The Philosophical Breakfast Club (66 page)

1
     Babbage to Herschel, December 20, 1821, RS: HS 2.169.

2
     See Croarken, “Tabulating the Heavens.”

3
     Babbage’s “recollections” in his
Passages
are often inaccurate; later biographers who have relied heavily on Babbage’s account of key episodes in his life, without adequate fact-checking, have perpetuated Babbage’s self-promoting rewriting of history.

4
     Cited in Martin,
The Calculating Machines
, p. 38.

5
     Kistermann, “How to Use the Schickard Calculator,” p. 82.

6
     Williams, “Early Calculation,” p. 38.

7
     This method is also known as “clock arithmetic.” Imagine a clock with a certain number of digits around its face (either twelve, as in a regular clock, or another number, such as ten). In the operation of addition, the sum is expressed as if going around the clock. So, in a clock that goes up to 10, or with a 10 “modulus,” when we add 8 and 7 we get 5 (because after reaching 10 the numbers start at 1 again). Subtraction is performed by adding the complement of the number relative to the modulus. The complement of a number is the number that must be added to it to reach the modulus. The tens complement of the number 4 is the number 6, because 4 + 6 = 10. So if we want to subtract 4 from 8, we instead
add
6
to
8, to get the same result moving around the clock in the clockwise direction: 4.

8
     Williams, “Early Calculation,” p. 42.

9
     See Buxton,
Memoirs of the Life and Labours of the Late Charles Babbage Esq.
, pp. 49–50; and Williams, “Early Calculation,” pp. 40–42.

10
   Williams, “Early Calculation,” pp. 42–49.

11
   Cited in Lardner, “Babbage’s Calculating Engine,” p. 323.

12
   See Johnston, “Making the Arithmometer Count”; Williams, “Early Calculation”; and the site
www.arithmometre.org
.

13
   Anonymous, “Varieties, Literary and Philosophical,” p. 444.

14
   The “longitude problem” and its solution by John Harrison is discussed by Dava Sobel in her
Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time
.

15
   Croarken, “Tabulating the Heavens.”

16
   Swade,
The Difference Engine
, p. 13.

17
   Grattan-Guinness, “Work for the Hairdressers,” pp. 179–80.

18
   Babbage,
A Letter to Sir Humphry Davy
, in
Works
, vol. 2, p. 10.

19
   Babbage,
On the Economy of Machinery and Manufactures
, p. 195.

20
   For example, if we wish to compute a table of square numbers, the function F(x) = x
²
, we start by calculating the initial values of F(x) when x equals 0, 1, 2, 3, 4, 5, 6, 7, 8. We find that the square numbers at the start of the series are 0, 1, 4, 9, 16, 25, 36, 49, 64. The first order of difference is obtained by subtracting each number in the series from its successor, yielding 1, 3, 5, 7, 9, 11, 13, 15. By a further subtraction of the numbers from their successors in the first order of difference, the second order of difference is obtained, which we know will be constant: 2, 2, 2, 2, 2, 2, 2. To get the next numbers in the series of squares, all that is needed is to perform two additions. First, add 2 to the first order of difference; second, add the number obtained in this way to the square number preceding it. Thus, by adding 2 to 15 we get 17, and by adding
17 to 64 we get 81, the next square in the series. By adding 2 to 17 we get 19, and by adding 19 to 81 we get 100, the square of 10, and so on.

21
   See Buxton,
Memoirs
, p. 140.

22
   If the polynomial being calculated was F(x) = x
²
+ 4, for example, the mathematician would calculate the initial values of F(x) when x = 0, 1, 2, 3. He would find that the start of the series was 4, 5, 8, 13. By subtracting each number from its successor, the first order of difference would be obtained: 1, 3, 5. A further subtraction would yield the second order of difference: 2, 2. So for F(x) = x
²
+ 4 when x = 0, the result is 4, the first order of difference is 1, and the second order of difference is 2. In starting the machine, the results for x = 0 would be set into it: 4 in the results column, 1 in the first order of difference column, and 2 in the second difference column. The handle would be cranked four half-times, two in each direction. This would change the figure wheels automatically to the next values, for x = 1: 5 for the result, 3 for the first difference, and 2 for the second difference. With another four half-turns, the figure wheels would read 8, 5, and 2, the correct values for x = 2.

23
   See Swade,
The Difference Engine
, pp. 99–100.

24
   Babbage,
The Exposition of 1851
, p. 182.

25
   Colebrooke, in
The Works of Charles Babbage
, vol. 2, p. 57.

26
   Hare to Whewell, October 5, 1822, WP Add. ms. a. 211 f. 134.

27
   For more on the fragment, see Buxton,
Memoirs
, pp. 137–38.

28
   Babbage,
A Letter to Sir Humphry Davy
, in
Works
, vol. 2, p. 14.

29
   Babbage to Herschel, June 10, 1822, RS: HS 2.173, cited in Lindgren,
Glory and Failure
, p. 274.

30
   See Swade,
The Difference Engine
, pp. 37–38.

31
   Bacon,
Novum Organum
, book 2, aph. 44 in
Works
, vol. 4; he makes a similar point in aph. 36, and in his little-known work
History of Dense and Rare
.

32
   
Report of the Royal Society of London
, May 1, 1823,
Parliamentary Paper
, 370; quoted in a letter from Lord Rosse to Lord Derby, June 8, 1852. Reproduced in Babbage,
Passages from the Life of a Philosopher
, p. 77.

33
   Babbage to Herschel, June 27, 1823, RS: HS 2.184.

34
   See Gordon, “Simeon North, John Hall, and Mechanized Manufacturing.”

35
   Whewell to Babbage, December 29 [1824], BL Add. ms. 37,182 f. 144.

36
   For more on Babbage and his engines, see Schaffer, “Babbage’s Intelligence.”

1
     Whewell to Jones, December 10, 1833, in Todhunter,
William Whewell
, vol. 2, p. 173. It was not the first time Whewell had admonished Jones in this way.

2
     See Pullen, “Jones, Richard.”

3
     Whewell to Jones, December 23, 1825, WP Add. ms. c. 51 f. 25.

4
     Rose to Whewell, October 25, 1822, WP Add. ms. a. 211 f. 135.

5
     Jones to Whewell, April 17, 1832, WP Add. ms. c. 52 f. 52.

6
     Maria Edgeworth to Mrs. Ruxton, March 9, 1822, in Edgeworth,
Life and Letters
, vol. 2, p. 65.

7
     See, for example, letter from Jones to Whewell, March 9, 1831, WP Add. ms. c. 52 f. 48.

8
     See Porter,
English Society in the Eighteenth Century
, pp. 15–17.

9
     Colley,
Britons: Forging the Nation
, p. 158.

10
   See Porter,
English Society in the Eighteenth Century
, p. 129.

11
   Malthus,
Essay on the Principle of Population
, p. 100.

12
   In Carlyle’s essay “Chartism.” Later he would more directly use the phrase “the dismal science” in the context of expressing virulently racist views in an essay called “Occasional Discourse on the Negro Question” (1849), leading some scholars to note that the phrase was bound up with Carlyle’s racism. Whatever Carlyle’s meaning of the phrase, it is clear that to many in the 1820s and 1830s, even those like Whewell, who believed in the equality of the races, political economy was a “dismal science.”

13
   Rashid,
The Myth of Adam Smith
.

14
   Ricardo,
Works and Correspondence
, vol. 3, p. 181.

15
   Ibid., vol. 2, pp. 337–38.

16
   Bacon,
The Advancement of Learning
in
Works
, vol. 6.

17
   Whewell to Jones, November 1, 1826, WP Add. ms. c. 51 f. 31. Smith, the self-educated son of a blacksmith, received no recognition from the scientific elite until he was awarded the first Wollaston Medal of the Geological Society in 1831, an honor that Whewell—another working-class success story—was pleased to witness. See minutes of Geological Society Meeting, January 11, 1831; excerpted on Geological Society website,
http://www.geolsoc.org.uk/gsl/geoscientist/features/page863.html
.

18
   See Rashid, “Political Economy and Geology in the Early Nineteenth Century.”

19
   See Lyell,
The Life, Letters and Journals of Sir Charles Lyell
, vol. 2, pp. 38–39.

20
   De Quincey, “Confessions of an English Opium-Eater,” p. 371.

21
   Whewell, “Mathematical Exposition of Some of the Leading Doctrines in Mr. Ricardo’s
Principles of Political Economy and Taxation.
”

22
   See Jones to Whewell, February 17, 1832, WP Add. ms. c. 52 f. 48.

23
   Whewell to Jones, February 2, 1833, WP Add. ms. c. 51 f. 150.

24
   Whewell to Jones, February 19, 1832, WP Add. ms. 51 f. 129.

25
   Jones to Whewell, April 22, 1831, WP Add. ms. 52 f. 34.

26
   Whewell to Jones, November 3, 1822, WP Add. ms. c. 51 f. 16.

27
   Whewell to Jones, May 24, 1825, WP Add. ms. c. 51 f. 21.

28
   Whewell to Jones, September 9, 1828, in Todhunter,
William Whewell
, vol. 2, p. 93.

29
   Whewell to Jones, November 20, 1829, WP Add. ms. c. 51 f. 73.

30
   Whewell to Jones, May 21, 1830, WP Add. ms. c. 51 f. 84.

31
   Jones to Whewell, May 15, 1822, WP Add. ms. c. 52 f. 4.

32
   Jones,
Essay on the Distribution of Wealth
, p. xxi.

33
   Whewell to Jones, August 17, 1829, in Todhunter,
William Whewell
, vol. 2, pp. 102–4.

34
   Whewell to Jones, July 31, 1829, in Todhunter,
William Whewell
, vol. 2, p. 99.

35
   See Stair Douglas,
Life and Selections
, p. 129.

36
   See Herschel to Jones, September 11, 1822, RS: HS 19.31.

37
   Jones,
Literary Remains
, pp. 568–69.

38
   See Reinhart, “The Life of Richard Jones,” p. 6. See also Jones to Whewell, October 1, 1830, WP Add. ms. c. 52 f. 17, and Jones to Whewell, October 21, 1831, WP Add. ms. c. 52 f. 41.

39
   Whewell to Jones, December 7, 1830, WP Add. ms. c. 51 f. 93.

40
   Whewell to Jones, November 1, 1830, WP Add. ms. c. 51 f. 90.

41
   Reported in Whately,
Life and Correspondence of Richard Whately
, vol. 2, p. 114.

42
   A recent study found that the “ideal” workhouse diet for an adult male recommended in an 1843 book would have provided 1,600 to 1,700 calories a day, far less than the 4,500 calories consumed by farm workers in parts of England in the 1860s, and not as much, even, as the 2,700 calories in the diet of the modern American man, who engages in a fraction of the physical activity of farm laborers or of men in the workhouse. And that was the ideal; who knows how often it was met? See Pereira,
Treatise on Food and Diet with Observations on the Dietical Regime
, and Bakalar, “In Reality, Oliver’s Diet Wasn’t Truly Dickensian,” where the author concludes that in fact this was not such a bad diet. For the (important but unmentioned by Bakalar) comparison with laborers outside the workhouse, see Clark,
The Sun Kings
, p. 285.

43
   The ideal prison diet, in the same 1843 book mentioned above, included more bread and potatoes than the ideal workhouse diet. See Pereira,
Treatise on Food and Diet
.

44
   Becher,
The Anti-Pauper System
.

45
   Bentham,
Collected Works of Jeremy Bentham
, vol. 10, p. 226; Jones,
An Essay on the Distribution of Wealth
, pp. 317–18.

46
   Jones to Herschel, [n.d.], RS: HS 10.410.

47
   Whewell,
Elements of Morality
, vol. 2, p. 185.

48
   Cited in Porter,
English Society in the Eighteenth Century
, p. 165.

49
   See Soloway,
Prelates and People
, p. 188.

50
   See Whewell to Ann Lyon, October 6, 1827, WP Add. ms. c. 191 f. 37.

51
   Walker,
Poetical Remains
, pp. civ–cvi, cited in Distad,
Guessing at Truth
, p. 53.

52
   Hare,
The Story of My Life
, vol. 1, ch. 4.

53
   See Todhunter,
William Whewell
, vol. 1, p. 34.

54
   Whewell to Jones, September 7, 1827, WP Add. ms. c. 51 f. 40.

55
   Whewell to Jones, September 20, 1827, WP Add. ms. c. 51 f. 43.

56
   Jones to Whewell, September 27, 1827, WP Add. ms. c. 52 f. 15. A pen blot covers the two letters before “men,” but they seem to be “wo.”

57
   Herschel to Babbage, May 10, 1820, RS: HS 20.96.

58
   See Clerke,
The Herschels and Modern Astronomy
, pp. 70, 109, and Huggins and Miller, “On the Spectra of Some of the Nebulae.”

59
   See Clerke,
The Herschels and Modern Astronomy
, p. 155.

60
   John Herschel to Margaret Herschel, July 23, 1830; cited in Schaaf,
Out of the Shadows
, p. 16.

61
   Caroline Herschel to John Herschel, July 14, 1823, in Herschel,
Memoir and Correspondence of Caroline Herschel
, p. 168.

62
   Caroline Herschel to John Herschel, February 1, 1826, in ibid, pp. 196–99.

63
   Maria Edgeworth to Harriet Butler, March 29, 1831, in Edgeworth,
Life and Letters
, vol. 2, p. 180.

64
   Babbage to Herschel, May 6, 1829, RS: HS 2.239.

65
   Whewell to Jones, February 4, 1829, WP Add. ms. c. 51 f. 60.

66
   See Herschel to Matthew Boulton, April 1, 1829, in Crowe et al., p. 104, and Matthew Boulton to Herschel, April 2, 1829, RS: HS 5.86.

67
   See Todhunter,
William Whewell
, vol. 1, pp. 57–58.

68
   Herschel,
Preliminary Discourse
, p. 144.

69
   See Whewell, “Lyell’s
Principles of Geology
, vol. II,”
Quarterly Review
47, p. 126.

70
   See Falconer, “Henry Cavendish.”

71
   Cavendish, “Experiment to Determine the Density of the Earth,” p. 469.

72
   Whewell,
Account of Experiments Made at Dolcoath Mine
.

73
   Whewell to Lady Malcolm, June 10, 1826, in Stair Douglas,
Life and Selections
, pp. 103–4.

74
   Later, in 1837, a Prof. F. Reich of the Academy of Mines in Freiburg would have more success, reaching the figure of 5.49, and in 1841 Babbage’s friend Francis Baily would get 5.68. Airy tried again in 1854, at the Horton colliery, but his result was 6.57, far from Cavendish’s more accurate result. See Thorpe, “Introduction,” pp. 71–73.

75
   See Herschel,
Preliminary Discourse
, pp. 48–57.

76
   Ibid., pp. 27–29.

77
   Ibid., p. 49.

78
   Ibid., p. 73.

79
   Cannon, “John Herschel and the Idea of Science.”

80
   Whewell, “Modern Science—Inductive Philosophy,” p. 378.

81
   Charles Darwin to T. H. Huxley, January 4 [1865], Darwin Correspondence Project, letter 4738.

82
   Jones to Herschel, January 10, 1831, RS: HS 10.350.

83
   Jones to Whewell, November 3, 1831, WP Add. ms. c. 52 f. 42.

84
   Babbage,
On the Economy of Machinery and Manufactures
, p. v.

85
   Ibid., pp. 115–17.

86
   Herschel,
Preliminary Discourse
, pp. 133–34.

87
   Georgiana Babbage to Herschel, [February] [n.d.] 1827, RS: HS 2.353.

88
   Elizabeth Plumleigh Babbage to Herschel, September 8, 1827, RS: HS 2.215.

89
   Jones to Whewell, September 8, 1827, WP Add. ms. c. 52 f. 14.

90
   Not Lucien’s daughter, as other sources have it. See Naef, “Who’s Who in Ingres’s Portrait of the Family of Lucien Bonaparte?”

91
   Babbage,
Passages from the Life of a Philosopher
, pp. 150–51.

92
   Ibid., p. 279.

93
   Babbage to Herschel, April 2, 1828, RS: HS 2:224.

94
   Babbage,
On the Economy of Machinery and Manufactures
, p. 156.

95
   Hyman,
Charles Babbage, Pioneer of the Computer
, p. 103. As Berg points out, it was not until the third edition of his
Principles
that Ricardo added a chapter on machinery, and this addition has seemed to modern students of Ricardo as contradictory to his other views. Berg,
The Machinery Question and the Making of Political Economy
, pp. 68–69.

96
   Babbage,
On the Economy of Machinery and Manufactures
, p. 4.

97
   See Hyman,
Charles Babbage, Pioneer of the Computer
, pp. 121–22.

98
   See Clark,
The Sun Kings
, pp. 285–88.

99
   Babbage,
On the Economy of Machinery and Manufactures
, pp. 250–51.

100
 Babbage, “To the Electors of the Borough of Finsbury,” in
Works
, vol. 4, p. 128.

101
 Babbage,
On the Economy of Machinery and Manufactures
, pp. 334–38.

102
 Jones to Whewell, February 17, 1832, WP Add. ms. c. 52 f. 48.

103
 Whewell to Jones, February 19, 1832, in Todhunter,
William Whewell
, vol. 2, pp. 141–42.

104
 Whewell to Jones, February 11, 1831, WP Add. ms. c. 51 f. 98.

105
 Reported in Jones to Whewell, March 9, 1831, WP Add. ms. c. 52 f. 27.

106
 Herschel to Jones, February 17, 1831, RS: HS 19.80.

107
 Jones,
Essay on the Distribution of Wealth
, p. vii.

108
 See ibid., p. 328.

109
 Whewell, “Jones–
On the Distribution of Wealth and the Sources of Taxation
.”

110
 Jones,
Literary Remains
, cited in Reinhart, “The Life of Richard Jones,” p. 80.

111
 See Jones,
Literary Remains
, pp. 255–56.

112
 Malthus modified this view somewhat in his second edition, where he did take account of the desire for a higher living standard as a factor in population control, but even there he did not see this as a real solution.

113
 See Clark,
The Sun Kings
, p. 113.

114
 See Reinhart, “The Life of Richard Jones,” p. 83.

115
 See Clark,
The Sun Kings
, p. 31.

116
 Ibid., p. 30.

117
 Whewell to Jones, December 26, 1832, in Todhunter,
William Whewell
, vol. 2, pp. 151–52.

118
 Scrope, “On Jones’ Essay,” p. 81.

119
 See Whewell to Jones, April 30, 1848, in Todhunter,
William Whewell
, vol. 2, pp. 345–46.

120
 For more on Jones’s influence on J. S. Mill, see Snyder,
Reforming Philosophy
, ch. 5.

121
 See Sen,
On Ethics and Economics
, p. x and
passim
.