The promise of analog computation

Abstract

Future computing paradigms and technologies will have to be more like the physical processes by which they are realized, and because these processes are primarily continuous, post-Moore’s law computing will involve an increased use of analog computation. Traditionally analog computers have computed ordinary differential equations of time, but analog field computation permits massively parallel temporal integration of partial differential equations. In principle many different physical media – not just electronics – can be exploited to implement the basic operations of analog computing, a small number of which are sufficient to approximate a wide variety of analog computations, thus providing a basis for universal analog computation and general-purpose analog computers. The contentious issue of the computational power of analog computers is addressed best on its own terms, rather by asking it within the context of Church-Turing computation, which distorts the relevant questions and their answers.

Keywords:

• analog computation
• continuous computation
• field computation
• Moore’s law
• post-Moore’s law computation

Notes

1 Fréchet and Gâteaux derivatives are the same for field transformations; see (MacLennan2009b).