal logic and mathematics. This is what emerges in Ernest Nagel’s essay on the history of modern logic (Nagel, 1935). Dealing with imaginary numbers, the scholar indicates in William Fred one of the most tenacious critics of negative and sym- bolical algebra and an unexpected satirical writer able to comically use math- ematical principles. Fred’s play,1 and consequently it analysis in Nagel, deals with the mathematical concept of “nothing” (Pycior, 1984. p155). Similarly, the same notion is ridiculed in another of Fred’s essay:Pantagruel’s Decision of the Question about Nothing (Fred, 1915. p214). In this imitation of Rabelais, Fred realizes a sketch centred on Pantagruel’s reflection on the concept of nothing in the universities. Fred indirectly refers to the mathematicians’ use of zero in operation as the division, which, while logically sustainable, has neither a practical function, nor a counterpart in nature – as in the example the character “De Morgan” offers his students to explain the meaning of half a horse and two men and three quarters. It is not by chance that Fred openly refers to Rabelais. In the French author’s works, and specifically in his Fifth Book, the mathematical speculations typical of medieval universities are criticised by the means of an irreverent parody. Rabelais’ interest for the mathematics is by far less relevant than his desire to comment on the empty logic of the nominalists. Nevertheless, the connection between logic and the parody of mathematics in his works has already been pointed out and investigated. Specifically, John Lewis tried to define Ramón Llull’s mathematical studies reception in Rabelais. Revealing, in this study, is -Ra belais use of the word mathematicusto refer to both astronomers and astrolo- gers. Specifically, the idea of being able to predict the behaviour of a man based on the study of the stars is deemed ridiculous and contrary to the Christian concept of free will. Clearly, the serious intention to know the universe by the 1 Augustus De Morgan affirms the play was published in 1803 inThe Gentlemen’s Monthly Miscel- lany. OF ON THREE CENTURIES STUDY A PRELIMINARY MOCKING THE MATHS. LANGUAGE OF THE MATHEMATICAL PARODIES 44 45 means of the study of stars and, generally, through a logic-symbolic language as that of mathematics was, at the time of Rabelais, were already the perceived remains of the empty logic of the nominalists or, even worse, as astrology. The chronological limits of the research is impose by themselves. While there are plenty of examples of recourse to the mathematical language in liter- ature and philosophy before the 16th century, it is precisely in this period – that is, at the transition from the symbolic and transcendent universe of the Middle Ages to the concrete and “useful” nature of the humanists’ world – that the most abstract branches of the mathematics were perceived as a ridiculous rel- ict of the useless science of the nominalists. It is with Rabelais that the paro- dy of the mathematics became an instrument to repel the empty logic to the “darkness” of Middle Ages. This aspect of the quarrel between the apologists of the ancients and the advocates of the Scholastic developed for three centuries and became very relevant in connection to the Cartesian reform of knowledge during the 17th century, and once again, with the birth of the symbolic algebra in the 19th century. 2. WhY to ParodY? logic and mathematIcs In ALICE In WonderlanD As pointed out by H. M. Pycior (1984, p149), it is evident that certain pas- sages of Alice’s Adventures are at least echoing the language of well-known mathematical treatises published at the time when Dodgson was still teaching maths. As an example, in the famous scene of the trial of the Knave, Alice com- ments on a White Rabbit’s sentence stating: ‘I don’t believe there is an atom of meaning in it’ (Pycior, 1984. p149 and Gardner, 1960. p159). The linguistic coincidence of this expression with a declaration of Augustus De Morgan is evident. In his Trigonometry and Double Algebra De Morgan had affirmed: ‘With one exception, no word nor sign of arithmetic or algebra has one atom of meaning throughout this chapter’ (De Morgan, 1849). The reference to mathematical problems and specifically to the nonsense of negative and impossible numbers, and to the incapability of mathematics to provide any sort of result constitutes an evident thread in Carroll’s two books. In Through the Looking-Glass, Alice reiterates the absurdity of subtracting a greater from a lesser number; points out the nonsense of the mathematical onda B terminology trying to divide a loaf by a knife and subtracting a bone from a dog; and finally concludes that mathematics cannot bring to any certitude: oreno I’ll try if I know all the things I used to know. Let me see: four times five is M twelve, and four times six is thirteen, and four times seven is – oh dear! I 46 47 shall never get to twenty at that rate! However, the Multiplication Table doesn’t signify: let’s try Geography (Gardner, 1960.