To solve the traveling-salesperson problem, mathematician Leonard Adleman of the University of Southern California performed the following steps: 1. 1. Generate a small strand of DNA with a unique code for each city. Generate a small strand of DNA with a unique code for each city.

2. 2. Replicate each such strand (one for each city) trillions of times using PCR. Replicate each such strand (one for each city) trillions of times using PCR.

3. 3. Next, put the pools of DNA (one for each city) together in a test tube. This step uses DNA'saffinity to link strands together. Longer strands will form automatically. Each such strand represents a possible route of multiple cities. The small strands representing each city link up with each other in a random fashion, so there is no mathematical certainty that a linked strand representing the correct answer (sequence of cities) will be formed. However, the number of strands is so vast that it is virtually certain that at least one strand-and probably millions-will be formed that represents the correct answer. Next, put the pools of DNA (one for each city) together in a test tube. This step uses DNA'saffinity to link strands together. Longer strands will form automatically. Each such strand represents a possible route of multiple cities. The small strands representing each city link up with each other in a random fashion, so there is no mathematical certainty that a linked strand representing the correct answer (sequence of cities) will be formed. However, the number of strands is so vast that it is virtually certain that at least one strand-and probably millions-will be formed that represents the correct answer.

The next steps use specially designed enzymes to eliminate the trillions of strands that represent wrong answers, leaving only the strands representing the correct answer: 4. Use molecules called "primers" to destroy those DNA strands that do not start with the start city, as well as those that do not end with the end city; then replicate the surviving strands, using PCR.

4. 4. Use an enzyme reaction to eliminate those DNA strands that represent a travel path greater than the total number of cities. Use an enzyme reaction to eliminate those DNA strands that represent a travel path greater than the total number of cities.

5. 5. Use an enzyme reaction to destroy those strands that do not include city 1. Repeat for each of the cities. Use an enzyme reaction to destroy those strands that do not include city 1. Repeat for each of the cities.

6. 6. Now, each of the surviving strands represents the correct answer. Replicate these surviving strands (using PCR) until there are billions of such strands. Now, each of the surviving strands represents the correct answer. Replicate these surviving strands (using PCR) until there are billions of such strands.

7. 7. Using a technique called electroph.o.r.esis, read out the DNA sequence of these correct strands (as a group). The readout looks like a set of distinct lines, which specifies the correct sequence of cities. Using a technique called electroph.o.r.esis, read out the DNA sequence of these correct strands (as a group). The readout looks like a set of distinct lines, which specifies the correct sequence of cities.

See L. M. Adleman, "Molecular Computation of Solutions to Combinatorial Problems," Science Science 266 (1994): 102124. 266 (1994): 102124.

27. 27. Charles Choi, "DNA Computer Sets Guinness Record," http://www.upi.com/view.cfm?StoryID=20030224-045551-7398r. See also Y. Benenson et al., "DNA Molecule Provides a Computing Machine with Both Data and Fuel," Charles Choi, "DNA Computer Sets Guinness Record," http://www.upi.com/view.cfm?StoryID=20030224-045551-7398r. See also Y. Benenson et al., "DNA Molecule Provides a Computing Machine with Both Data and Fuel," Proceedings of the National Academy of Sciences Proceedings of the National Academy of Sciences 100.5 (March 4, 2003): 219196, available at http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=12601148; Y. Benenson et al., "An Autonomous Molecular Computer for Logical Control of Gene Expression," 100.5 (March 4, 2003): 219196, available at http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=12601148; Y. Benenson et al., "An Autonomous Molecular Computer for Logical Control of Gene Expression," Nature Nature 429.6990 (May 27,2004): 42329 (published online, April 28, 2004), available at http://www.wisdom.weizmann.ac.il/~udi/ShapiroNature2004. pdf. 429.6990 (May 27,2004): 42329 (published online, April 28, 2004), available at http://www.wisdom.weizmann.ac.il/~udi/ShapiroNature2004. pdf.

28. 28. Stanford University news release, " 'Spintronics' Could Enable a New Generation of Electronic Devices, Physicists Say," http://www.eurekalert.org/pub_releases/2003-08/su-ce080803.php, referring to Shuichi Murakami, Naoto Nagaosa, and Shou-Cheng Zhang, "Dissipationless Quantum Spin Current at Room Temperature," Stanford University news release, " 'Spintronics' Could Enable a New Generation of Electronic Devices, Physicists Say," http://www.eurekalert.org/pub_releases/2003-08/su-ce080803.php, referring to Shuichi Murakami, Naoto Nagaosa, and Shou-Cheng Zhang, "Dissipationless Quantum Spin Current at Room Temperature," Science Science 301.5638 (September 5, 2003): 134851. 301.5638 (September 5, 2003): 134851.

29. 29. Celeste Biever, "Silicon-Based Magnets Boost Spintronics," NewScientist.com, March 22, 2004, http://www.newscientist.com/news/news.jsp?id=ns99994801, referring to Steve Pearton, "Silicon-Based Spintronics," Celeste Biever, "Silicon-Based Magnets Boost Spintronics," NewScientist.com, March 22, 2004, http://www.newscientist.com/news/news.jsp?id=ns99994801, referring to Steve Pearton, "Silicon-Based Spintronics," Nature Materials Nature Materials 3.4 (April 2004): 2034. 3.4 (April 2004): 2034.

30. 30. Will Knight, "Digital Image Stored in Single Molecule," NewScientist.com, December 1, 2002, http://www.newscientist.com/news/news.jsp?id=ns99993129, referring to Anatoly K. Khitrin, Vladimir L. Ermakov, and B. M. Fung, "Nuclear Magnetic Resonance Molecular Photography," Will Knight, "Digital Image Stored in Single Molecule," NewScientist.com, December 1, 2002, http://www.newscientist.com/news/news.jsp?id=ns99993129, referring to Anatoly K. Khitrin, Vladimir L. Ermakov, and B. M. Fung, "Nuclear Magnetic Resonance Molecular Photography," Journal of Chemical Physics Journal of Chemical Physics 117.15 (October 15,2002): 6903-{5. 117.15 (October 15,2002): 6903-{5.

31. 31. Reuters, "Processing at the Speed of Light," Reuters, "Processing at the Speed of Light," Wired News Wired News, http://www.wired.com/news/technology/0,1282,61009,00.html.

32. 32. To date, the largest number to be factored is one of 512 bits, according to RSA Security. To date, the largest number to be factored is one of 512 bits, according to RSA Security.

33. 33. Stephan Gulde et al., "Implementation of the Deutsch-Iozsa Algorithm on an Ion-Trap Quantum Computer," Stephan Gulde et al., "Implementation of the Deutsch-Iozsa Algorithm on an Ion-Trap Quantum Computer," Nature Nature 421 (January 2,2003): 4850. See http://heart-c704.uibk.ac.at/Papers/Nature03-Gulde.pdf. 421 (January 2,2003): 4850. See http://heart-c704.uibk.ac.at/Papers/Nature03-Gulde.pdf.

34. 34. Since we are currently doubling the price-performance of computation each year, a factor of a thousand requires ten doublings, or ten years. But we are also (slowly) decreasing the doubling time itself, so the actual figure is eight years. Since we are currently doubling the price-performance of computation each year, a factor of a thousand requires ten doublings, or ten years. But we are also (slowly) decreasing the doubling time itself, so the actual figure is eight years.

35. 35. Each subsequent thousandfold increase is itself occurring at a slightly faster rate. See the previous note. Each subsequent thousandfold increase is itself occurring at a slightly faster rate. See the previous note.

36. 36. Hans Moravec, "Rise of the Robots," Hans Moravec, "Rise of the Robots," Scientific American Scientific American (December 1999): 12435, http://www.sciam.com and http://www.frc.ri.cmu.edu/~hpm/project.archive/robot.papers/1999/SciAm.scan.html. Moravec is a professor at the Robotics Inst.i.tute at Carnegie Mellon University. His Mobile Robot Laboratory explores how to use cameras, sonars, and other sensors to give robots 3-D spatial awareness. In the 1990s, he described a succession of robot generations that would "essentially [be] our off-spring, by unconventional means. Ultimately, I think they're on their own and they'll do things that we can't imagine or understand-you know, just the way children do" (Nova Online interview with Hans Moravec, October 1997, http://www.pbs.org/wgbh/nova/robots/moravec.html). His books (December 1999): 12435, http://www.sciam.com and http://www.frc.ri.cmu.edu/~hpm/project.archive/robot.papers/1999/SciAm.scan.html. Moravec is a professor at the Robotics Inst.i.tute at Carnegie Mellon University. His Mobile Robot Laboratory explores how to use cameras, sonars, and other sensors to give robots 3-D spatial awareness. In the 1990s, he described a succession of robot generations that would "essentially [be] our off-spring, by unconventional means. Ultimately, I think they're on their own and they'll do things that we can't imagine or understand-you know, just the way children do" (Nova Online interview with Hans Moravec, October 1997, http://www.pbs.org/wgbh/nova/robots/moravec.html). His books Mind Children: The Future of Robot and Human Intelligence Mind Children: The Future of Robot and Human Intelligence and and Robot: Mere Machine to Transcendent Mind Robot: Mere Machine to Transcendent Mind explore the capabilities of the current and future robot generations. explore the capabilities of the current and future robot generations.

Disclosure: The author is an investor in and on the board of directors of Moravec's robotics company, Seegrid.

37. 37. Although instructions per second as used by Moravec and calculations per second are slightly different concepts, these are close enough for the purposes of these order-of-magnitude estimates. Moravec developed the mathematical techniques for his robot vision independent of biological models, but similarities (between Moravec's algorithms and those performed biologically) were noted after the fact. Functionally, Moravec's computations re-create what is accomplished in these neural regions, so computational estimates based on Moravec's algorithms are appropriate in determining what is required to achieve functionally equivalent transformations. Although instructions per second as used by Moravec and calculations per second are slightly different concepts, these are close enough for the purposes of these order-of-magnitude estimates. Moravec developed the mathematical techniques for his robot vision independent of biological models, but similarities (between Moravec's algorithms and those performed biologically) were noted after the fact. Functionally, Moravec's computations re-create what is accomplished in these neural regions, so computational estimates based on Moravec's algorithms are appropriate in determining what is required to achieve functionally equivalent transformations.

38. 38. Lloyd Watts, "Event-Driven Simulation of Networks of Spiking Neurons," seventh Neural Information Processing Systems Foundation Conference, 1993;LloydWatts, "The Mode-Coupling Liouville-Green Approximation for a Two-Dimensional Cochlear Model," Lloyd Watts, "Event-Driven Simulation of Networks of Spiking Neurons," seventh Neural Information Processing Systems Foundation Conference, 1993;LloydWatts, "The Mode-Coupling Liouville-Green Approximation for a Two-Dimensional Cochlear Model," Journal of the Acoustical Society of America Journal of the Acoustical Society of America 108.5 (November 2000): 226671. Watts is the founder of Audience, Inc., which is devoted to applying functional simulation of regions of the human auditory system to applications in sound processing, including creating a way of preprocessing sound for automated speech-recognition systems. For more information, see http://www.lloydwatts.com/ neuroscience.shtml. 108.5 (November 2000): 226671. Watts is the founder of Audience, Inc., which is devoted to applying functional simulation of regions of the human auditory system to applications in sound processing, including creating a way of preprocessing sound for automated speech-recognition systems. For more information, see http://www.lloydwatts.com/ neuroscience.shtml.

Disclosure: The author is an adviser to Audience.

39. 39. U.S. Patent Application 20030095667, U.S. Patent and Trademark Office, May 22, 2003. U.S. Patent Application 20030095667, U.S. Patent and Trademark Office, May 22, 2003.

40. 40. The Medtronic MiniMed closed-loop artificial pancreas currently in human clinical trials is returning encouraging results. The company has announced that the device should be on the market within the next five years. Medtronic news release, "Medtronic Supports Juvenile Diabetes Research Foundation's Recognition of Artificial Pancreas as a Potential 'Cure' for Diabetes," March 23, 2004, http://www.medtronic.com/newsroom/news_2004323a.html. Such devices require a glucose sensor, an insulin pump, and an automated feedback mechanism to monitor insulin levels (International Hospital Federation, "Progress in Artificial Pancreas Development for Treating Diabetes," http://www.hospitalmanagement.net/informer/technology/tech10). Roche is also in the race to produce an artificial pancreas by 2007. See http://www.roche.com/pages/downloads/science/pdf/rtdcmannh02-6.pdf. The Medtronic MiniMed closed-loop artificial pancreas currently in human clinical trials is returning encouraging results. The company has announced that the device should be on the market within the next five years. Medtronic news release, "Medtronic Supports Juvenile Diabetes Research Foundation's Recognition of Artificial Pancreas as a Potential 'Cure' for Diabetes," March 23, 2004, http://www.medtronic.com/newsroom/news_2004323a.html. Such devices require a glucose sensor, an insulin pump, and an automated feedback mechanism to monitor insulin levels (International Hospital Federation, "Progress in Artificial Pancreas Development for Treating Diabetes," http://www.hospitalmanagement.net/informer/technology/tech10). Roche is also in the race to produce an artificial pancreas by 2007. See http://www.roche.com/pages/downloads/science/pdf/rtdcmannh02-6.pdf.

41. 41. A number of models and simulations have been created based on a.n.a.lyses of individual neurons and interneuronal connections. Tomaso Poggio writes, "One view of the neuron is that it is more like a chip with thousands of logical-gates-equivalents rather than a single threshold element," Tomaso Poggio, private communication to Ray Kurzweil, January 2005. A number of models and simulations have been created based on a.n.a.lyses of individual neurons and interneuronal connections. Tomaso Poggio writes, "One view of the neuron is that it is more like a chip with thousands of logical-gates-equivalents rather than a single threshold element," Tomaso Poggio, private communication to Ray Kurzweil, January 2005.

See also T. Poggio and C. Koch, "Synapses That Compute Motion," Scientific American Scientific American 256 (1987): 4652. 256 (1987): 4652.C. Koch and T. Poggio, "Biophysics of Computational Systems: Neurons, Synapses, and Membranes," in Synaptic Function Synaptic Function, G. M. Edelman, W. E. Gall, and W. M. Cowan, eds. (New York: John Wiley and Sons, 1987), pp. 63797.Another set of detailed neuron-level models and simulations is being created at the University of Pennsylvania's Neuroengineering Research Lab based on reverse engineering brain function at the neuron level. Dr. Leif Finkel, head of the laboratory, says, "Right now we're building a cellular-level model of a small piece of visual cortex. It's a very detailed computer simulation which reflects with some accuracy at least the basic operations of real neurons. [My colleague Kwabena Boahen] has a chip that accurately models the retina and produces output spikes that closely match real retinae." See http://nanodot.org/article.pl?sid=0l/12/18/1552221.Reviews of these and other models and simulations at the neuron level indicate that an estimate of 103 calculations per neural transaction (a single transaction involving signal transmission and reset on a single dendrite) is a reasonable upper bound. Most simulations use considerably less than this. calculations per neural transaction (a single transaction involving signal transmission and reset on a single dendrite) is a reasonable upper bound. Most simulations use considerably less than this.

42. 42. Plans for Blue Gene/L, the second generation of Blue Gene computers, were announced in late 2001. The new supercomputer, planned to be fifteen times faster than today's supercomputers and one twentieth the size, is being built jointly by the National Nuclear Security Agency's Lawrence Livermore National Laboratory and IBM. In 2002, IBM announced that open-source Linux had been chosen as the operating system for the new supercomputers. By July 2003, the innovative processor chips for the supercomputer, which are complete systems on chips, were in production. "Blue Gene/L is a poster child for what is possible with the system-on-a-chip concept. More than 90 percent of this chip was built from standard blocks in our technology library," according to Paul Coteus, one of the managers of the project (Timothy Morgan, "IBM's Blue Gene/L Shows Off Minimalist Server Design," Plans for Blue Gene/L, the second generation of Blue Gene computers, were announced in late 2001. The new supercomputer, planned to be fifteen times faster than today's supercomputers and one twentieth the size, is being built jointly by the National Nuclear Security Agency's Lawrence Livermore National Laboratory and IBM. In 2002, IBM announced that open-source Linux had been chosen as the operating system for the new supercomputers. By July 2003, the innovative processor chips for the supercomputer, which are complete systems on chips, were in production. "Blue Gene/L is a poster child for what is possible with the system-on-a-chip concept. More than 90 percent of this chip was built from standard blocks in our technology library," according to Paul Coteus, one of the managers of the project (Timothy Morgan, "IBM's Blue Gene/L Shows Off Minimalist Server Design," The Four Hundred The Four Hundred, http://www.midrangeserver.com/tfh/tfh120103-story05.html). By June 2004, the Blue Gene/L prototype systems appeared for the first time on the list of top ten supercomputers. IBM press release, "IBM Surges Past HP to Lead in Global Supercomputing," http://www.research.ibm.com/bluegene.

43. 43. This type of network is also called peer-to-peer, many-to-many, and "multihop," In it, nodes in the network can be connected to all the other nodes or to a subset, and there are multiple paths through meshed nodes to each destination. These networks are highly adaptable and self-organizing. "The signature of a mesh network is that there is no central orchestrating device. Instead, each node is outfitted with radio communications gear and acts as a relay point for other nodes." Sebastian Rupley, "Wireless: Mesh Networks," This type of network is also called peer-to-peer, many-to-many, and "multihop," In it, nodes in the network can be connected to all the other nodes or to a subset, and there are multiple paths through meshed nodes to each destination. These networks are highly adaptable and self-organizing. "The signature of a mesh network is that there is no central orchestrating device. Instead, each node is outfitted with radio communications gear and acts as a relay point for other nodes." Sebastian Rupley, "Wireless: Mesh Networks," PC Magazine PC Magazine, July 1,2003, http://www.pcmag.com/article2/0, 1759,1139094,00.asp; Robert Poor, "Wireless Mesh Networks," Sensors Online, February 2003, http://www.sensorsmag.com/articles/0203/38/main.shtml; Tomas Krag and Sebastian Buettrich, "Wireless Mesh Networking," O'Reilly Wireless DevCenter, January 22, 2004, http://www.oreillynet.com/pub/a/wirelessl2004/01/22/wirelessmesh.html.

44. 44. Carver Mead, founder of more than twenty-five companies and holder of more than fifty patents, is pioneering the new field of neuromorphic electronic systems, circuits modeled on the brain and nervous system. See Carver A. Mead, "Neuromorphic Electronic Systems," Carver Mead, founder of more than twenty-five companies and holder of more than fifty patents, is pioneering the new field of neuromorphic electronic systems, circuits modeled on the brain and nervous system. See Carver A. Mead, "Neuromorphic Electronic Systems," IEEE Proceedings IEEE Proceedings 78.10 (October 1990): 162936. His work led to the computer touch pad and the cochlear chip used in digital hearing aids. His 1999 start-up company Foveon makes a.n.a.log image-sensors that imitate the properties of film. 78.10 (October 1990): 162936. His work led to the computer touch pad and the cochlear chip used in digital hearing aids. His 1999 start-up company Foveon makes a.n.a.log image-sensors that imitate the properties of film.

45. 45. Edward Fredkin, "A Physicist's Model of Computation," Edward Fredkin, "A Physicist's Model of Computation," Proceedings of the Twenty-sixth Recontre de Moriond, Texts of Fundamental Symmetries Proceedings of the Twenty-sixth Recontre de Moriond, Texts of Fundamental Symmetries (1991): 28397, http://digitalphilosophy.org/physicists_model.htm. (1991): 28397, http://digitalphilosophy.org/physicists_model.htm.

46. 46. Gene Frantz, "Digital Signal Processing Trends," Gene Frantz, "Digital Signal Processing Trends," IEEE Micro IEEE Micro 20.6 (November/December 2000): 5259, http://csdl.computer.org/comp/mags/mi/2000/06/m6052abs.htm. 20.6 (November/December 2000): 5259, http://csdl.computer.org/comp/mags/mi/2000/06/m6052abs.htm.

47. 47. In 2004 Intel announced a "right hand turn" switch toward dual-core (more than one processor on a chip) architecture after reaching a "thermal wall" (or "power wall") caused by too much heat from ever-faster single processors: http://www.intel.com/employee/retiree/circuit/righthandturn.htm. In 2004 Intel announced a "right hand turn" switch toward dual-core (more than one processor on a chip) architecture after reaching a "thermal wall" (or "power wall") caused by too much heat from ever-faster single processors: http://www.intel.com/employee/retiree/circuit/righthandturn.htm.

48. 48. R. Landauer, "Irreversibility and Heat Generation in the Computing Process," R. Landauer, "Irreversibility and Heat Generation in the Computing Process," IBM Journal of Research Development IBM Journal of Research Development 5 (1961): 18391, http://www.research.ibm.com/journal/rd/053/ibmrd0503C.pdf. 5 (1961): 18391, http://www.research.ibm.com/journal/rd/053/ibmrd0503C.pdf.

49. 49. Charles H. Bennett, "Logical Reversibility of Computation," Charles H. Bennett, "Logical Reversibility of Computation," IBM Journal of Research Development IBM Journal of Research Development 17 (1973): 52532, http://www.research.ibm.com/journal/rd/176/ibmrd1706G.pdf; Charles H. Bennett, "The Thermodynamics of Computation-a Review," 17 (1973): 52532, http://www.research.ibm.com/journal/rd/176/ibmrd1706G.pdf; Charles H. Bennett, "The Thermodynamics of Computation-a Review," International Journal of Theoretical Physics International Journal of Theoretical Physics 21 (1982): 90540; Charles H. Bennett, "Demons, Engines, and the Second Law," 21 (1982): 90540; Charles H. Bennett, "Demons, Engines, and the Second Law," Scientific American Scientific American 257 (November 1987): 10816. 257 (November 1987): 10816.

50. 50. Edward Fredkin and Tommaso Toffoli, "Conservative Logic," Edward Fredkin and Tommaso Toffoli, "Conservative Logic," International Journal of Theoretical Physics International Journal of Theoretical Physics 21 (1982): 21953, http://digitalphilosophy.org/download_doc.u.ments/ConservativeLogic.pdf. Edward Fredkin, "A Physicist's Model of Computation," 21 (1982): 21953, http://digitalphilosophy.org/download_doc.u.ments/ConservativeLogic.pdf. Edward Fredkin, "A Physicist's Model of Computation," Proceedings of the Twenty-sixth Recontre de Moriond, Tests of Fundamental Symmetries Proceedings of the Twenty-sixth Recontre de Moriond, Tests of Fundamental Symmetries (1991): 28397, http://www.digitalphilosophy.org/physicists_model.htm. (1991): 28397, http://www.digitalphilosophy.org/physicists_model.htm.

51. 51. Knight, "Digital Image Stored in Single Molecule," referring to Khitrin et aI., "Nuclear Magnetic Resonance Molecular Photography"; see note 30 above. Knight, "Digital Image Stored in Single Molecule," referring to Khitrin et aI., "Nuclear Magnetic Resonance Molecular Photography"; see note 30 above.

52. 52. Ten billion (10 Ten billion (1010) humans at 1019 cps each is 10 cps each is 1029 cps for all human brains; 10 cps for all human brains; 1042 cps is greater than this by ten trillion (10 cps is greater than this by ten trillion (1013).

53. 53. Fredkin, "Physicist's Model of Computation"; see notes 45 and 50 above. Fredkin, "Physicist's Model of Computation"; see notes 45 and 50 above.

54. 54. Two such gates are the Interaction Gate, a two-input, four-output universal, reversible-logic gate Two such gates are the Interaction Gate, a two-input, four-output universal, reversible-logic gate

[image]

and the Feynman Gate, a two-input, three-output reversible, universal-logic gate.

[image]

Both images are from ibid., p. 7.

55. 55. Ibid., p. 8. Ibid., p. 8.

56. 56. C. 1. Seitz et al., "Hot-Clock nMOS," C. 1. Seitz et al., "Hot-Clock nMOS," Proceedings of the 1985 Chapel Hill Conference on VLSI Proceedings of the 1985 Chapel Hill Conference on VLSI (Rockville, Md.: Computer Science Press, 1985), pp. 117, http://caltechcstr.library.caltech.edu/archive/00000365; Ralph C. Merkle, "Reversible Electronic Logic Using Switches," (Rockville, Md.: Computer Science Press, 1985), pp. 117, http://caltechcstr.library.caltech.edu/archive/00000365; Ralph C. Merkle, "Reversible Electronic Logic Using Switches," Nanotechnology Nanotechnology 4 (1993): 2140; S. G. Younis and T. F. Knight, "Practical Implementation of Charge Recovering Asymptotic Zero Power CMOS," 4 (1993): 2140; S. G. Younis and T. F. Knight, "Practical Implementation of Charge Recovering Asymptotic Zero Power CMOS," Proceedings of the 1993 Symposium on Integrated Systems Proceedings of the 1993 Symposium on Integrated Systems (Cambridge, Ma.s.s.: MIT Press, 1993), pp. 23450. (Cambridge, Ma.s.s.: MIT Press, 1993), pp. 23450.

57. 57. Hiawatha Bray, "Your Next Battery," Hiawatha Bray, "Your Next Battery," Boston Globe Boston Globe, November 24, 2003, http://www.boston.com/business/technology/articles/2003/11/24/your_next_battery.

58. 58. Seth Lloyd, "Ultimate Physical Limits to Computation," Seth Lloyd, "Ultimate Physical Limits to Computation," Nature Nature 406 (2000): 104754. 406 (2000): 104754.

Early work on the limits of computation was done by Hans J. Bremermann in 1962: Hans J. Bremermann, "Optimization Through Evolution and Recombination," in M. C. Yovits, C. T. Jacobi, c. D. Goldstein, eds., Self-Organizing Systems Self-Organizing Systems (Washington, nc. Spartan Books, 1962), pp. 93106. (Washington, nc. Spartan Books, 1962), pp. 93106.In 1984 Robert A. Freitas Jr. built on Bremermann's work in Robert A. Freitas Jr., "Xenopsychology," a.n.a.log a.n.a.log 104 (April 1984): 4153, http://www.rfreitas.com/Astro/Xenopsychology.htm#SentienceQuotient. 104 (April 1984): 4153, http://www.rfreitas.com/Astro/Xenopsychology.htm#SentienceQuotient.

59. 59. p i maximum energy (10 p i maximum energy (1017 kg i meter kg i meter2/second2) / (6.6 i 1034) joule-seconds = ~ 5 i 1050 operations/second. operations/second.

60. 60. 5 i 10 5 i 1050 cps is equivalent to 5 i 10 cps is equivalent to 5 i 1021 (5 billion trillion) human civilizations (each requiring 10 (5 billion trillion) human civilizations (each requiring 1029 cps). cps).

61. 61. Ten billion (10 Ten billion (1010) humans at 1016 cps each is 10 cps each is 1026 cps for human civilization. So 5 i 10 cps for human civilization. So 5 i 1050 cps is equivalent to 5 i 10 cps is equivalent to 5 i 1024 (5 trillion trillion) human civilizations. (5 trillion trillion) human civilizations.

62. 62. This estimate makes the conservative a.s.sumption that we've had ten billion humans for the past ten thousand years, which is obviously not the case. The actual number of humans has been increasing gradually over the past to reach about 6.1 billion in 2000. There are 3 i 10 This estimate makes the conservative a.s.sumption that we've had ten billion humans for the past ten thousand years, which is obviously not the case. The actual number of humans has been increasing gradually over the past to reach about 6.1 billion in 2000. There are 3 i 107 seconds in a year, and 3 i 10 seconds in a year, and 3 i 1011 seconds in ten thousand years. So, using the estimate of 10 seconds in ten thousand years. So, using the estimate of 1026 cps for human civilization, human thought over ten thousand years is equivalent to certainly no more than 3 i 10 cps for human civilization, human thought over ten thousand years is equivalent to certainly no more than 3 i 1037 calculations. The ultimate laptop performs 5 i 10 calculations. The ultimate laptop performs 5 i 1050 calculations in one second. So simulating ten thousand years of ten billion humans' thoughts would take it about 10 calculations in one second. So simulating ten thousand years of ten billion humans' thoughts would take it about 1013 seconds, which is one ten-thousandth of a nanosecond. seconds, which is one ten-thousandth of a nanosecond.

63. 63. Anders Sandberg, "The Physics of the Information Processing Superobjects: Daily Life Among the Jupiter Brains," Anders Sandberg, "The Physics of the Information Processing Superobjects: Daily Life Among the Jupiter Brains," Journal of Evolution & Technology Journal of Evolution & Technology 5 (December 22, 1999), http://www.transhumanist.com/volume5/Brains2.pdf. 5 (December 22, 1999), http://www.transhumanist.com/volume5/Brains2.pdf.

64. 64. See note 62 above; 10 See note 62 above; 1042 cps is a factor of 10 cps is a factor of 108 less than 10 less than 1050 cps, so one ten-thousandth of a nanosecond becomes 10 microseconds. cps, so one ten-thousandth of a nanosecond becomes 10 microseconds.

65. 65. See http://e-drexler.com/p/04/04/0330drexPubs.html for a list of Drexler's publications and patents. See http://e-drexler.com/p/04/04/0330drexPubs.html for a list of Drexler's publications and patents.

66. 66. At the rate of $10 At the rate of $1012 and 10 and 1026 cps per thousand dollars ($10 cps per thousand dollars ($103), we get 1035 cps per year in the mid-2040s. The ratio of this to the 10 cps per year in the mid-2040s. The ratio of this to the 1026 cps for all of the biological thinking in human civilization is 109 (one billion). cps for all of the biological thinking in human civilization is 109 (one billion).

67. 67. In 1984 Robert A. Freitas proposed a logarithmic scale of "sentience quotient" (SQ) based on the computational capacity of a system. In a scale that ranges from 70 to 50, human brains come out at 13. The Cray 1 supercomputer comes out at 9. Freitas's sentience quotient is based on the amount of computation per unit ma.s.s. A very fast computer with a simple algorithm would come out with a high SQ. The measure I describe for computation in this section builds on Freitas's SQ and attempts to take into consideration the usefulness of the computation. So if a simpler computation is equivalent to the one actually being run, then we base the computational efficiency on the equivalent (simpler) computation. Also in my measure, the computation needs to be "useful." Robert A. Freitas Jr., "Xenopsychology," a.n.a.log 104 (April 1984): 4153, http://www.rfreitas.comfAstro/Xeno psychology.htm#SentienceQuotient. In 1984 Robert A. Freitas proposed a logarithmic scale of "sentience quotient" (SQ) based on the computational capacity of a system. In a scale that ranges from 70 to 50, human brains come out at 13. The Cray 1 supercomputer comes out at 9. Freitas's sentience quotient is based on the amount of computation per unit ma.s.s. A very fast computer with a simple algorithm would come out with a high SQ. The measure I describe for computation in this section builds on Freitas's SQ and attempts to take into consideration the usefulness of the computation. So if a simpler computation is equivalent to the one actually being run, then we base the computational efficiency on the equivalent (simpler) computation. Also in my measure, the computation needs to be "useful." Robert A. Freitas Jr., "Xenopsychology," a.n.a.log 104 (April 1984): 4153, http://www.rfreitas.comfAstro/Xeno psychology.htm#SentienceQuotient.

68. 68. As an interesting aside, engravings on the side of small rocks did in fact represent an early form of computer storage. One of the earliest forms of written language, cuneiform, which was developed in Mesopotamia circa 3000 B.C., used pictorial markings on stones to store information. Agricultural records were maintained as cuneiform markings on stones placed in trays, and organized in rows and columns. These marked stones were essentially the first spreadsheet. One such cuneiform stone record is a prized artifact in my collection of historical computers. As an interesting aside, engravings on the side of small rocks did in fact represent an early form of computer storage. One of the earliest forms of written language, cuneiform, which was developed in Mesopotamia circa 3000 B.C., used pictorial markings on stones to store information. Agricultural records were maintained as cuneiform markings on stones placed in trays, and organized in rows and columns. These marked stones were essentially the first spreadsheet. One such cuneiform stone record is a prized artifact in my collection of historical computers.

69. 69. One thousand (10 One thousand (103) bits is less than the theoretical capacity of the atoms in the stone to store information (estimated at 1027 bits) by a factor of 10 bits) by a factor of 1024.

70. 70. 1 cps (100 cps) is less than the theoretical computing capacity of the atoms in the stone (estimated at 10 1 cps (100 cps) is less than the theoretical computing capacity of the atoms in the stone (estimated at 1042 cps) by a factor of 10 cps) by a factor of 1042.

71. 71. Edgar Buckingham, "Jet Propulsion for Airplanes," NACA report no. 159, in Edgar Buckingham, "Jet Propulsion for Airplanes," NACA report no. 159, in Ninth Annual Report of NACA-1923 Ninth Annual Report of NACA-1923 (Washington, D.C.: NACA, 1924), pp. 7590. See http://naca.larc.nasa.gov/reports/1924/naca-report-159/. (Washington, D.C.: NACA, 1924), pp. 7590. See http://naca.larc.nasa.gov/reports/1924/naca-report-159/.

72. 72. Belle Dume, "Microscopy Moves to the Picoscale," Belle Dume, "Microscopy Moves to the Picoscale," PhysicsWeb PhysicsWeb, June 10, 2004, http://physicsweb.org/artide/news/8/6/6, referring to Stefan Hembacher, Franz J. Giessibl, and Iochen Mannhart, "Force Microscopy with Light-Atom Probes," Science Science 305.5682 (July 16, 2004): 38083. This new "higher harmonic" force microscope, developed by University of Augsburg physicists, uses a single carbon atom as a probe and has a resolution that is at least three times better than that of traditional scanning tunneling microscopes. How it works: as the tungsten tip of the probe is made to oscillate at subnanometer amplitudes, the interaction between the tip atom and the carbon atom produces higher harmonic components in the underlying sinusoidal-wave pattern. The scientists measured these signals to obtain an ultrahigh-resolution image of the tip atom that showed features just 77 picometers (thousandths of a nanometer) across. 305.5682 (July 16, 2004): 38083. This new "higher harmonic" force microscope, developed by University of Augsburg physicists, uses a single carbon atom as a probe and has a resolution that is at least three times better than that of traditional scanning tunneling microscopes. How it works: as the tungsten tip of the probe is made to oscillate at subnanometer amplitudes, the interaction between the tip atom and the carbon atom produces higher harmonic components in the underlying sinusoidal-wave pattern. The scientists measured these signals to obtain an ultrahigh-resolution image of the tip atom that showed features just 77 picometers (thousandths of a nanometer) across.

73. 73. Henry Fountain, "New Detector May Test Heisenberg's Uncertainty Principle," Henry Fountain, "New Detector May Test Heisenberg's Uncertainty Principle," New York Times New York Times, July 22, 2003.

74. 74. Mitch Jacoby, "Electron Moves in Attoseconds," Mitch Jacoby, "Electron Moves in Attoseconds," Chemical and Engineering News Chemical and Engineering News 82.25 (June 21, 2004): 5, referring to Peter Abbamonte et al., "Imaging Density Disturbances in Water with a 41.3-Attosecond Time Resolution," 82.25 (June 21, 2004): 5, referring to Peter Abbamonte et al., "Imaging Density Disturbances in Water with a 41.3-Attosecond Time Resolution," Physical Review Letters Physical Review Letters 92.23 (June 11,2004): 237401. 92.23 (June 11,2004): 237401.

75. 75. S. K. Lamoreaux and 1. R. Torgerson, "Neutron Moderation in the Oklo Natural Reactor and the Time Variation of Alpha," S. K. Lamoreaux and 1. R. Torgerson, "Neutron Moderation in the Oklo Natural Reactor and the Time Variation of Alpha," Physical Review Physical Review D 69 (2004): 1217016, http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000069000012121701000001&idtype=cvips&gifs=yes; Eugenie S. Reich, "Speed of Light May Have Changed Recently," D 69 (2004): 1217016, http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000069000012121701000001&idtype=cvips&gifs=yes; Eugenie S. Reich, "Speed of Light May Have Changed Recently," New Scientist New Scientist, June 30, 2004, http://www.newscientist.com!news/news.jsp?id=ns99996092.

76. 76. Charles Choi, "Computer Program to Send Data Back in Time," UPI, October 1, 2002, http://www.upi.com/view.efm?StoryID=20021001-125805-3380r; Todd Brun, "Computers with Closed Timelike Curves Can Solve Hard Problems," Charles Choi, "Computer Program to Send Data Back in Time," UPI, October 1, 2002, http://www.upi.com/view.efm?StoryID=20021001-125805-3380r; Todd Brun, "Computers with Closed Timelike Curves Can Solve Hard Problems," Foundation of Physics Letters Foundation of Physics Letters 16 (2003): 24553. Electronic edition, September 11,2002, http://arxiv.org/PS_cache/gr-qc/pdf/0209/0209061.pdf. 16 (2003): 24553. Electronic edition, September 11,2002, http://arxiv.org/PS_cache/gr-qc/pdf/0209/0209061.pdf.

Chapter Four: Achieving the Software of Human Intelligence:.

How to Reverse Engineer the Human Brain 1. 1. Lloyd Watts, "Visualizing Complexity in the Brain," in D. Fogel and C. Robinson, eds., Lloyd Watts, "Visualizing Complexity in the Brain," in D. Fogel and C. Robinson, eds., Computational Intelligence: The Experts Speak Computational Intelligence: The Experts Speak (Piscataway, N.J.: IEEE Press/Wiley, 2003), http://www.lloydwatts.com/wcci.pdf. (Piscataway, N.J.: IEEE Press/Wiley, 2003), http://www.lloydwatts.com/wcci.pdf.

2. 2. J. G. Taylor, B. Horwitz, and K. J. Friston, "The Global Brain: Imaging and Modeling," J. G. Taylor, B. Horwitz, and K. J. Friston, "The Global Brain: Imaging and Modeling," Neural Networks Neural Networks 13, special issue (2000): 827. 13, special issue (2000): 827.

3. 3. Neil A. Busis, "Neurosciences on the Internet," http://www.neuroguide.com; "Neuroscientists Have Better Tools on the Brain," Neil A. Busis, "Neurosciences on the Internet," http://www.neuroguide.com; "Neuroscientists Have Better Tools on the Brain," Bio IT Bulletin Bio IT Bulletin, http://www.bio-it.world.com/news/041503_report2345.html; "Brain Projects to Reap Dividends for Neurotech Firms," Neurotech Reports Neurotech Reports, http://www.neurotechreports.com/pages/brainprojects.html.

4. 4. Robert A. Freitas Jr., Robert A. Freitas Jr., Nanomedicine Nanomedicine, vol. 1, Basic Capabilities Basic Capabilities, section 4.8.6, "Noninvasive Neuroelectric Monitoring" (Georgetown, Tex.: Landes Bioscience, 1999), pp. 11516, http://www.nanomedicine.com/NMI/4.8.6.htm.

5. 5. Chapter 3 a.n.a.lyzed this issue; see the section "The Computational Capacity of the Human Brain." Chapter 3 a.n.a.lyzed this issue; see the section "The Computational Capacity of the Human Brain."

6. 6. Speech-recognition research and development, Kurzweil Applied Intelligence, which I founded in 1982, now part of ScanSoft (formerly Kurzweil Computer Products). Speech-recognition research and development, Kurzweil Applied Intelligence, which I founded in 1982, now part of ScanSoft (formerly Kurzweil Computer Products).

7. 7. Lloyd Watts, U.S. Patent Application, U.S. Patent and Trademark Office, 20030095667, May 22, 2003, "Computation of Multi-sensor Time Delays." Abstract: "Determining a time delay between a first signal received at a first sensor and a second signal received at a second sensor is described. The first signal is a.n.a.lyzed to derive a plurality of first signal channels at different frequencies and the second signal is a.n.a.lyzed to derive a plurality of second signal channels at different frequencies. A first feature is detected that occurs at a first time in one of the first signal channels. A second feature is detected that occurs at a second time in one of the second signal channels. The first feature is matched with the second feature and the first time is compared to the second time to determine the time delay." See also Nabil H. Farhat, U.S. Patent Application 20040073415, U.S. Patent and Trademark Office, April 15, 2004, "Dynamical Brain Model for Use in Data Processing Applications." Lloyd Watts, U.S. Patent Application, U.S. Patent and Trademark Office, 20030095667, May 22, 2003, "Computation of Multi-sensor Time Delays." Abstract: "Determining a time delay between a first signal received at a first sensor and a second signal received at a second sensor is described. The first signal is a.n.a.lyzed to derive a plurality of first signal channels at different frequencies and the second signal is a.n.a.lyzed to derive a plurality of second signal channels at different frequencies. A first feature is detected that occurs at a first time in one of the first signal channels. A second feature is detected that occurs at a second time in one of the second signal channels. The first feature is matched with the second feature and the first time is compared to the second time to determine the time delay." See also Nabil H. Farhat, U.S. Patent Application 20040073415, U.S. Patent and Trademark Office, April 15, 2004, "Dynamical Brain Model for Use in Data Processing Applications."

8. 8. I estimate the compressed genome at about thirty to one hundred million bytes (see note 57 for chapter 2); this is smaller than the object code for Microsoft Word and much smaller than the source code. See Word 2003 system requirements, October 20, 2003, http://www.microsoft.com/office/word/prodinfo/sysreq.mspx. I estimate the compressed genome at about thirty to one hundred million bytes (see note 57 for chapter 2); this is smaller than the object code for Microsoft Word and much smaller than the source code. See Word 2003 system requirements, October 20, 2003, http://www.microsoft.com/office/word/prodinfo/sysreq.mspx.

9. 9. Wikipedia, http://en.wikipedia.org/wiki/Epigenetics. Wikipedia, http://en.wikipedia.org/wiki/Epigenetics.

10. 10. See note 57 in chapter 2 for an a.n.a.lysis of the information content in the genome, which I estimate to be 30 to 100 million bytes, therefore less than 10 See note 57 in chapter 2 for an a.n.a.lysis of the information content in the genome, which I estimate to be 30 to 100 million bytes, therefore less than 109 bits. See the section "Human Memory Capacity" in chapter 3 (p. 126) for my a.n.a.lysis of the information in a human brain, estimated at 10 bits. See the section "Human Memory Capacity" in chapter 3 (p. 126) for my a.n.a.lysis of the information in a human brain, estimated at 1018 bits. bits.

11. 11. Marie Gustafsson and Christian Balkenius, "Using Semantic Web Techniques for Validation of Cognitive Models against Neuroscientific Data," AILS04 Workshop, SAIS/SSLS Workshop (Swedish Artificial Intelligence Society; Swedish Society for Learning Systems), April 1516, 2004, Lund, Sweden, www.lucs.lu.se/People/Christian.Balkenius/PDF/Gustafsson.Balkenius.2004.pdf. Marie Gustafsson and Christian Balkenius, "Using Semantic Web Techniques for Validation of Cognitive Models against Neuroscientific Data," AILS04 Workshop, SAIS/SSLS Workshop (Swedish Artificial Intelligence Society; Swedish Society for Learning Systems), April 1516, 2004, Lund, Sweden, www.lucs.lu.se/People/Christian.Balkenius/PDF/Gustafsson.Balkenius.2004.pdf.

12. 12. See discussion in chapter 3. In one useful reference, when modeling neuron by neuron, Tomaso Poggio and Christof Koch describe the neuron as similar to a chip with thousands of logical gates. See T. Poggio and C. Koch, "Synapses That Compute Motion," See discussion in chapter 3. In one useful reference, when modeling neuron by neuron, Tomaso Poggio and Christof Koch describe the neuron as similar to a chip with thousands of logical gates. See T. Poggio and C. Koch, "Synapses That Compute Motion," Scientific American Scientific American 256 (1987): 4652. Also C. Koch and T. Poggio, "Biophysics of Computational Systems: Neurons, Synapses, and Membranes," in 256 (1987): 4652. Also C. Koch and T. Poggio, "Biophysics of Computational Systems: Neurons, Synapses, and Membranes," in Synaptic Function Synaptic Function, G. M. Edelman, W. E. Gall, and W. M. Cowan, eds. (New York: John Wiley and Sons, 1987), pp. 63797.

13. 13. On Mead, see http://www.technology.gov/Medal/2002/bios/Carver_A._Mead.pdf. Carver Mead, On Mead, see http://www.technology.gov/Medal/2002/bios/Carver_A._Mead.pdf. Carver Mead, a.n.a.log VLSI and Neural Systems a.n.a.log VLSI and Neural Systems (Reading, Ma.s.s.: Addison-Wesley, 1986). (Reading, Ma.s.s.: Addison-Wesley, 1986).

14. 14. See note 172 in chapter 5 for an algorithmic description of a self-organizing neural net and note 175 in chapter 5 for a description of a self-organizing genetic algorithm. See note 172 in chapter 5 for an algorithmic description of a self-organizing neural net and note 175 in chapter 5 for a description of a self-organizing genetic algorithm.

15. 15. See Gary Dudley et al., "Autonomic Self-Healing Systems in a Cross-Product IT Environment," See Gary Dudley et al., "Autonomic Self-Healing Systems in a Cross-Product IT Environment," Proceedings of the IEEE International Conference on Autonomic Computing Proceedings of the IEEE International Conference on Autonomic Computing, New York City, May 1719, 2004, http://csdl.computer.org/comp/proceedings/icac/2004/2114/00121140312.pdf; "About IBM Autonomic Computing," http://www-3.ibm.com/autonomic/about.shtml; and Ric Telford, "The Autonomic Computing Architecture," April 14, 2004, http://www.dcs.st-andrews.ac.uk/undergrad/current/dates/disclec/20032/RicTelfordDistinguished2.pdf.

16. 16. Christine A. Skarda and Walter J. Freeman, "Chaos and the New Science of the Brain," Christine A. Skarda and Walter J. Freeman, "Chaos and the New Science of the Brain," Concepts in Neuroscience Concepts in Neuroscience 1.2 (1990): 27585. 1.2 (1990): 27585.

17. 17. C. Geoffrey Woods, "Crossing the Midline," C. Geoffrey Woods, "Crossing the Midline," Science Science 304.5676 (June 4, 2004): 145556; Stephen Matthews, "Early Programming of the Hypothalamo-Pituitary-Adrenal Axis," 304.5676 (June 4, 2004): 145556; Stephen Matthews, "Early Programming of the Hypothalamo-Pituitary-Adrenal Axis," Trends in Endocrinology and Metabolism Trends in Endocrinology and Metabolism 13.9 (November 1,2002): 37380; Justin Crowley and Lawrence Katz, "Early Development of Ocular Dominance Columns," 13.9 (November 1,2002): 37380; Justin Crowley and Lawrence Katz, "Early Development of Ocular Dominance Columns," Science Science 290.5495 (November 17. 2000): 132124; Anna Penn et al., "Compet.i.tion in the Retinogeniculate Patterning Driven by Spontaneous Activity," 290.5495 (November 17. 2000): 132124; Anna Penn et al., "Compet.i.tion in the Retinogeniculate Patterning Driven by Spontaneous Activity," Science Science 279.5359 (March 27, 1998): 210812; M. V. Johnston et al., "Sculpting the Developing Brain," 279.5359 (March 27, 1998): 210812; M. V. Johnston et al., "Sculpting the Developing Brain," Advances in Pediatrics Advances in Pediatrics 48 (2001): 138; P.La Cerra and R. Bingham, "The Adaptive Nature of the Human Neurocognitive Architecture: An Alternative Model," 48 (2001): 138; P.La Cerra and R. Bingham, "The Adaptive Nature of the Human Neurocognitive Architecture: An Alternative Model," Proceedings of the National Academy of Sciences Proceedings of the National Academy of Sciences 95 (September 15, 1998): 1129094. 95 (September 15, 1998): 1129094.

18. 18. Neural nets are simplified models of neurons that can self-organize and solve problems. See note 172 in chapter 5 for an algorithmic description of neural nets. Genetic algorithms are models of evolution using s.e.xual reproduction with controlled mutation rates. See note 175 in chapter 5 for a detailed description of genetic algorithms. Markov models are products of a mathematical technique that are similar in some respects to neural nets. Neural nets are simplified models of neurons that can self-organize and solve problems. See note 172 in chapter 5 for an algorithmic description of neural nets. Genetic algorithms are models of evolution using s.e.xual reproduction with controlled mutation rates. See note 175 in chapter 5 for a detailed description of genetic algorithms. Markov models are products of a mathematical technique that are similar in some respects to neural nets.

19. 19. Aristotle, Aristotle, The Works of Aristotle The Works of Aristotle, trans. W. D. Ross (Oxford: Clarendon Press, 19081952 (see, in particular, Physics Physics); see also http://www.encyclopedia.com/html/section/aristotl_philosophy.asp.

20. 20. E. D. Adrian, E. D. Adrian, The Basis of Sensation: The Action of Sense Organs The Basis of Sensation: The Action of Sense Organs (London: Christophers, 1928). (London: Christophers, 1928).

21. 21. A. L. Hodgkin and A. F. Huxley, "Action Potentials Recorded from Inside a Nerve Fibre," A. L. Hodgkin and A. F. Huxley, "Action Potentials Recorded from Inside a Nerve Fibre," Nature Nature 144 (1939): 71012. 144 (1939): 71012.

22. 22. A. L. Hodgkin and A. F. Huxley, "A Quant.i.tative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve," A. L. Hodgkin and A. F. Huxley, "A Quant.i.tative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve," Journal of Physiology Journal of Physiology 117 (1952): 500544. 117 (1952): 500544.

23. 23. W. S. McCulloch and W. Pitts, "A Logical Calculus of the Ideas Immanent in Nervous Activity," W. S. McCulloch and W. Pitts, "A Logical Calculus of the Ideas Immanent in Nervous Activity," Bulletin of Mathematical Biophysics Bulletin of Mathematical Biophysics 5 (1943): 115-33. This seminal paper is a difficult one to understand. For a clear introduction and explanation, see "A Computer Model of the Neuron," the Mind Project, Illinois State University, http://www.mind.ilstu.edu/curriculum/perception/mpneuron1.html. 5 (1943): 115-33. This seminal paper is a difficult one to understand. For a clear introduction and explanation, see "A Computer Model of the Neuron," the Mind Project, Illinois State University, http://www.mind.ilstu.edu/curriculum/perception/mpneuron1.html.

24. 24. See note 172 in chapter 5 for an algorithmic description of neural nets. See note 172 in chapter 5 for an algorithmic description of neural nets.

25. 25. E. Salinas and P. Thier, "Gain Modulation: A Major Computational Principle of the Central Nervous System," E. Salinas and P. Thier, "Gain Modulation: A Major Computational Principle of the Central Nervous System," Neuron 27 Neuron 27 (2000): 1521. (2000): 1521.