A Dialética entre a obra Ex Ludis Rerum Mathematicarum (1450) e seu contexto social, histórico e cultural: um estudo sob a perspectiva da Teoria da Objetivação

Abstract

This thesis is the result of an investigation whose object of study was the relationship between the work Ex Ludis Rerum Mathematicarum by Leon Battista Alberti (14041472) and the social, historical and cultural context of its production. The work was written in 1450 as a gift to Prince Meliaduse d’Este of the court of Ferrara in Italy upon his supposed accession as Marquis d’Este. Starting from old desires expressed by Meliaduse, related to procedures that could be used to measure fields and to control the waters of rivers and streams, Alberti addresses in the work a set of practical problems involving technical knowledge linked to the manual arts of the time - surveying , cartography, navigation, architecture, among others - which could be solved through procedures that made use of various mathematical concepts, mainly geometric and arithmetic. Assuming the Theory of Objectification as a theoretical and conceptual framework, our main purpose was to achieve a greater understanding of the process of historical, social and cultural constitution of mathematical knowledge through the analysis of the relationship between a textual work and the context of its production. The investigation was guided by the following question: how does the work Ex Ludis Rerum Mathematicarum emerge and, at the same time, reproduce and ideologically affirm the social, historical and cultural context of its production? Starting from the assumption that the relationship between a work and its context is dialectical, we define as a general objective: to analyze the way in which the dialectic between the work Ex Ludis Rerum Mathematicarum and the social, historical and cultural context of its production is put into operation. . The analysis of the functioning of the dialectic between the work Ex Ludis Rerum Mathematicarum and its context demonstrated, among other things, that this work is an artifact that incorporates, refracts and affirms the ideologies that operated in fourteenth-century Italy. Two ideologies were identified behind the work: the humanist ideology and the artists’ ideology. The historical-cultural forms of mediation that explain the emergence of Ex Ludis Rerum Mathematicarum are: the process of secularization of society and culture and a new way of relating intellectual and manual work (or theory and practice). These two forms are closely related and also explain the political project that existed behind the work, which involved: the constitution of a new ideal of prince, the inclusion of architecture among the liberal arts and the elevation of the architect's social status. Throughout the investigation, it was also noticed the close connection that the content of Ex Ludis Rerum Mathematicarum has with other works by Alberti, mainly with his architectural treatise De re aedificatoria. In view of the investigation carried out and the results obtained, the thesis defended is that: the Theory of Objectification constitutes a theoretical and conceptual framework with analytical potential to explore the process of historical, social and cultural constitution of mathematical knowledge through the analysis of the relationship between a textual mathematical work and the social, historical and cultural context of its production.