1 Calculation and Tabulation in the Nineteenth Century: Airy versus Babbage Doron David Swade Thesis submitted for the degree of PhD University College London 2003 2 Abstract Charles Babbage (1791-1871) is widely recognised as the great ancestral figure in the history of computing. He designed the first automatic calculating engines and failed to realise a complete design in physical form. This thesis argues that historical accounts of Babbage’s work are based on a set of contemporary sources provided by Babbage himself and that the subsequent interpretation of the major movement to automate calculation and tabulation in the nineteenth century is dominated by Babbage’s own account of events. George Biddell Airy (1801-1891), Astronomer Royal for forty five years, consistently rejected arguments advocating the utility of the engines. Airy had a defining influence on the fate of the engines yet his views barely feature in the canon. Using new archival sources, Airy’s views are explored through a series of case studies: Babbage’s Difference Engine No. 1 and the Swedish calculating engine used at the General Register Office for the 1864 Life Table. In addition, his views on the use of calculating aids are explored using instances in which he was petitioned by inventors, specifically by Thomas Fowler and William Bell. The thesis situates Airy’s views in the context of manual methods used in the production of printed mathematical tables – techniques that automatic calculating engines were intended to replace – and in the context of contemporary expectations of the largely unbuilt engines. The treatment includes new work on the mathematical implications of the engines, specifically Babbage’s speculations on computation as a systematic method of solution, and presents a revisionist view of tabular errors as the primary motive for the development of the engines. 3 CONTENTS List of Illustrations 4 Introduction 8 PART I: TABLE MAKING 1. Calculation 29 2. Verification, and Generic Processes 73 PART II: BABBAGE AND THE UTOPIAN IDEAL 3. Babbage’s Expectations for his Engines 111 PART III: AIRY AND PRAGMATISM 4. Airy and Babbage’s Difference Engine No. 1 180 5. Airy, the Scheutzes, Fowler and Bell 240 Conclusions 302 Bibliography 317 Appendix I: “This is the Engine which Charles Built” 337 Appendix II: Airy’s Questionnaires 342 Appendix III: Illustrations 348 4 List of Illustrations: Appendix III 1. Charles Babbage (1791-1871). Daguerreotype by Antoine Claudet, 1847-51. (National Portrait Gallery). 348 2. George Biddel Airy (1810-1892). (Illustrated London News, 4 January 1868). 348 3. Charles Babbage, 1860. (Bernard Howarth-Loomes). 348 4. George Biddell Airy in old age (Amati Papers, Cambridge). 348 5. Page of tables from Thesaurus Logarithmorum by Von Vega, 1794 (Detail). (Science Museum). 349 6. Thesaurus Logarithmorum by Von Vega, 1794. (Science Museum).I 349 7. Pascal’s Calculator, 1642 (Replica). (Science Museum). 350 8. Johann Müller’s ‘Universal’ Calculator, 1784. (Hessisches Landesmuseum, Darmstadt). 350 9. De Colmar Arithmometer, c. 1890. (Science Museum). 350 10. Charles Babbage’s Difference Engine No. 1 – Portion, 1832. (Science Museum). 351 11. Woodcut of Babbage Difference Engine No. 1, 1853, by B. H. Babbage. (Science Museum). 351 12. Scheutz Difference Engine by Bryan Donkin for the General Register Office, 1859. (Science Museum). 352 13. Prototype Difference Engine by Georg and Edvard Scheutz, 1843. (Nordiska Museet, Stockholm). 352 14. Charles Babbage’s Difference Engine No. 2, 2002. (Science Museum). 353 15. Stereotyping Punches for Difference Engine No. 2, 2002. (Science Museum). 353 16. Stereotype Mould in Plaster of Paris, Difference Engine No. 2, 2002. (Science Museum). 353 5 ‘I wish to god these calculations had been executed by steam' – Charles Babbage, 1821 ‘What shall we do to get rid of Mr. Babbage and his Calculating Machine?' – Sir Robert Peel, 1842 ‘I think it likely that he lives in a sort of dream as to its utility' – George Biddell Airy, 1842 ‘Professor Airey says the thing is a humbug; other scientific men say directly the contrary' – William Charles Macready, 1837 ‘There exists no memory except upon paper' – George Biddell Airy, 1854 ‘It is the Age of Machinery, in every outward and inward sense of that word’ – Thomas Carlyle, 1838 6 Abbreviations The following abbreviations are used in footnotes to refer to frequently cited sources. Biog. Airy, Wilfrid, ed. Autobiography of Sir George Biddell Airy. Cambridge: Cambridge University Press, 1896. CDNB The Concise Dictionary of National Biography. Oxford: Oxford University Press, 1994. 3 vols. CWB Swade, Doron. The Cogwheel Brain: Charles Babbage and the Quest to Build the First Computer. London: Little, Brown, 2000. Expo Babbage, Charles. The Exposition of 1851 or Views on the Industry, the Science, and the Government of England. 2 ed. London: John Murray, 1851. G&F Lindgren, Michael. Glory and Failure: The Difference Engines of Johann Müller, Charles Babbage, and Georg and Edvard Scheutz. Trans. McKay, Craig G. 2 ed. Cambridge, Massachusetts: MIT Press, [1987], 1990. GoS Morrell, Jack, and Arnold Thackray. Gentlemen of Science: Early Years of the British Association for the Advancement of Science. Oxford: Clarendon Press, 1981. LEC Collier, Bruce. The Little Engines that Could've: The Calculating Engines of Charles Babbage. 2 ed. New York: Garland, [1970], 1990. Notice Fowler, Hugh. "Biographical Notice of the late Mr. Thomas Fowler, of Torrington with some account of his inventions." Transactions of the Devonshire Association for the Advancement of Science, Literature and Arts 7 (1875): pp. 171-178. 7 Passages Babbage, Charles. Passages from the Life of a Philosopher. London: Longman, Green, Longman, Roberts & Green, 1864. PC Hyman, Anthony. Charles Babbage: Pioneer of the Computer. Oxford: Oxford University Press, 1982. Works Campbell-Kelly, Martin, ed. The Works of Charles Babbage. 11 vols. London: William Pickering, 1989. 8 Introduction Another age must be the judge – Charles Babbage, 1837. The starting point of this work lies in curatorial life in a museum, in this case the Science Museum, London, where I worked as curator of computing for fourteen years. The central article of faith in museums is a belief in the primacy of original artefacts. Physical artefacts are the explanandum of curatorial life, and history is one of the main discourses that curators invoke to ‘explain’ artefacts and articulate their meanings. The cultural environment of object-rich museums and the constituencies from which curators are recruited encourage a technocentric approach to history, especially in science museums. This has certainly been the case in the past, though noticeably less so latterly, as history graduates have taken their place alongside science and engineering graduates, reflecting perhaps the cultural and intellectual movements of relativism and contextualisation that began to occupy the methodological high ground in the 1960s and 1970s. However, the internalist legacy, though weakened, is not dead, and to some the thesis that ‘machines make history’, the rallying call of the technological determinist, still operates as a subjective presupposition even to those with a self-conscious knowledge of the narrowness of this view.1 Physical artefacts, specifically the mechanical relics, incomplete assemblies, and a large technical archive are the material legacy of 1 The quoted phrase is borrowed from the title of Robert Heilbroner’s classic paper “Do Machines Make History?”. See Heilbroner ([1967], 1994). For a discussion of the ‘tenacious grip [of technological determinism] on the popular and academic imagination’ see Bimber (1994), p. 80. Introduction 9 Charles Babbage’s efforts to build his calculating engines. This material provided the initial stimulus for this work. Charles Babbage (1791-1871) is widely recognised as the great ancestral figure in the history of computing.2 He famously invented computers – vast automatic mechanical calculating engines – and equally famously failed to build them. Genius and failure are inextricably linked with his name. He failed despite substantial government funding, decades of design and development, the benefit of the finest engineering, and the social advantages of an affluent and well- connected Victorian gentleman of science. Summary histories of computing overwhelmingly ascribe the reasons for Babbage's failures to the limitations of Victorian mechanical engineering. Martin Davis, for example, writes, ‘Babbage never succeeded in constructing his engine, in large part because of the limitations of nineteenth century technology'.3 A history of the Science Museum published in 1957 states that ‘[Babbage's] ideas were eminently sound and it was only the backwardness of light-engineering and instrument-making techniques . which robbed him of the success he deserved'.4 Nathan Rosenberg, in Perspectives on Technology, writes, ‘Babbage's failure to complete his ingenious scheme was due to the inability of contemporary British metal-working to deliver the components which were indispensable to the 5 machine's success'. 2 There has been confusion about the date and location of Babbage’s birth. He is variously reported as being born in London, Teignmouth or Totnes in 1791 or 1792. Hyman resolved this by reference to parish baptismal records and established that Babbage was born in Walworth, Surrey on 26 December 1791. See PC, p. 11. Errors continue in secondary sources as well as many biographical reference works. 3 Davis