The controversy about whether analytic or synthetic methods should be preferred for the solution of geometrical problems was common all over Europe, in the first half of the nineteenth century. It was related to important issues such as the definition of the new discipline of “pure mathematics”, and it has been taken by recent historiography of science as an exemplary case for the analysis of conceptual change in mathematics. In this study, historical material relating to the under-researched case of Naples is presented, and used to support a new interpretation for the controversy. The study begins by describing the technical contents of the Neapolitan version of the controversy, referring publications involved in one important, emblematic episode: the public challenge between the two rival geometrical schools, which took place in 1839. The competing methods are presented, and it is argued that, far which being caused by some mere “technical” divergence, the controversy arose from two very different conceptions of the nature and goals of geometry, and of mathematics in general. The following step is to look at the cultural environment where these two contrasting conceptions of mathematics were elaborated. Historical evidence supports the claim that both schools emerged in the very same period, the 1780s, and that the common interpretation of a preexisting synthetic school challenged by a new analytic school is misleading. Rather, the synthetic school emerged in reaction to the diffusion of analytic methods in Naples. It is also argued that the synthetic geometers were not simply “backward”, and that they did not ignore the modern analytic methods; they chose to oppose the analytic conception of mathematics; they made the choice of being anachronistic. The wider philosophical and theological meaning of opposing the “spirit of analysis” is investigated, which brings us to the heart of the political and cultural upheaval which Naples experienced in the revolutionary and Napoleonic period. Two opposite networks of philosophers, ecclesiastics, scientists and literati emerge, one siding with the modernization of the country according to the French example, the other defending the semi-feudal structure of the Neapolitan state. It is only against the background of this crucial debate, over the re-shaping Neapolitan society, that the apparently detached controversy over geometrical methods is best understood. It is indeed argued that the production of scientific and mathematical knowledge, as that of any other form of knowledge, was shaped by the wider cultural and social goals of the actors involved. And, in fact, the controversy over geometrical methods, originally emerging in correspondence with the reaction to the French Revolution, eventually lost its scientific relevance in the early 1840s, as the cultural hegemony of Neapolitan reactionary forces declined. It is finally suggested that this socio-historical interpretation of the Neapolitan case could cast light on other similar mathematical controversies of the first half of the nineteenth century.

In Artifacts, Revolutionaries and Bureaucrats, I have combined oral accounts with primary and secondary documentation, to reconstruct a sociotechnical history of the National Aeronautic and Space Administration's (NASA's) space shuttle, from 1968 to 1985. Encompassed within the thesis is an exploration of the design, development, fabrication and operation of technology. Drawing from literature in the social studies of science and technology, the thesis aims to map the relations between the social and the technological and survey the underlying dynamics of technological change. A principal objective of this thesis is to show that the creation of technology is as much a social activity as a technical one: that social matters were as significant an influence on the content of the shuttle as technological or scientific matters. The thesis does not, however, neglect the role of the material world and also provides an analysis of the technical shaping of technology. However, the aim of a historical sociology of technology is to reveal the error in assuming that technology is entirely under the control of rational decision making; that the process of technological change takes place along a well defined, sequential path; and that technological progress is inherently predictable. The practitioners of technology may strive to create order, system and control, but the history of technology is usually complex and contradictory.

This dissertation proposes a revised understanding of the place of science in British literary and political culture during the early atomic era. It builds on recent scholarship that discards the cultural pessimism and alleged ‘two-cultures’ dichotomy which underlay earlier histories. Countering influential narratives centred on a beleaguered radical scientific Left in decline, this account instead recovers an early postwar Britain whose intellectual milieu was politically heterogeneous and culturally vibrant. It argues for different and unrecognised currents of science and society that informed the debates of the atomic age, most of which remain unknown to historians. Following a contextual overview of British scientific intellectuals active in mid-century, this dissertation then considers four individuals and episodes in greater detail. The first shows how science and scientific intellectuals were intimately bound up with George Orwell’s Nineteen Eighty Four (1949). Contrary to interpretations portraying Orwell as hostile to science, Orwell in fact came to side with the views of the scientific right through his active wartime interest in scientists’ doctrinal disputes; this interest, in turn, contributed to his depiction of Ingsoc, the novel’s central fictional ideology. Jacob Bronowski’s remarkable transition from pre-war academic mathematician and Modernist poet to a leading postwar BBC media don is then traced. A key argument is that rather than publicly engaging with actual relations of science and the British state, Bronowski actively downplayed the perils of nuclear weapons, instead promoting an idealist vision of science through his scientific humanism philosophy. Finally, the political activism of J.G. Crowther and P.M.S. Blackett are analysed, Crowther through his chairmanship of the Communist-linked British Peace Committee, and Blackett through his controversial book Military and Political Consequences of Atomic Energy (1948). In neither case, as might be expected, did their nuclear politics stem from scientific ideology but rather from personal convictions.

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The connection between topology and computer science is based on two fundamental insights: the first, which can be traced back to the beginning ofrecursion theory, and even intuitionism, is that computable functions are necessarily continuous when input and output domains are equipped with their natural topologies. The second, due to M. B. Smyth in 1981, is that the observable properties of computational domains are contained in the collection of open sets. The first insight underlies Dana Scott's cate}ories ofsemantics domains, which are certain topological spaces with continuous functions. The second insight was made fruitful for computer science by Samson Abramsky, who showed in his 'Domain Theory in Logical Fonn' that instead ofworking with Scott's domains one can equivalently work with lattices of observable properties. Thus he established a precise link between denotational semantics and program logic. MathematicaIly, the framework for Abramsky's approach is that of Stone duality, which in general tenns studies the relationship between topological spaces and their lattices of opens sets. While for his purposes, Abramsky could rely· on existing duality results established by Stone in 1937, it soon became clear that in order to capture continuous domains, the duality had to be extended. Continuous domains are of interest to semantics because of the need to model the probabilistic behavior and computation over real numbers. The extension of the Stone duality was achieved by Jung and Siinderhaufin 1996; the main outcome of this investigation is the realization that the observable properties of a continuous space fonn a strong proximity lattice. The present thesis examines strong proximity lattices with the tools of Priestley duality, which was introduced in 1970 as an alternative to Stone's duality for distributive lattices. The advantage of Priestley duality is that it yields compact Hausdorff spaces and thus stays within classical topological ideas. The thesis shows that Priestley duality can indeed be extended to cover strong proximity lattices, and identifies the additional structure on Priestley spaces that corresponds to·the proximity relation. At least three different types of morphism have been defmed between strong proximity lattices, and the thesis shows that each of them can be used in Priestley duality. The resulting maps between Priestley spaces are characterized and given a computational interpretation. . This being an alternative to the Jung-Siinderhauf duality, it is examined how the two dualities are related on the side of topological spaces. FinaIly, strong proximity lattices can be seen as algebras ofthe logic MLS, introduced by Jung, Kegelmann, and Moshier. The thesis examines how the central notions ofMLS are transfonned by Priestley duality.

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