Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems



Slide Rules. Edmund Gunter devised in 1620 a method for calculation that used a single log scale with dividers along a linear scale; this anticipated key elements of the first slide rule described by William Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems Oughtred [O32] in 1632. A very large variety of slide machines were later constructed.








Digital Mechanical Devices for Mathematical Tables and Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems Functions












^ Mechanical Devices for Timing, Sequencing and Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems Logical Control

We will use the term mechanical automata here to denote mechanical devices that exhibit autonomous control of their movements. These can require sophisticated mechanical mechanisms for timing, sequencing and logical control.











^ Mechanical Devices used in Cryptography






^ Mechanical and Electro-Optical Devices for Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems Integer Factorization





^ Mechanical Computation at the Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems Micro Scale: MEMS Computing Devices. Mechanical computers can have advantages over electronic computation at certain scales; they are already having widespread use at the microscale. MEMS (Micro-Electro-Mechanical Systems) are manufactured by lithographic Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems etching methods similar in nature to the processes microelectronics are manufactured, and have a similar microscale. A wide variety of MEMS devices [M02] have been constructed for sensors and actuators, including accelerometers used Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems in automobile safety devices and disk readers, and many of these MEMS devices execute mechanical computation do their task. Perhaps the MEMS device most similar in architecture to the Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems mechanical calculators described above is the Recodable Locking Device [PD+99] constructed in 1998 at Sandia Labs, which мейд use of microscopic gears that acted as a mechanical lock, and which was intended for mechanically Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems locking strategic weapons.


^ VI. Future Directions


Mechanical Self-Assembly Processes.

Most of the mechanical devices discussed in this chapter have been assumed to be constructed top-down; that is they are designed and Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems then assembled by other mechanisms generally of large scale. However a future direction to consider are bottom-up processes for assembly and control of devices. Self-assembly is a basic bottom-up Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems process found in many natural processes and in particular in all living systems.


Mechanical Computation at the Molecular Scale: DNA Computing Devices. Due to the difficulty of constructing electrical circuits at the molecular scale, alternative methods for computation, and in particular mechanical methods, may provide unique opportunities Slide Rules - Iii. Computational Complexity of Mechanical Devices and their Movement Problems for computing at the molecular scale. In particular the bottom-up self-assembly processes described above have unique applications at the molecular scale.


Acknowledgements

We sincerely thank Charles Bennett for his numerous suggests and very important improvements to this survey.


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