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Savage numbers and the evolution of civilization in Victorian prehistory

Published online by Cambridge University Press:  09 August 2013

Princeton University, Program in History of Science, 129 Dickinson Hall, Princeton, NJ 08544, USA. Email: Website:


This paper identifies ‘savage numbers’ – number-like or number-replacing concepts and practices attributed to peoples viewed as civilizationally inferior – as a crucial and hitherto unrecognized body of evidence in the first two decades of the Victorian science of prehistory. It traces the changing and often ambivalent status of savage numbers in the period after the 1858–1859 ‘time revolution’ in the human sciences by following successive reappropriations of an iconic 1853 story from Francis Galton's African travels. In response to a fundamental lack of physical evidence concerning prehistoric men, savage numbers offered a readily available body of data that helped scholars envisage great extremes of civilizational lowliness in a way that was at once analysable and comparable, and anecdotes like Galton's made those data vivid and compelling. Moreover, they provided a simple and direct means of conceiving of the progressive scale of civilizational development, uniting societies and races past and present, at the heart of Victorian scientific racism.

Research Article
Copyright © British Society for the History of Science 2013 

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1 See Gamble, Clive and Moutsiou, Theodora, ‘The time revolution of 1859 and the stratification of the primeval mind’, Notes and Records of the Royal Society (2011) 65, pp. 4363CrossRefGoogle Scholar.

2 Charles Lyell, ‘Geology. Introductory Address by the President, Sir. Lyell, C.. On the occurrence of works of human art in post-pliocene deposits’, Notices and Abstracts of Miscellaneous Communications to the Sections. Report of the Twenty-Ninth Meeting of the British Association for the Advancement of Science; Held at Aberdeen in September 1859, London: John Murray, 1860, p. 95Google Scholar.

3 Wallace, Alfred Russel, ‘Biology. Opening Address by the President, Alfred Russel Wallace. Rise and progress of modern views as to the antiquity and origin of man’, Nature (1876) 14, pp. 408412Google Scholar, 409.

4 Bowler, Peter J., ‘From “savage” to “primitive”: Victorian evolutionism and the interpretation of marginalized peoples’, Antiquity (1992) 66, pp. 721729CrossRefGoogle Scholar; Stocking, George W., Victorian Anthropology, New York: The Free Press, 1987, esp. pp. 144185Google Scholar; Stepan, Nancy, The Idea of Race in Science: Great Britain 1800–1960, London: Macmillan, 1982, pp. 1110CrossRefGoogle Scholar; Kuper, Adam, The Invention of Primitive Society: Transformations of an Illusion, London: Routledge, 1988Google Scholar, Part 1.

5 For example, Stocking, op. cit. (4), pp. 238–273; Livingstone, David N., Adam's Ancestors: Race, Religion, and the Politics of Human Origins, Baltimore: Johns Hopkins University Press, 2008, pp. 109200Google Scholar; Pettitt, Paul B. and White, Mark J., ‘Cave men: stone tools, Victorian science, and the “primitive mind” of deep time’, Notes and Records of the Royal Society (2011) 65, pp. 2542CrossRefGoogle ScholarPubMed.

6 Stepan, op. cit. (4).

7 Adas, Michael, Machines as the Measure of Men: Science, Technology, and Ideologies of Western Dominance, Ithaca: Cornell University Press, 1989Google Scholar; Murray, Tim, ‘Tasmania and the constitution of “the dawn of humanity”’, Antiquity (1992) 66, pp. 730743Google Scholar; Gamble and Moutsiou, op. cit. (1).

8 Eddy, Matthew D., ‘The line of reason: Hugh Blair, spatiality and the progressive structure of language’, Notes and Records of the Royal Society (2011) 65, pp. 924CrossRefGoogle Scholar. Eddy's incisive remarks on the rectilinear spatiality of Western philology offer a provocative counterpoint to my argument below regarding the progressive implications of the linear scale of counting numbers.

9 Three influential representatives of this vast literature are Porter, Theodore M., The Rise of Statistical Thinking, 1820–1900, Princeton: Princeton University Press, 1986Google Scholar; Hacking, Ian, The Taming of Chance, Cambridge: Cambridge University Press, 1990CrossRefGoogle Scholar; Porter, Theodore M., Trust in Numbers: The Pursuit of Objectivity in Science and Public Life, Princeton: Princeton University Press, 1995Google Scholar.

10 See Stepan, op. cit. (4), especially Chapter 4; Sommer, Marianne, Bones and Ochre: The Curious Afterlife of the Red Lady of Paviland, Cambridge, MA: Harvard University Press, 2007Google Scholar, Part 2.

11 Where number words or practices are mentioned, such as by Stocking, op. cit. (4), or Pettitt and White, op. cit. (5), p. 35, they do not factor significantly into the analysis.

12 See, for example, Zaslavsky, Claudia, Africa Counts: Number and Pattern in African Culture, Westport, CT: Lawrence Hill & Company, 1979Google Scholar (first published 1973), p. 9.

13 Dr Thomas Hodgkin to Dr Norton Shaw, 1 February 1858, Royal Geographical Society, London, RGS/CB4 Hodgkin. Hodgkin added, ‘Numbers may be varied from the ordinary continued series’.

14 Thus poets are lampooned in Montgomery, R., ‘The omnipresence of the Deity’, Blackwood's Edinburgh Magazine (1828) 23, pp. 751771Google Scholar, 752, as ‘being naturally incapacitated for counting … feet and toes, or yet their own fingers … the enumeration of his digits is a work often beyond the reach of the most respectable powers of arithmetic’. In a similar vein, a story titled ‘Idiots again’ in Dickens, Charles (ed.), Household Words (1854) 9, p. 198Google Scholar, could be coloured with the observation that ‘the law declared anybody an idiot “who could not count twenty pence”’. An essay on ‘Rustic controversies’ in Fraser's Magazine for Town and Country (1840) 22, p. 605, began by distinguishing ‘The Vulgar’ from ‘all who can count their fingers’.

15 Lubbock, John, The Origin of Civilisation and the Primitive Condition of Man: Mental and Social Condition of Savages, London: Longmans, Green, and Co., 1870, p. 293Google Scholar.

16 Galton, Francis, The Narrative of an Explorer in Tropical South Africa, London: John Murray, 1853Google Scholar. Publication information is from the ledger books (Ms.42730, pp. 316, 318) and stockbooks (Ms.42787, p. 256) in the John Murray archive, National Library of Scotland, Edinburgh. For the book's production and highly favourable initial reception see Gilham, Nicholas Wright, A Life of Sir Francis Galton: From African Exploration to the Birth of Eugenics, Oxford: Oxford University Press, 2001, pp. 9196Google Scholar. For the book's context in John Murray III's successful foray into popular travel writings see Carpenter, Humphrey, The Seven Lives of John Murray: The Story of a Publishing Dynasty, 1768–2002, London: John Murray, 2008, pp. 166167Google Scholar, 179–181, 190–199.

17 Galton, op. cit. (16), pp. 133–134. Readers of the Athenaeum may have sought or recognized this particular ‘almost incredible’ passage from a lengthy excerpt in a review of 11 June 1853 (no. 1337, pp. 701–702).

18 Galton, op. cit. (16), p. 194. The word lists in Galton's notebooks from the expedition, held in University College London's Galton collection (multiple lists in Files 97–98), appear to show just seven terms for ‘to deceive’, ‘deceit’, and ‘deception’, and there are no entries between ‘village’ and ‘vomit’.

19 I was present at a 2010 conference where a distinguished speaker on the history and philosophy of mathematics quoted Galton as unproblematic evidence in this regard.

20 A prominent recent study is Dehaene, Stanislas, Izard, Véronique, Spelke, Elizabeth and Pica, Pierre, ‘Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures’, Science (2008) 320(5880), pp. 12171220CrossRefGoogle ScholarPubMed.

21 Strictly speaking, Galton's own gloss of the situation in terms of lacking numerals is consistent with the story he presents, but later writers used the anecdote without further evidence or argument to make the stronger claim that Damara could not count past three at all. In any event, the scene clearly belies the ‘inability to count’ heading that accompanies it. Perhaps this is why the second anecdote is so rarely remarked upon in comparison to the others.

22 These materials are held principally in Files 97–99 of the Galton collection at University College London. I cannot rule out the possibility that Galton retained notes beyond those I have located; manuscripts for Galton's Narrative have not been preserved in the principal archives of either the publisher or the author.

23 Wilson, Daniel, Prehistoric Man: Researches into the Origin of Civilisation in the Old and the New World, 2 vols., London: Macmillan and Co., 1862, vol. 1, p. 469Google Scholar. For the history of ‘prehistoric’ and several variants see Clermont, Norman and Smith, Philip E.L., ‘Prehistoric, prehistory, prehistorian … who invented the terms?’, Antiquity (1990) 64, pp. 97102CrossRefGoogle Scholar.

24 Lubbock, John, Pre-historic Times, as Illustrated by Ancient Remains, and the Manners and Customs of Modern Savages, London: Williams and Norgate, 1865, p. 293Google Scholar.

25 Wood, J.G., The Natural History of Man; Being an Account of the Manners and Customs of the Uncivilized Races of Men, London: George Routledge and Sons, 1868, pp. 344345Google Scholar.

26 ‘Scores and tallies’, Cornhhill Magazine (April 1886) 6, pp. 436–448. The manuscript for the essay is listed in the ‘Grant Allen Literary Manuscripts and Correspondence, 1872–1937’ collection in the Pennsylvania State University Special Collections Library, Box 3/vault/7.

27 For example, ‘Are twice two four?’, Troy [New York] Weekly Times, 6 May 1886; ‘Are twice two four?’, Daily Evening Bulletin (San Francisco, CA), 8 May 1886; ‘Twice two: the mathematical problem which puzzled a savage’, San Francisco Chronicle, 13 June 1886; ‘Young folks’ column’, Atchison [Kansas] Daily Globe, 29 December 1886.

28 For example, Heath, Thomas, Mathematics in Aristotle, Oxford: Clarendon Press, 1949, pp. 258260Google Scholar.

29 The earliest to receive substantial attention in this period is Flacourt's, Etienne deHistoire de la Grande Isle Madagascar, Paris: Jean Henault, 1658, p. 88Google Scholar. Commentators found close parallels between Galton's account and that of Austrian Jesuit Martin Dobrizhoffer's description of his years as a missionary in Paraguay, published in Latin and German in 1784 and available in English by 1822: An Account of the Abipones, an Equestrian People of Paraguay, London: Murray. Savage numbers appear incidentally in a much-cited work by von Humboldt, Alexander, Researches Concerning the Institutions and Monuments of the Ancient Inhabitants of America, tr. Helen Maria Williams, 2 vols., London: Longman, Hurst, Rees, Orme & Brown, J. Murray & H. Colburn, 1814, vol. 1, p. 307Google Scholar, and von Spix, Johann Baptist und von Martius, Carl Friedrich Philipp, Travels in Brazil, in the Years 1817–1820, tr. H.E. Lloyd, 2 vols., London: Longman, Hurst, Rees, Orme, Brown, and Green, 1824, vol. 2, p. 255Google Scholar.

30 Influential authors outside Britain included Montucla, , Histoire des mathématiques, Paris: Jombert, 1758, p. 48Google Scholar; and Humboldt, Wilhelm von, On Language: The Diversity of Human Language-Structure and Its Influence on the Mental Development of Mankind, tr. Peter Heath, Cambridge: Cambridge University Press, 1988, pp. 286287Google Scholar. Within Britain, mathematicians Augustus De Morgan and George Peacock provided explanations of the origin of numbers that included savage practices as a heuristic for thinking about early man. For example, Morgan, Augustus De, The Elements of Arithmetic, London: John Taylor, 1830, pp. 36Google Scholar; Library of Useful Knowledge. Mathematics. I. Study and Difficulties of Mathematics. Arithmetic and Algebra. Examples of the Processes of Arithmetic and Algebra, London: Baldwin and Cradock, 1836, pp. 4–6. See also Mill, John Stuart, A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation, 4th edn, 2 vols., London: John W. Parker and Son, 1856 (first published 1843), vol. 1, pp. 283286; vol. 2, pp. 139145Google Scholar.

31 Wilson, op. cit. (23), p. ix.

32 Wilson, op. cit. (23), pp. xi–xii.

33 Wilson, op. cit. (23), pp. 455, 469–471.

34 Bowler, op. cit. (4), p. 722, likewise notes the prejudicial orientation of traveller accounts.

35 Crawfurd, John, ‘On the numerals as evidence of the progress of civilization’, Transactions of the Ethnological Society of London (1863) 2, pp. 84111CrossRefGoogle Scholar.

36 Crawfurd, op. cit. (35), pp. 84, 102.

37 Crawfurd, John, ‘On Sir Charles Lyell's “Antiquity of Man”, and on Professor Huxley's “Evidence as to Man's Place in Nature”’, Transactions of the Ethnological Society of London (1865) 3, pp. 5870CrossRefGoogle Scholar. On the notion of evolutionary stasis in debates over monogenism and a unified scale of racial development see Stepan, op. cit. (4), pp. 85–86; Bowler, op. cit. (4), p. 722.

38 See Timothy L. Alborn, ‘Lubbock, John, first Baron Avebury (1834–1913)’, Oxford Dictionary of National Biography, Oxford: Oxford University Press, 2004 (accessed online, May 2009); Stocking, op. cit. (4), pp. 150–151.

39 Lubbock, op. cit. (24), pp. 334–336.

40 Lubbock, op. cit. (24), pp. 466–468.

41 I have preserved Lubbock's variant spelling of ‘Dammaras’ in my paraphrase.

42 The Brazilians of Spix and Martius, op. cit. (29), were often paired, or later conflated, with Galton's Damara.

43 Lubbock, op. cit. (24), p. 491.

44 Lubbock, John, ‘The early condition of Man’, Anthropological Review (1868) 6(20), pp. 121CrossRefGoogle Scholar, 8. Lubbock gave a nearly identical address to the Ethnological Society of London that same year: ‘On the origin of civilisation and the primitive condition of Man’, Transactions of the Ethnological Society of London (1868) 6, pp. 328–341. Recall that numbers’ usefulness, particularly among the lowest savages, was frequently in doubt. Alfred Russel Wallace observed in 1889 that like ‘wit and humour … almost unknown among savages’, the ability to count and reckon ‘is altogether removed from utility in the struggle for life, and appears sporadically in a very small percentage of the population.’ Wallace, Alfred Russel, Darwinism: An Exposition of the Theory of Natural Selection with Some of Its Applications, London: Macmillan and Co., 1889, pp. 472Google Scholar (see also 466–467). On Wallace's insistence on selection pressures and ‘the struggle for life’ see Stepan, op. cit. (4), pp. 66–69.

45 See Stepan, op. cit. (4), pp. 56–57.

46 Lubbock, op. cit. (24), p. 492.

47 Tylor, Edward Burnet, ‘Prehistoric times’, Nature (1869) 1, pp. 103105CrossRefGoogle Scholar.

48 Lubbock, ‘The early condition of Man’, op. cit. (44), pp. 15–16.

49 Argyll, Duke of, Primeval Man: An Examination of Some Recent Speculations, London: Strahan & Co., 1869Google Scholar.

50 On Lubbock's shifting approach to the humanity and import of savages between 1865 and 1870 see Stocking, op. cit. (4), pp. 150–156. Bowler, op. cit. (4), p. 726, notes that the depictions underwriting Lubbock's progressive message were rather grim even in 1865.

51 Lubbock, op. cit. (15), p. 299.

52 Tylor, Edward B., Primitive Culture: Researches into the Development of Mythology, Philosophy, Religion, Art, and Custom, 2 vols., London: John Murray, 1871Google Scholar. On the work's biographical and intellectual context see especially Leopold, Joan, Culture in Comparative and Evolutionary Perspective: E.B. Tylor and the Making of Primitive Culture, Berlin: Dietrich Reimer Verlag, 1980Google Scholar; Stocking, op. cit. (4), pp. 157–158. The work far outstripped Tylor's less influential 1865 Researches into the Early History of Mankind and the Development of Civilization, London: John Murray, whose argument focused on contemporary deaf-and-dumb education.

53 Tylor's second edition (Tylor, Edward Burnet, Primitive Culture: Researches into the Development of Mythology, Philosophy, Religion, Language, Art, and Custom, 2nd edn, 2 vols., London: John Murray, 1873, vol. 1, p. viiGoogle Scholar) apologizes for having mostly omitted explicit references to Darwin and Spencer in the first edition. The intervening two years had seen the publication of Charles Darwin's Descent of Man, in which Tylor, along with Lubbock, was frequently and generously cited (The Descent of Man, and Selection in Relation to Sex, vol. 1, Brussels: Culture et Civilisation, 1969 (first published London: John Murray, 1871), pp. 181, 234). For Darwin's favourable impression of Tylor see Burkhardt, Frederick et al. (eds.), The Correspondence of Charles Darwin, Cambridge: Cambridge University Press, 2002–, vol. 13, p. 194Google Scholar; vol. 14, pp. 171, 179; vol. 16, p. 851. Contemporaries immediately associated Primitive Culture with Descent of Man (‘Primitive Culture’ (unsigned review), Nature (1871) 4, pp. 117–119).

54 Tylor, op. cit. (52), pp. 3–4, 17.

55 Tylor, op. cit. (52), p. 6.

56 Tylor, op. cit. (52), p. 243.

57 Tylor, op. cit. (52), p. 6–7. Bowler, op. cit. (4), p. 725 and passim gives further context for Tylor's thesis of ‘psychic unity’ and its role in his view of savages and human evolution.

58 Tylor, op. cit. (52), pp. 8–9.

59 Tylor, op. cit. (52), p. 14 (see also 19–20).

60 Tylor, op. cit. (52), pp. 245–246.

61 See Stepan, op. cit. (4), p. 55.

62 Sayce, A.H., The Principles of Comparative Philology, London: Trübner & Co., 1874, p. 25Google Scholar and passim. Sayce, like Lubbock (see note 41 above), spells ‘Dammaras’ with two ‘m's.

63 Spencer, Herbert, The Principles of Sociology, vol. 1, London: Williams and Norgate, 1876, pp. 8186Google Scholar.

64 Lubbock, John, ‘On the intelligence of the dog’, Nature (1885) 33, pp. 4546Google Scholar. Romanes, George J., ‘Can an animal count?Nature (1885) 33, p. 80CrossRefGoogle Scholar.

65 Wallace, op. cit. (44), pp. 464–472.

66 Conant, Levi Leonard, The Number Concept: Its Origin and Development, New York: Macmillan and Co., 1896Google Scholar.

67 Unsigned (Grant Allen), ‘Scores and tallies’, op. cit. (26), p. 437.

68 Unsigned (Grant Allen), ‘Scores and tallies’, op. cit. (26), p. 448. More succinctly (p. 447): ‘Counting by tens is a legacy of savagery.’

69 Unsigned (Grant Allen), ‘Scores and tallies’, op. cit. (26), pp. 436–437. The essay continues, ‘The man who first definitely said to himself, Two and two make four, was a prehistoric Newton, a mute, inglorious, and doubtless very black-skinned but intelligent Laplace.’

70 Tylor, op. cit. (52), p. 224.

71 Cunnington, Susan, The Story of Arithmetic: A Short History of Its Origin and Development, London: Swan Sonnenschein & Co., 1905, p. 5Google Scholar. On this consequential conflation of savage man and modern child see Kuklick, Henrika, The Savage Within: The Social History of British Anthropology, 1885–1945, Cambridge: Cambridge University Press, 1991, p. 86Google Scholar.

72 For example, Absolon, Karl, ‘The world's earliest portrait – 30,000 years old’, Illustrated London News, 2 October 1937, pp. 549553Google Scholar.

73 For example, Burton, David M., The History of Mathematics: An Introduction, Boston: Allyn and Bacon, Inc., 1985, p. 2Google Scholar; Kline, Morris, Mathematics in Western Culture, London: Penguin, 1972, p. 31Google Scholar; Scriba, Christoph J. and Ellis, M.E. Dormer, The Concept of Number: A Chapter in the History of Mathematics, with Applications of Interest to Teachers, Mannheim and Zürich: Bibliographisches Institut, 1968, p. 7Google Scholar. Even Stocking, op. cit. (4), p. 93, bluntly misrepresents Galton's remark about his dog, Dinah.

74 This is all the more striking given the influence of his African travels on other aspects of his later work – see Stocking, op. cit. (4), pp. 95–96; Fancher, Raymond E., ‘Francis Galton's African ethnography and its role in the development of his psychology’, BJHS (1983) 16, pp. 6779CrossRefGoogle ScholarPubMed – and the fact that he spent most of his career in the same scientific communities as Lubbock, Tylor and their peers. Even some of Galton's later writings would seem to offer openings for such considerations, for example Galton, Francis, Hereditary Genius: An Inquiry into Its Laws and Consequences, London: Macmillan and Co., 1869, p. 198CrossRefGoogle Scholar, pp. 336–340, 350. The prehistory of numbers seems absent as well in the large selection of Galton's correspondence at University College London (throughout their Galton collection), the Royal Geographical Society (in Correspondence Block 4), and the National Library of Scotland (various MSS, especially in letterbook Ms.40435).