A Review of Analog Computing

Although analog computation was eclipsed by digital computation in the second half of the twentieth century, it is returning as an important alternative computing technology. Indeed, as explained in this report, theoretical results imply that analog computation can escape from the limitations of digital computation. Furthermore, analog computation has emerged as an important theoretical framework for discussing computation in the brain and other natural systems. The report (1) summarizes the fundamentals of analog computing, starting with the continuous state space and the various processes by which analog computation can be organized in time; (2) discusses analog computation in nature, which provides models and inspiration for many contemporary uses of analog computation, such as neural networks; (3) considers general-purpose analog computing, both from a theoretical perspective and in terms of practical general-purpose analog computers; (4) discusses the theoretical power of analog computation and in particular the issue of whether analog computing is in some sense more powerful than digital computing; (5) briefly addresses the cognitive aspects of analog computing, and whether it leads to a different approach to computation than does digital computing; and (6) concludes with some observations on the role of analog computation in “post-Moore’s Law computing.” ∗This report is based on an unedited draft for an article to appear in the Encyclopedia of Complexity and System Science (Springer, 2008) and may be used for any non-profit purpose provided that the source is credited.