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Babbage's two lives


Babbage wrote two relatively detailed, yet significantly incongruous, autobiographical accounts of his pre-Cambridge and Cambridge days. He published one in 1864 and in it advertised the existence of the other, which he carefully retained in manuscript form. The aim of this paper is to chart in some detail for the first time the discrepancies between the two accounts, to compare and assess their relative credibility, and to explain their author's possible reasons for knowingly fabricating the less credible of the two.

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1 Babbage, Charles, Passages from the Life of a Philosopher, with new introduction by Martin Cambell-Kelly, New Brunswick: Rutgers University Press, 1994 (originally published by Longman in 1864).

2 Charles Babbage, ‘The history of the origin and progress of the Calculus of Functions during the years 1809, 1810 … 1817’, MSS Buxton 13, History of Science Museum, Oxford.

3 It ‘earnestly requests’ the finder of this book, should it be ‘mislaid or lost … to return it to the author if living or in case of his death to present it to the public library of the University of Cambridge’. It is signed, ‘No 1 Dorset St. Manchester Sq. 14 May 1869’. See also Chapman, Allan, ‘A year of gravity: the astronomical anniversaries of 1992’, Quarterly Journal of the Royal Astronomical Society (1993) 34, pp. 3351, 50n. 47.

4 See Phillip C. Enros, ‘The Analytical Society: mathematics at Cambridge University in the early nineteenth century’, PhD dissertation, University of Toronto, 1979; Enros, ‘Cambridge University and the adoption of analytics in early nineteenth-century England’, in Mehrtens, Herbert, Bos, Henk and Schneider, Ivo (eds.), Social History of Nineteenth-Century Mathematics, Boston, Basel and Stuttgart: Birkhauser, 1981, pp. 135–48; and Enros, ‘The Analytical Society’, Historia Mathematica (1983) 10, pp. 2447; Wilkes, Maurice V., ‘Herschel, Peacock, Babbage and the development of the Cambridge curriculum’, Notes and Records of the Royal Society of London (1990) 44, pp. 205219; Grattan-Guinness, Ivor, ‘Charles Babbage as an algorithmic thinker’, IEEE Annals of the History of Computing (1992) 14, pp. 3448; and Grier, David A., ‘The inconsistent youth of Charles Babbage’, IEEE Annals of the History of Computing (2010) 32, pp. 1831, who all follow the uncritical meshing of the two accounts found in Buxton, Harry W., Memoir of the Life and Labours of the Late Charles Babbage Esq. F.R.S. (ed. Hyman, Anthony), Cambridge, MA: The MIT Press, 1988.

5 Babbage, op. cit. (1), p. 327.

6 It ended up in the hands of Harry W. Buxton, who testifies to have received from Babbage ‘some years before his death’ the ‘small MS volume … referred to at page 435 of the Passages from the Life of a Philosopher’, along with other papers, in order ‘that I should, after his decease, give to the world some account of his life and scientific labours’. Buxton, op. cit. (4), p. 3.

7 The term is Martin Campbell-Kelly's. See his ‘Introduction’ to Babbage, op. cit. (1), p. 11.

8 Seven guineas, according to Babbage – an extraordinarily high price for someone whose annual allowance was £300.

9 Namely Silvestre Lacroix's, F.Traité du calcul différentiel et du calcul intégral, 3 vols., Paris: Chez Courcier, 1797–1800. For a detailed appraisal of the work see Domingues, João Caramalho, Lacroix and the Calculus, Basel: Birkhauser, 2008, p. 23.

10 Snyder, Laura J., The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World, New York: Broadway Books, 2011, points to several occasions in which Passages takes credit for the achievements of others, such as hosting the Sunday ‘breakfast club’ and masterminding the establishment of Section F of the British Association. See also Schweber, Silvan S., Aspects of the Life and Thought of Sir John Frederick Herschel, New York: Arno Press, 1981.

11 Koppelman, Elaine, ‘The calculus of operations and the rise of abstract algebra’, Archives for History of Exact Science (1971–1972) 8, pp. 155242, 178. See also Fraser, Craig G., ‘Joseph Louis Lagrange, Théorie des Fonctions Analytiques', in Grattan-Guinness, Ivor (ed.), Landmark Writings in Western Mathematics 1640–1940, Amsterdam: Elsevier, 2005, pp. 258276.

12 Pagination in square brackets refers to Buxton, op. cit. (4), pp. 24–41, where the relevant passages of MS 13 are conveniently copied. I have retained Babbage's original spelling and punctuation, which Buxton frequently amends.

13 See also Babbage, Charles, ‘An essay towards the calculus of functions, Part I’, Philosophical Transactions (1815) 105, pp. 389423, esp. 391–392.

14 See Philosophical Transactions of the Royal Society of London (1809) 99, p. 473 (mistakenly marked 373).

15 Enros, ‘The Analytical Society’, op. cit. (4), p. 136.

16 His obituary, published on 13 February 1857 in the Monthly Notices of the Royal Astronomical Society (1857) 17(4), pp. 98–99, talks laconically of ‘his college life’ exhibiting ‘faults of a very grave kind, to which we cannot avoid allusion, as their consequences were so notorious’.

17 Though Pollock, Frederick, Personal Remembrances of Sir Frederich Pollock, Second Baronet, Sometime Queen's Remembrancer, 2 vols., New York, Macmillan and Co., 1887, vol. 1, p. 40, deemed him ‘a person of little account’, Bromhead refers to him mockingly as ‘one very high man’. Bromhead to Babbage, 9 February 1816, British Museum Add Mss 37182, No 46, cited by Dubbey, John M., The Mathematical Work of Charles Babbage, Cambridge: Cambridge University Press, 1978, p. 62, who fails, however, to identify the ‘high man’ as Higman.

18 Buxton, op. cit. (4), juxtaposes the two accounts uncritically, giving 1811 as the purchase date when citing Passages (pp. 18, 21), and 1810 when citing MS 13 (p. 25). As editor, Hyman (Buxton, op. cit. (4), p. xv), overrules his author and sets the date consistently at 1810, including in his direct citations from Passages (p. 21).

19 Wilkes, op. cit. (4), p. 206; Grier, op. cit. (4), p. 20 n. 20; and Snyder, op. cit. (10), p. 30. Dubbey, op. cit. (17), p. 32, is more careful in this respect, but confuses the Lacroix purchased with the same author's Traité élémentaire de Calcul différentiel et de Calcul intégral, Paris: Duprat, 1802 (later editions published by Courcier), which he, Herschel and Peacock eventually translated.

20 See, for example, Herschel, John F.W., ‘On equations of differences and their application to the determination of functions from given conditions’, in Herschel, John F.W. and Babbage, Charles, Memoirs of the Analytical Society 1813, Cambridge, 1813, pp. 65114, 100 n.; Ortiz, Eduardo L., ‘Babbage and French idéologie: functional equations, language, and the analytical method’, in Gray, Jeremy J. and Parshall, Karen Hunger (eds.), Episodes in the History of Modern Algebra (1800–1950), Providence: The American Mathematical Society, 2007, pp. 1347, esp. 19–29; and Domingues, op. cit. (9), pp. 27, 200, 214 and 263.

21 Which explains why Enros, ‘The Analytical Society’, op. cit. (4), who relies heavily on MS 13, insists that the society was ultimately formed to promote research, not to reform Cambridge (e.g. Chapter 3).

22 Which, as I have noted elsewhere, is supported by external evidence. See Schweber, op. cit. (10), pp. 59–60, citing Maule to Babbage, 16 January 1812, British Museum Add MS 37182, f3.

23 MS 13 describes Bromhead's list of invitees as ‘those of his acquaintances who were most attached to mathematical subjects’ (24, emphasis added).

24 See especially Herschel, John F.W., ‘On trigonometrical series, particularly those whose terms are multiplied by the tangents, cotangents, secants, &c. of quantities in arithmetic progression, together with some singular transformations; with notes relating to a variety of subjects connected with the preceding memoir’, in Herschel, John F.W. and Babbage, Charles, Memoirs of the Analytical Society 1813, Cambridge, 1813, pp. 3364; ‘On a remarkable application of Cotes's theorem’, Philosophical Transactions (1813) 103, pp. 8–26; and Herschel, op. cit. (20).

25 This alone renders the MSS 13's dating of the formation of the society quite unrealistic.

26 The entire episode, pp. 32–37, is conveniently skipped by Buxton, op. cit. (4).

27 By contrast, the credit granted to Herschel in Babbage, op. cit. (13), pp. 393–395, is unqualified: Herschel's ‘excellent paper on functional equations’ (p. 394) is praised as correcting an oversight of Babbage's, and extending Laplace's ‘peculiarly elegant’ reduction of functional equations of the first order to those of finite difference, in a manner ‘equally elegant and quite general’.

28 MS 13 goes on the describe an additional method of Herschel's for solving Ψ2x = x again as an equation of finite differences. And, again, credits Herschel not for discovering, but for realizing, the viability of an approach they had both previously dismissed. Similarly, the ‘very ingenious mode’ of solving the equation Ψnx = x, proposed by Herschel ‘about this time’, is described as having been anticipated more generally by Maule in a letter of 15 May 1814 (pp. 67–76 [pp. 38–39]). See also De Morgan, Augustus, A Treatise on the Calculus of Functions (Extracted from the Encyclopaedia Metropolitana), London: Baldwin and Cradock, Paternoster Row, 1836, p. 14; and Grattan-Guinness, op. cit. (4), p. 38.

29 Herschel and Babbage, op. cit. (20), pp. 97 ff.

30 Herschel and Babbage, op. cit. (20), p. 111.

31 The annotated copy of the Memoirs Babbage presented to his son also attributes the preface to himself alone, as does the information he apparently conveyed to Ivory in campaigning for the East India College chair of mathematics in 1816. Schweber, op. cit. (10), pp. 60–62.

32 Spence, William, Mathematical Essays by the late William Spence, edited by J.F.W. Herschel, Edinburgh: Oliver and Boyd, 1819, pp. xxviixxxii and 151–170 respectively.

33 An Essay on the Various Orders of logarithmic Transcendents; with an Inquiry into their Applications to the Integral Calculus, and the Summation of Series, London and Edinburgh: John Murray and Archibald Constable, 1809.

34 On 30 January 1817 Herschel had written to Babbage asking that they meet because ‘Spence's papers have set me mad. After wading through immense heaps of trash … I … struck upon an unfinished Essay full of the most beautiful properties of strange transcendents of the form

… I devoured the Essay with avidity – the field it opens is immense’. Royal Society of London, Correspondence of Sir John F.W. Herschel: Herschel to Babbage: (f) HS.20.38, 30 January 1817.

35 ‘Consideration of various points of analysis’, Philosophical Transactions (1814) 104, pp. 440–468.

36 Babbage, op. cit. (13); and Part II, Philosophical Transactions (1816) 106, pp. 179–256.

37 This time to Babbage, ‘Observations on the analogy which subsists between the calculus of functions and other branches of analysis’, Philosophical Transactions 107 (1817), pp. 197–216.

38 With explicit reference ‘to the distinction between these terms in Mr. Babbage's second paper, prob. xxviii’.

39 De Morgan, op. cit. (28), p. 39.

40 Written by Sir Robinson, Thomas Romney, Proceedings of the Royal Society of London (1872) 20, pp. xviixxiii

41 Cannon, Walter F., ‘John Herschel’, Encyclopedia of Philosophy (ed. P. Edwards), New York: Collier and Macmillan, vol. 3, 1967.

42 On Whewell's ‘tidology’ see Reidy, Michael S., Tides of History: Ocean Science and Her Majesty's Navy, Chicago: The University of Chicago Press, 2008, Chapter 4; and Snyder, op. cit. (10), Chapter 7.

43 Ruskin, Steven, John Herschel's Cape Voyage: Private Science, Public Imagination and the Ambitions of Empire, Burlington: Ashgate, 2004, follows Cannon, Walter F., ‘John Herschel and the idea of science’, Journal of the History of Ideas (1961) 22, pp. 215237, in claiming that Herschel's ‘near deification’ and rise to ‘living legend’ came as a result of his voyage to the Cape. Secord, James A., Victorian Sensation: The Extraordinary Publication, Reception, and Secret Authorship of Vestiges of the Natural History of Creation, Chicago: The University of Chicago Press, 2000, attributes his standing to the ‘ideal of the Christian Philosopher’ presented by the Preliminary Discourse.

44 See Snyder's touching description of his failure to interest anyone to attend his lecture on the Analytical Engine at the 1869 meeting of the British Association, but for ‘two American gentleman’. Snyder, op. cit. (10), p. 356.

45 The term is Juliet Margaret Cameron's, cited by Snyder, op. cit. (10), p. 349.

46 Babbage to Margaret Herschel, draft, May 1871, British Library 37,199 f.537, cited in Snyder, op. cit. (10), p. 410 n. 67.

47 Snyder, op. cit. (10), pp. 353–354.

48 For a more detailed appraisal of Herschel's scientific and metascientific achievements, see my forthcoming Creatively Undecided: Toward a History and Philosophy of Scientific Agency, Chapter 7.

49 See Babbage, op. cit. (1), p. 327.

50 See note 6 above; and Hyman, Anthony, Charles Babbage: Pioneer of the Computer, Princeton: Princeton University Press, 1982, p. 246.

51 Snyder, op. cit. (10), pp. 358–359.

This paper was written during my residence at Collegium Budapest in 2011. I wish to thank Joan L. Richards, Laura J. Snyder, Kevin Lambert and two anonymous readers for extremely helpful criticism.

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