Historical studies of quaternion mathematics have usually placed Sir William Rowan Hamilton's "discovery" of quaternions within the context of the history of modern vector analysis. Exemplary of this technique is the seminal study A History of Vector Analysis by Michael Crowe (1967), in which Hamilton's development of quaternions is seen as an important precursor to the eventual development of contemporary vector calculus. Within Crowe's account, the reader also finds the story of two transitional figures: Peter Guthrie Tait (1831-1901) and William Kingdon Clifford (1845- 1879). Tait is described as a propagator of Hamiltonian methods - someone who wrote about them more succinctly than did Hamilton, and someone who applied them to various topical problems in dynamics. Meanwhile, Clifford is described as a secondary, minor figure - a transitional character whose development of bi-quaternions figures not at all in Crowe's historiography. This thesis redresses those categorizations by effectively "stopping the clock" at 1880, before the "modern" conception of vector analysis had emerged. Following a brief account of the state of British mathematics and science in the first half of the century (1800-1850), the present study focuses on the motivations behind Tait and Clifford's respective engagements with and uses of quaternion mathematics in the second half of the 19th-century. Using the analytical metaphor of "terrains of knowledge" (which is inspired in part by the Wittgensteinian metaphor of language games, and the Strong Program account of finitism in scientific knowledge), I aim to describe the environments - philosophical, institutional, political, and religious - within which Tait and Clifford worked. By describing those "terrains of knowledge", the historian is able to explain why Tait and Clifford, two actors who lived in a similar time and similar place, engaged with the conceptual artifacts of "quaternions" in divergent ways. In the case of Tait, the crucial "terrains of knowledge" to consider in identifying the conceptual environment requisite for him to have used quaternions in the manner that he did includes Cambridge and Belfast mathematics, the University of Edinburgh as an institution in flux (1840-1870), the "science of energy" (1850-1870), and Presbyterian politics and Tait's attack on secularism. In Clifford's case, the salient "terrains of knowledge" include the University of Cambridge and the morphing of symbolical algebra (1860-1870), non-Euclidean geometries in Britain, Clifford's Darwinism, and University College, London as a secularist urban educational institution. When combined, these terrains constitute the varied intellectual environments within which each actor engaged with "quaternion" mathematics, and within which each actor found the resources needed to justify and render meaningful his respective view of that particular concept.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:726424 |
| Date | January 2009 |
| Creators | Petrunić, Josipa Gordana |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/25078 |
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