Part 31 (1/2)

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 fas.h.i.+on, 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 fas.h.i.+on, 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,” /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,” /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 , March 22, 2004, /news/news.jsp?id=ns99994801, referring to Steve Pearton, ”Silicon-Based Spintronics,” Celeste Biever, ”Silicon-Based Magnets Boost Spintronics,” NewScientist.com, March 22, 2004, /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, /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, /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, /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 heart-c704.uibk.ac.at/Papers/Nature03-Gulde.pdf. 421 (January 2,2003): 4850. See 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,andand pany, 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 / 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 / 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, /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,” /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, /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,” /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 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, /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,” /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, /article2/0, 1759,1139094,00.asp; Robert Poor, ”Wireless Mesh Networks,” Sensors Online, February 2003, /articles/0203/38/main.shtml; Tomas Krag and Sebastian Buettrich, ”Wireless Mesh Networking,” O'Reilly Wireless DevCenter, January 22, 2004, /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, digitalphilosophy.org/physicists_model.htm. (1991): 28397, 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, csdl.computer.org/comp/mags/mi/2000/06/m6052abs.htm. 20.6 (November/December 2000): 5259, 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: /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: /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, /journal/rd/053/ibmrd0503C.pdf. 5 (1961): 18391, /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, /journal/rd/176/ibmrd1706G.pdf; Charles H. Bennett, ”The Thermodynamics of Computation-a Review,” 17 (1973): 52532, /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, digitalphilosophy.org/download_doc.u.ments/ConservativeLogic.pdf. Edward Fredkin, ”A Physicist's Model of Computation,” 21 (1982): 21953, 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, /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 (Was.h.i.+ngton, nc. Spartan Books, 1962), pp. 93106. (Was.h.i.+ngton, 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, /Astro/Xenopsychology.htm#SentienceQuotient. 104 (April 1984): 4153, /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.