ABSTRACT In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest (...) arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's “principle of equivalent forms,” which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra. (shrink)

Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, (...) Hamilton's defense of algebra, like Newton's defense of geometry, is driven by the claim that a mathematical science must have a proper object and thus a basis in truth. In particular, Hamilton aims to show that algebra is not a mere language, or tool, or a mere “art”; instead, he argues, algebra is a bona fide mathematical science, like geometry, because its methods also provide true and accurate insight into a genuine subject matter, namely, the pure form of temporal intuition. (shrink)

More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...) Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’. (shrink)

Scholars in both digital humanities and media studies have noted an apparent disconnect between computation and the interpretive methods of the humanities. Alan Liu has argued that literary scholars employing digital methods encounter a “meaning problem” due to the difficulty of reconciling algorithmic methods with interpretive ones. Conversely, the media scholar Friedrich Kittler has questioned the adequacy of hermeneutics as a means of studying computers. This paper argues that that this disconnect results from a set of contingent decisions made in (...) both humanistic and mathematical disciplines in the first half of the nineteenth century that delineated, with implications that continue to resonate in the present day, which aspects of human activity would come to be formalized in algorithms and which would not. I begin with a discussion of Nicolas de Condorcet, who attempted, at the height of the 1789 revolution, to turn algebra into a universal language; his work, I argue, exemplifies the form of algorithmic thinking that existed before the Romantic turn. Next, I discuss William Wordsworth’s arguments about the relationship of poetry and science. While Wordsworth is sometimes viewed as a critic of science, I argue that his polemic is specifically targeted at highly politicized projects like Condorcet’s that sought to supplant existing modes of thought with scientific rationality. Finally, I demonstrate the importance of Romantic thought for George Boole, creator of the logic system that would eventually form the basis of digital electronics. The reason Boole was able to succeed where Condorcet had failed, I argue, was that Romantic notions of culture enabled him to reconcile a mechanical view of mathematical reasoning with an organic view of the development of meaning—a dichotomy that remains a key assumption of computer interfaces in the twenty-first century. (shrink)