9.
Mark A. Richards and Gary A. Shaw, "Chips, Architectures and Algorithms: Reflections on the
Exponential Growth of Digital Signal Processing Capability," submitted to
IEEE Signal
Processing
, December 2004.
10.
Jon Bentley, "Programming Pearls,"
Communications of the ACM
27.11 (November 1984): 1087–
92.
11.
C. Eldering, M. L. Sylla, and J. A. Eisenach, "Is There a Moore's Law for Bandwidth,"
IEEE
Communications
(October 1999): 117–21.
12.
J. W. Cooley and J. W. Tukey, "An Algorithm for the Machine Computation of Complex
Fourier
Series,"
Mathematics of Computation
19 (April 1965): 297–301.
13.
There are an estimated 100 billion neurons with an estimated interneuronal connection "fan out" of
about 1,000, so there are about 100 trillion (10
14
) connections. Each connection requires at least 70
bits to store an ID for the two neurons at either end of the connection. So that's approximately 10
16
bits. Even the uncompressed genome is about 6 billion bits (about 10
10
), a ratio of at least 10
6
: 1.
See chapter 4.
14.
Robert A. Freitas Jr.,
Nanomedicine
, vol. I,
Basic Capabilities
, section 6.3.4.2, "Biological
Chemomechanical Power Conversion" (Georgetown, Tex.: Landes Bioscience, 1999), pp. 147–48,
http://www.nanomedicine.com/NMI/6.3.4.2.htm#p4; see illustration at
http://www.nanomedicine.com/NMI/Figures/6.2.jpg.
15.
Richard Dawkins, "Why Don't Animals Have Wheels?"
Sunday Times
, November 24, 1996,
http://www.simonyi.ox.ac.uk/dawkins/WorldOfDawkins-archive/Dawkins/Work/Articles/1996-11-
24wheels.shtml.
16.
Thomas Ray, "Kurzweil's Turing Fallacy," in Richards et al.,
Are We Spiritual Machines?
17.
Ibid.
18.
Anthony J. Bell, "Levels and Loops: The Future of Artificial
Intelligence and Neuroscience,"
Philosophical Transactions of the Royal Society of London B
354 (1999): 2013–20,
http://www.cnl.salk.edu/~tony/ptrsl.pdf.
19.
Ibid.
20.
David Dewey, "Introduction to the Mandelbrot Set," http://www.ddewey.net/mandelbrot.
21.
ChristofKoch quoted in John Horgan,
The End of Science
(Reading, Mass.: Addison-Wesley,
1996).
22.
Roger Penrose,
Shadows of the Mind: A Search for the Missing Science of Consciousness
(New
York: Oxford University Press, 1996); Stuart Hameroff and Roger Penrose, "Orchestrated
Objective Reduction of Quantum Coherence in Brain Microtubules: The 'Orch OR' Model for
Consciousness,"
Mathematics and Computer Simulation
40 (1996): 453–80,
http://www.quanturnconsciousness.org/penrosehameroff/orchOR.html.
23.
Sander Olson, "Interview with Seth Lloyd," November 17, 2002, http://www.nano
magazine.com/i.php?id=2002_11_17.
24.
Bell, "Levels and Loops."
25.
See the exponential growth of computing graphs in chapter 2 (pp. 67, 70).
26.
Alfred N. Whitehead and Bertrand Russell,
Principia Mathematica
, 3 vols. (Cambridge, U.K.:
Cambridge University Press, 1910, 1912, 1913).
27.
Gödel's incompleteness theorem first appeared in his "Uberformal unenscheiderbare Satze der
Principia Mathematica
und verwandter Systeme I,"
Monatshefte für Mathematik und Physik
38
(1931): 173–98.
28.
Alan M. Turing, "On Computable Numbers with an Application to the Entscheidungsproblem,"
Proceedings of the London Mathematical Society
42 (1936): 230-65. The "Entscheidungsproblem"
is the decision or halting problem—that is, how to determine ahead of time whether an algorithm
will halt (come to a decision) or continue in an infinite loop.
29.
Church's version appeared in Alonzo Church, "An Unsolvable Problem of Elementary Number
Theory,"
American Journal of Mathematics
58 (1936): 345–63.
30.
For an entertaining introductory account of some of the implications of the Church-Turing thesis,
see Douglas R. Hofstadter,
Gödel; Escher, Bach: An Eternal Golden Braid
(New York: Basic
Books, 1979).
31.
The busy-beaver problem is one example of a large class of noncomputable functions, as seen in
Tibor Rado, "On Noncomputable Functions,"
Bell System Technical Journal
41.3 (1962): 877–84.
32.
Ray, "Kurzweil's Turing Fallacy."
33.
Lanier, "One Half of a Manifesto."
34.
A human, that is, who is not asleep and not in a coma and of sufficient development (that is, not a
prebrain fetus) to be conscious.
35.
John R. Searle, "I
Married a Computer," in Richards et al.,
Are We Spiritual Machines?
36.
John R. Searle,
The Rediscovery of the Mind
(Cambridge, Mass.: MIT Press, 1992).
37.
Hans Moravec,
Letter to the Editor,
New York Review of Books
,
http://www.kurzweiltech.com/Searle/searle_response_letter.htm.
38.
John Searle to Ray Kurzweil, December 15, 1998.
39.
Lanier, "One Half of a Manifesto."
40.
David Brooks, "Good News About Poverty,"
New York Times
November 27, 2004, A35.
41.
Hans Moravec, Letter to the Editor,
New York Review of Books
,
http://www.kurzweiltech.com/Searle/searle_response_letter.htm.
42.
Patrick Moore, "The Battle for Biotech Progress—GM Crops Are Good for the Environment and
Human Welfare,"
Greenspirit
(February 2004), http://www.greenspirit.com/logbook.cfm?msid=62.
43.
Joel Cutcher-Gershenfeld, private communication to Ray Kurzweil, February 2005.
44.
William A. Dembski, "Kurzweil's Impoverished Spirituality," in Richards et al.,
Are We Spiritual
Machines?
45.
Denton, "Organism and Machine."
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