Darwin Among the Machines (45 page)

4
.
E. T. Bell,
Men of Mathematics
(New York: Simon & Schuster, 1937), 120, 122.

5
.
Leibniz to Henry Oldenburg, 18 December 1675, in H. W. Turnbull, ed.,
The Correspondence of Isaac Newton
, vol. 1 (Cambridge: Cambridge University Press, 1959), 401.

6
.
Leibniz to Nicolas Remond, 10 January 1714, in Leroy E. Loemker, trans, and ed.,
Philosophical Papers and Letters
, vol. 2 (Chicago: University of Chicago Press, 1956), 1063.

7
.
Leibniz, 1685, “Machina arithmetica in qua non additio tantum et subtractio sed et multiplicatio nullo, divisio vero pæne nullo animi labore peragantur,” translated as “Leibniz on his Calculating Machine,” in D. E. Smith, ed.,
A Source Book in Mathematics
, vol. 1 (New York: Dover, 1929), 180.

8
.
Leibniz, letter, n.d., quoted in H. W. Buxton, 1871,
Memoir of the Life and Labours of the Late Charles Babbage Esq. F.R.S. (MS, 1871)
, Charles Babbage Institute Reprint Series for the History of Computing, vol. 13 (Cambridge: MIT Press, 1988), 51, 381.

9
.
Leibniz, 1685, in Smith,
Source Book
, vol. 1, 180–181.

10
.
Leibniz, 1716, in Henry Rosemont, Jr., and Daniel J. Cook, trans, and eds.,
Discourse on the Natural Theology of the Chinese
(translation of “Lettre sur la philosophie chinoise à Nicolas de Remond”), Monograph of the Society for Asian and Comparative Philosophy, no. 4 (Honolulu: University of Hawaii Press, 1977), 158.

11
.
Leibniz, “De Progressione Dyadica—Pars I,” (MS, 15 March 1679), published in facsimile (with German translation) in Erich Hochstetter and Hermann-Josef Greve, eds.,
Herrn von Leibniz' Rechnung mit Null und Eins
(Berlin: Siemens Aktiengesellschaft, 1966), 46–47. (English translation by Verena Huber-Dyson, 1995.)

12
.
Leibniz, ca. 1679, in Loemker,
Philosophical Papers
, vol. 1, 342.

13
.
Ibid., 344.

14
.
Leibniz, supplement to a letter to Christiaan Huygens, 8 September 1679, in Loemker,
Philosophical Papers
, vol. 1, 384–385.

15
.
Charles Babbage,
Passages from the Life of a Philosopher
(London: Longman, Green, 1864), 142. Facsimile reprint, New York: A. M. Kelley, 1969.

16
.
Buxton,
Babbage
, 158.

17
.
Ibid., 155.

18
.
Leibniz, 1710, “Reflexions on the Work that Mr. Hobbes Published in English on ‘Freedom, Necessity and Chance,'” in E. M. Huggard, trans., and Austin Farrer, ed.,
Theodicy: Essays on the Goodness of God the Freedom of Man and the Origin of Evil
, (La Salle, Ill.: Open Court, 1951), 393.

19
.
Babbage,
Passages
, 42.

20
.
Buxton,
Babbage
, 46.

21
.
Babbage,
Passages
, 118–119.

22
.
Doron D. Swade, “Redeeming Charles Babbage's Mechanical Computer,”
Scientific American
268, no. 2 (February 1993): 86.

23
.
Charles Darwin, 1876, in Nora Barlow, ed.,
The Autobiography of Charles Darwin, 1809–1882: with Original Omissions Restored, edited with Appendix and Notes by his Grand-daughter
(New York: Harcourt Brace, 1958), 108. This reference to Babbage, and accompanying comments on Herbert Spencer, were deleted from the version published by Francis Darwin in 1896.

24
.
Ada Augusta Lovelace, Note A to L. F. Menabrea's “Sketch of the Analytical Engine invented by Charles Babbage, Esq.,”
Taylor's Scientific Memoirs
, vol. 3 (London: J. E. & R. Taylor, 1843), reprinted in Henry Provost Babbage, ed.,
Babbage's Calculating Engines: Being a Collection of Papers Relating to them; their History, and Construction
(London: E. and F. Spon, 1889), 25. Facsimile reprint, Charles Babbage Institute Reprint Series for the History of Computing, vol. 2 (Cambridge, Mass.: MIT Press, 1982).

25
.
Babbage,
Ninth Bridgewater Treatise
, 97.

26
.
Ibid., vii.

27
.
Charles Babbage,
On the Economy of Machinery and Manufactures
, 4th ed., enlarged (London: Charles Knight, 1835), 273–276.

28
.
Babbage,
Passages
, 128.

29
.
George Boole,
An Investigation of the Laws of Thought, on which are founded the mathematical theories of Logic and Probabilities
(London: Macmillan, 1854), 1.

30
.
Herman Goldstine,
The Computer from Pascal to von Neumann
(Princeton, N.J.: Princeton University Press, 1972), 153.

31
.
John von Neumann, “Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components,” in Claude E. Shannon and John McCarthy, eds.,
Automata Studies
(Princeton, N.J.: Princeton University Press, 1956), 43–99.

32
.
Boole,
Laws of Thought
, 21.

33
.
Ibid., 408.

34
.
Leibniz, ca. 1702, “Reflections on the Common Concept of Justice,” in Loemker,
Philosophical Papers
, vol. 2, 919.

35
.
D'arcy Power, in
Dictionary of National Biography
, vol. 18 (London: Smith, Elder & Co., 1898), 399.

36
.
Alfred Smee,
Principles of the Human Mind deduced from Physical Laws
(London: Longman, Brown, Green, & Longmans, 1849); reprinted in Elizabeth Mary (Smee) Odling,
Memoir of the late Alfred Smee, F. R. S., by his daughter; with a selection from his miscellaneous writings
(London: George Bell & Sons, 1878), 271.

37
.
Alfred Smee,
The Process of Thought Adapted to Words and Language, together with a description of the Relational and Differential Machines
(London: Longman, Brown, Green, & Longmans, 1851), ix.

38
.
Ibid., 2.

39
.
Ibid., 25.

40
.
Ibid., 39.

41
.
Ibid., 42–43.

42
.
Ibid., 48–49.

43
.
Ibid., 49–50.

44
.
Alfred Smee,
Instinct and Reason: Deduced from Electro-Biology
(London: Reeve, Benham & Reeve, 1850), 97.

45
.
Alfred Smee,
Elements of Electro-Biology; or, the Voltaic Mechanism of Man; of Electro-Pathology, Especially of the Nervous System; and of Electro-Therapeutics
(London: Reeve, Benham & Reeve, 1849), 20.

46
.
Smee,
Instinct and Reason
, 28–29.

47
.
Ibid., 200, 221.

48
.
Saturday Review
(London), 10 August 1872, 194.

49
.
Power,
Dictionary
, vol. 18, 399.

50
.
Kurt Gödel, “Über formal unentscheidbare Sätze der
Principia Mathematica
und verwandter Systeme I,”
Monatshefte für Mathematik und Physik
38 (1931); translated by Elliott Mendelson as “On Formally Undecidable Propositions of
Principia Mathematica
and Related Systems I,” in Martin Davis, ed.,
The Undecidable
(Hewlett, N.Y.: Raven Press, 1965), 5.

51
.
Leibniz to Clarke, 18 August 1716, in H. G. Alexander, ed.,
The Leibniz–Clarke Correspondence
(Manchester, England: Manchester University Press, 1956), 193.

52
.
Leibniz, 1714,
The Monadology
, in George R. Montgomery, trans.,
Basic Writings: Discourse on Metaphysics; Correspondence with Arnauld; Monadology
(La Salle, Ill.: Open Court, 1902), 254.

53
.
Leibniz to Caroline, Princess of Wales, ca. 1716, in Alexander,
Correspondence
, 191.

1
.
Alan Turing, “Computing Machinery and Intelligence,”
Mind
59 (October 1950): 443.

2
.
A. K. Dewdney,
The Turing Omnibus
(Rockville, Md.: Computer Science Press, 1989), 389.

3
.
Robin Gandy, “The Confluence of Ideas in 1936,” in Rolf Herken, ed.,
The Universal Turing Machine: A Half-century Survey
(Oxford: Oxford University Press, 1988), 85.

4
.
Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem,”
Proceedings of the London Mathematical Society
, 2d ser. 42 (1936–1937); reprinted, with corrections, in Martin Davis, ed.,
The Undecidable
(Hewlett, N.Y.: Raven Press, 1965), 117.

5
.
Ibid., 136.

6
.
Kurt Gödel, 1946, “Remarks Before the Princeton Bicentennial Conference on Problems in Mathematics,” reprinted in Davis,
The Undecidable
, 84.

7
.
W. Daniel Hillis,
The Difference That Makes a Difference
(New York: Basic Books, forthcoming).

8
.
Malcolm MacPhail to Andrew Hodges, 17 December 1977, in Andrew Hodges,
Alan Turing: The Enigma
(New York: Simon & Schuster, 1983), 138.

9
.
Allan Marquand, “A New Logical Machine,”
Proceedings of the American Academy of Arts and Sciences
21 (1885): 303.

10
.
Charles Peirce to Allan Marquand, 1866, in Arthur W. Burks, “Logic, Computers, and Men,”
Proceedings and Addresses of the American Philosophical Association
46 (1973): 47–48.

11
.
Wolfe Mays, “The First Circuit of an Electrical Logic-Machine,”
Science
118 (4 September 1953): 281.

12
.
George W. Patterson, “The First Electric Computer, a Magnetological Analysis,”
Journal of the Franklin Institute
270 (1960): 130.

13
.
Charles S. Peirce, “Logical Machines,”
American Journal of Psychology
1 (November 1887): 165.

14
.
Ibid., 170.

15
.
Ibid., 168.

16
.
Ibid., 169.

17
.
Theodosia Talcott to H. Talcott, 6 January 1889, in Geoffrey D. Austrian,
Herman Hollerith: Forgotten Giant of Information Processing
(New York: Columbia University Press, 1982), 39–40.

18
.
Emmanuel Scheyer, “When Perforated Paper Goes to Work: How Strips of Paper Can Endow Inanimate Machines with Brains of Their Own,”
Scientific American
127 (December 1922): 395.

19
.
Vannevar Bush, “Instrumental Analysis,”
Bulletin of the American Mathematical Society
42 (October 1936): 652.

20
.
John W. Tukey, 9 January 1947, “Sequential Conversion of Continuous Data to Digital Data,” in Henry S. Tropp, “Origin of the Term Bit,”
Annals of the History of Computing
6, no. 2 (April 1984): 153–154.

21
.
Claude E. Shannon, “A Mathematical Theory of Communication,”
Bell System Technical Journal
27 (July and October 1948): 379–423, 623–656.

22
.
Bush, “Instrumental Analysis,” 653–654.

23
.
Irving J. Good, “Pioneering Work on Computers at Bletchley,” in Nicholas Metropolis, J. Howlett, and Gian-Carlo Rota, eds.,
A History of Computing in the Twentieth Century
(New York: Academic Press, 1980), 35.

24
.
Peter Hilton, “Reminiscences of Bletchley Park, 1942–1945,” in
A Century of Mathematics in America
, part 1 (Providence, R.I.: American Mathematical Society, 1988), 293–294.

25
.
Diana Payne, “The Bombes,” in F. H. Hinsley and Alan Stripp, eds.,
Codebreakers: The Inside Story of Bletchley Park
(Oxford: Oxford University Press, 1993), 134.

26
.
Thomas H. Flowers, “The Design of Colossus,”
Annals of the History of Computing
5 (1983): 244.

27
.
Irving J. Good, “A Report on a Lecture by Tom Flowers on the Design of the Colossus,”
Annals of the History of Computing
4, no. 1 (1982): 57–58.

28
.
Howard Campaigne, introduction to Flowers, “Design of Colossus,” 239.

29
.
Irving J. Good, “Enigma and Fish,” revised, with corrections, in F. H. Hinsley and Alan Stripp, eds.,
Codebreakers: The Inside Story of Bletchley Park
, 2d ed. (Oxford: Clarendon Press, 1994), 164.

30
.
Hodges,
Turing
, 278.

31
.
Irving J. Good, “Turing and the Computer,” review of
Alan Turing: The Enigma
, by Andrew Hodges,
Nature
307 (1 February 1984): 663.

32
.
Brian Randell, “The Colossus,” in Metropolis, Howlett, and Rota,
History of Computing
, 78.

33
.
Hilton, “Reminiscences,” 293.

34
.
Alan Turing, “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE),” reprinted in B. E. Carpenter and R. W. Doran, eds.,
A. M. Turing's A.C.E. Report of 1946 and Other Papers
, Charles Babbage Reprint Series for the History of Computing, vol. 10 (Cambridge: MIT Press, 1986), 20–105.