The earliest computing machines in wide use were not digital but analog. In analog representation, properties of the representational medium ape (or reflect or model) properties of the represented state-of-affairs. (In obvious contrast, the strings of binary digits employed in digital representation do not represent by means of possessing some physical property — such as length — whose magnitude varies in proportion to the magnitude of the property that is being represented.) Analog representations form a diverse class. Some examples: the longer a line on a road map, the longer the road that the line represents; the greater the number of clear plastic squares in an architect's model, the greater the number of windows in the building represented; the higher the pitch of an acoustic depth meter, the shallower the water. In analog computers, numerical quantities are represented by, for example, the angle of rotation of a shaft or a difference in electrical potential. Thus the output voltage of the machine at a time might represent the momentary speed of the object being modelled. As the case of the architect's model makes plain, analog representation may be discrete in nature (there is no such thing as a fractional number of windows). Among computer scientists, the term ‘analog’ is sometimes used narrowly, to indicate representation of one continuously-valued quantity by another (e.g., speed by voltage). As Brian Cantwell Smith has remarked: ‘Analog’ should … be a predicate on a representation whose structure corresponds to that of which it represents … That continuous representations should historically have come to be called analog presumably betrays the recognition that, at the levels at which it matters to us, the world is more foundationally continuous than it is discrete. (Smith , p. 271) James Thomson, brother of Lord Kelvin, invented the mechanical wheel-and-disc integrator that became the foundation of analog computation (Thomson...
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