This article argues that Pulcinella, a figure of classical Italian commedia dell’arte, could also be considered as emblematic for the reordering of politics in the early-modern and modern periods. By placing emphasis on the common underlying theatrical aspects of ‘representation’, it effectively connects the absolutist and democratic periods and helps us to understand why actors and acting came to play such a prominent role in contemporary politics, whether as politicians imitating actors, or as actors actually becoming politicians. The article also (...) shows that this sublimation of theatre into politics is not even a contemporary phenomenon but can be traced back to the ancient mime, following the origins of Pulcinella, and the first crisis of democracy, in classical Athens, in the footsteps of Plato. (shrink)

Archimedes’ Sand-Reckoner presents a system for naming extraordinarily large numbers, larger than the number of grains of sand that would fill the cosmos. Curiously, Archimedes addresses the treatise not to another specialist but to King Gelon II of Syracuse. While the treatise has thus been seen as evidence for the dynamics of patronage, difficulties in both Archimedes’ treatment of Gelon and his discussion of astronomical models make it fit incongruously within contemporary court and scientific contexts. This article offers a new (...) reading of the Sand-Reckoner based on a reconsideration of the relationship between author and addressee: deferring assumptions about the historicity of that relationship, it analyzes Gelon’s role in the treatise with respect to both the stylistic features of Archimedes’ prose and a broader tradition of narratives about a variety of cultural actors who engage with kings, speaking not so much truth as wit to power. Such a reading resolves the social and scientific difficulties of the treatise, and develops the literary-experimental qualities of Hellenistic science. In turn, the article proposes a revised approach, sensitive to broader patterns of authorship, to understanding ancient scientific authors’ relationship to royal authority. It concludes, finally, that the royal patronage seemingly exemplified by the Sand-Reckoner had greater significance as a cultural trope than as a social institution. (shrink)

This article discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.

The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also (...) central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity. (shrink)

Medieval Arabic algebra is a good example of an artificial language.Yet despite its abstract, formal structure, its utility was restricted to problem solving. Geometry was the branch of mathematics used for expressing theories. While algebra was an art concerned with finding specific unknown numbers, geometry dealtwith generalmagnitudes.Algebra did possess the generosity needed to raise it to a more theoretical level—in the ninth century Abū Kāmil reinterpreted the algebraic unknown “thing” to prove a general result. But mathematicians had no motive to (...) rework their theories in algebraic form. Because it offered no advantage over geometry, algebra remained a practical art in both the Islamic world and in Europe until the scientific uphevals of the 17th–18th centuries. (shrink)

The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that the geometrical algebra interpretation should be reinstated as a viable historical hypothesis.