merkle@parc.xerox.com (Ralph Merkle) (05/04/91)
The error rate of 10^-12 for Drexler's rod logic was simply the design objective. Simple design changes could be used to achieve dramatically lower error rates. The simplest method of reducing the error rate is to make the parts twice as big. This results in stiffer parts (stiffness scales with length. Double the size, double the stiffness) hence smaller positional errors. Because positional errors caused by thermal noise are described by a gaussian distribution, doubling the size will result in a dramatic reduction in error rates. Instead of 10^-12, we'd get (much) better than 10^-24. Reducing the temperature will also result in dramatic reductions in error rates. Operating at liquid nitrogen temperatures (77 Kelvins) would reduce thermal noise by almost a factor of 4, which would result in error rates much less than 10^-40. By selectively changing certain "critical" lengths, the overall reliability could be dramatically improved with only modest impact on performance. Finally, Drexler's design called for a 16 input 16 output logic element. Reliability was limited by the distance along the linear rod between the most distant input and output. By reducing the number of inputs and outputs, hence reducing rod length, the total "stretch" of the rod can be substantially reduced with no other design changes at all. Again, this would produce a dramatic decrease in the error rate. Thus, by reducing fan-in and fan-out, we can get higher reliability. Error rates are design parameters, and can be traded off against other design parameters. Increasing the error rate of the logic elements leads to faster and less complicated designs for the logic elements, but increases the complexity of the system because system-level error handling must be made more robust. Decreasing the error rate of the logic elements makes them slower and perhaps more complex, but simplifies the system-level error handling requirements. The basic design of rod logic is simple and robust, so specific implementations can be selected to lie almost anywhere along the spectrum of reliability that we find interesting.
piety@hplred.hpl.hp.com (Bob Piety) (05/14/91)
/ merkle@parc.xerox.com (Ralph Merkle) / 11:42 am May 3, 1991 / > parts (stiffness scales with length. Double the size, ^^^^^^ > double the stiffness) hence smaller positional errors. > Because positional errors caused by thermal noise are > described by a gaussian distribution, doubling the > size will result in a dramatic reduction in error rates. > Instead of 10^-12, we'd get (much) better than 10^-24. ^^^^^^ ^^^^^^ > temperatures (77 Kelvins) would reduce thermal noise by > almost a factor of 4, which would result in error rates ^^^^^^^^^^^ > much less than 10^-40. ^^^^^^ I don't understand your mathematics-- please explain how you arrive at these figures. Thanks, Bob piety@hplred.hpl.hp.com (415)857-4759 [In Drexler's paper "Rod Logic and Thermal Noise..." the probability of error (after three pages of calculus) comes out in the form 2 exp [1/2 (sigma phi/kT)^2 -D phi/kT] Where phi is alignment force (a design constant), D is minimum displacement for error (ditto), and sigma is std. dev. of knob displacement, a function of T whose leading term is linear in kT (k is Boltzmann's constant). Thus the first term in the exponential is second-order; ignoring it, if we drop the temperature by a factor of 2 we divide the probability of error by exp(D phi) (which can be arbitrarily large, depending on the design). The whole paper can be found in Molecular Electronic Devices III (1988, Elsevier). --JoSH]