Mathematizing Space Birkhauser

Vincenzo De Risi Editor Mathematizing Space The Objects of Geometry from Antiquity to the Early Modern Age Birkhauser Subject, Space, Object: The Birth of Modernity Franco Farinelli According to Hans Blumenberg, there are two inventions whereby the modern age cleanly breaks with the past: Florentine linear perspective and absolute space.1 They are the same thing in many ways since one is unthinkable without the other and vice versa. But this is of little import at the moment. Of immediate concern, although it has heretofore escaped notice, is that the first sighting of the New World was an avowedly perspective view in the Florentine sense of the term. Indeed, as in ancient myths, the real significance of the discovery of America resides in what at first sight appears to be a useless, even misleading complication, if not a glaring incongruity or logical contradiction. An entry in what remains of Columbus's blog2 notes the complicated event of that sighting under the date of 11 October. At 2 h past midnight, the crew of the Pinta sighted land, and Rodrigo de Triana claimed the promised reward. Yet he would never receive it because Columbus asserted he had already seen it about 10 pm the evening before when, standing on the poop deck, he had glimpsed in the same direction a flickering light like that of a wax candle. Much excited talk ensued. As calculated later, Columbus's position was about 56 miles, nearly 90 km, from land, a distance which seemingly would have made it hard to have seen anything of the kind. Even the versions of Las Casas and Fernando Columbus, which mention people walking along the coast carrying a sort of lantern, are less than convincing. In the event, the reward went to Columbus, and one tradition has it that poor Rodrigo, resentful and embittered, converted to Islam F. Farinelli (E3) Dipartimento di Filosofia e Comunicazione, Università di Bologna, Via Azzo Gardino 23, 40122 Bologna, Italy e-mail: [email protected] ' Blumenberg (2009, pp. 324-5). 2 Varela and Gil (1992, pp. 23-4 e nn. 26-8). © Springer International Publishing Switzerland 2015 143 V. De Risi (ed.), Mathematizing Space, Trends in the History of Science, DOI 10.1007/978-3-319-12102-4_6 144 F. Farinelli and emigrated to Africa. Yet what are we to make of this story? Indeed, is it possible to find a sense whose 'real content' coincides perfectly with its 'truth content', or, as Benjamin3 might have put it, the content whose import is what comes to light with time because it is exemplary and acknowledged as the key to what is to follow? Christopher means Christo ferens (as Columbus will unfailingly sign his name from 1502 on), i.e. not he who bears Christ but bears to or by virtue of Christ.4 In order to solve the enigma of what the name meant to Columbus and, hence, to grasp the sense we are seeking, it is enough to recall that in every circular medieval world map, such as those that adorned cathedral walls or even fifteenth-century missals, the figures of the Earth and of Christ formed a single whole, and that, as the host becomes the real body of the Redeemer through the Eucharist, the map—the host of the Earth—turns into his real body. All modernity develops through, and ends in, this transformation, albeit progressively losing cognizance of it at the same time. For Columbus, however, the map consciously remained what it had been throughout the Middle Ages—a prophecy.5 According to the principle that Bau- drillard will call the "precession of simulacra"6 Columbus, loyal executor of the injunction incorporated in the "Map of the Ocean" by Toscanelli of Florence which he carried with him,7 could not but oppose Rodrigo's assertion and claim as his the real first sighting of the New World. He alone had to be the first to proclaim the fulfilment of the prediction, to personally validate the precedence of the prophetic image over reality, thereby sanctioning the derivative nature of the latter with respect to the former. In effect, had Rodrigo been right, any assimilation of knowledge to acknowledgement of the cartographical model (the fundamental but almost always implicit proposition of modern epistemology) would have been placed in doubt. As King Ferdinand and Queen Isabella will write to Columbus on 16 August 1494 in acknowledging his feat: "What you had announced to us has been achieved, as if you had seen it before speaking to us."8 Christo ferens is thus the one who leads to Christ by virtue of Christ, that is, the map, and where the only word, the name of the Saviour, stands for both means and end. This is precisely the meaning of the passage in which Heidegger asserts that the "Modern World is the triumph of the world resolved into image", that is, according to "the configuration of the representing production",9 the most icastic of definitions of cartographical depiction. With this we know exactly how to understand what Jacob Burckhardt intended at the beginning of his Zurich lectures in referring to the Renaissance as a more or less direct retrieval of the "image of Ancient Rome". 3 Benjamin (1962, pp. 157-8). 4 Varela and Gii (1992, pp. L-LI). 5 Farinelli (2009, pp. 20-6). 6 Baudrillard (1981). 7 Farinelli (201 la, p. 7). 8 Todorov (1992, p. 27). 9 Heidegger (1968, p. 100). Subject, Space, Object: The Birth of Modernity 145 Before becoming something ideal, as it was for Burckhardt and even for his interpreters,10 there is something material about this image, a tangible code as all codes which practices are built upon are in the end, i.e. processes that make it possible to act on what is real through what is symbolic." The image of Rome is the material figure that Rome produces of itself at the Empire's apogee, the genitive case being understood in its double sense of possession and specification: it is the spatial map that Claudius Ptolemy, the last heir to Greek science,12 showed us how to construct. Historians of art have long kept his memory alive: it is from the Quattrocento rediscovery in Florence of his Geographia that Renaissance linear perspective derives,13 which (except for a decisive difference discussed shortly infra) is nothing but projection—the Ptolomeic procedure of "depiction of the world on a plane that has proportional measurements and a correspondence to what is depicted as round, or in spherical form", in the words of an authoritative fifteenth- century commentator.14 The image in perspective is much more than a way to access a new kind of "truth" through representation.15 Nor is it simply the figure before which the modern agent "discovers himself'.16 Just as it is not the only artefact marking the birth of modern science.17 Understanding what Panofsky has called "artificial perspective"18 does not involve breaking down its isolated ele- ments and individual effects. A total institution, "total social phenomenon", in the precise sense that Marcel Mauss attributed to the expression, i.e. one capable of moving society in its entirety,19 modern perspective produces a habitus, exactly according to the meaning Pierre Bourdieu sees in the term: that of a system of "durable arrangements", of a "structured structure intended to function as a struc- turing structure" of practices and representations at once objectively regulated but free of any conscience and control of the operations involved.20 In short, an ethic within which physical stature and ideal conception, practice and theory (in the term's original visual meaning), are inseparable. It is on the basis of this connection that Florentine perspective apodictically states its constrictive and totalitarian les- son, one capable of colonising all modernity starting from the relationship between civitas and urbs, between its civic component and urban element. No one understood all of this—the subversive import of the modern perspective gaze—better or more deeply than Pavel Florenskij. Nor is it just a matter of 10 Ghelardi (1991, pp. 129, 134, 135). 11 Schiavone (2005, pp. 8-13). 12 Aujac (1993, p. 7). 13 Edgerton (1975, pp. 93-), Veltman (1980, pp. 403-7), Edgerton (1991, pp. 151-). 14 Ptolemy (1621, p. 8). 15 Damisch (1987, p. 170). 16 Belting (2010, p. 12). 17 Gioseffi (1980. pp. 81-91). 18 Panofsky (1961, pp. 35-114). 19 Mauss (1991, p. 172). 20 Bourdieu (2000. pp. 256 e 393, n. 39). 146 F. Farinelli phenomenology or of his insight into the spatial mechanism built on a quantitative standard that is connected to it. He also apprehended its more general consequences. It would be hard to find a simpler, clearer explanation of the mechanism: the construction rests on the invariance of the bi-ratios between a straight line on which lay several points, another straight line corresponding to the plane of representation and all of the points intersecting with a bundle of straight lines that start from a single point outside the first two.2' Thus having unveiled "the basis of the artist's perspective", the consequences he sees deriving from its use become clear in a flash: the onlooker, motionless, "paralysed as though poisoned by curare", is no longer a "living person" and the image becomes "a morbid optical illusion largely deprived of any humanity".2" The absence of humanity within the mechanism of perspective corresponds in effect to the triumph of the quantitative and brings us back to Heidegger, to America and to Columbus. Heidegger writes that as soon as the quantitative takes on a quality of its own, it is transformed through the gigantic into the incalculable "invisible shadow cast over everything when man has become subjectum and the world image".23 Yet when does all this occur? When is sub- jection (being-already-at-hand) of man to the quantitative, i.e.

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