Rubel’s view of the Extended Analog Computer. The Extended Analog Computer (EAC) originated in Bush’s differential analyzer and Shannon’s General-Purpose Analog Computer (GPAC). The EAC was developed by Rubel to support his idea that the brain is an analog computer by addressing the problem that many functions of the brain could not be modeled with a GPAC [37].1 Rubel also believed that no single device could implement the EAC in its entirety. Rather, he envisioned many problem-specific devices, each implementing a specific analogy: “Since the EAC is so broad, [we can never implement it] in practice, but one can build up a large array of devices that handle many cases…heat-conduction devices for dealing with Laplace’s equation…devices that form soap films for solving the minimal-surface equation…the wave equation will be dealt with via vibrating strings and membranes” [23].

Rubel repeatedly emphasized that the EAC was a conceptual machine. While the components derived from the GPAC had physical implementations, as did some of the added functions (the “inversion black box” and the “boundary-value problem black box”), Rubel did not define analog implementations for the rest of the EAC’s black boxes, including the “differential boxes”, the “restricted limit box” and the “analytic continuation” box. The “extremely well-posed” (EWP) p…

What the EAC is. In general, the EAC is a family of devices that compute specific functions by analogy: heat-conduction devices, soap films, vibrating strings and membranes, etc., to which unconventional computing researchers have added plasmas, slime mold, neural tissue, DNA and so forth [30]. All of these connect a user’s problem to a natural object that solves it by means of a specific analogy. The EAC model defines a group of components, but not all can be directly implemented. It took years of experience with various EACs to recognize that all of the functions of the EAC model are present in the current generally-applicable EAC implementation, but that some of the functions are laws of nature inherent in the materials from which the machine is built [7], [8].

Since the EAC requires the user to draw an analogy between it and an application, it can only be completely understood as a machine whose computation consists of two parts: (1) the EAC configuration, which constrains the physical properties of its operation (similar to Denning’s definition of computation [42]), and (2) the meaning ascribed to the evolution of those physical processes. Each of these two parts is necessary to define computation by analogy. It is also important to recognize that one EAC configuration may have many meanings, possibly very different. For example, the same EAC configuration, unchanged, can compute butterfly wing pattern morphogenesis…

The current implementation of Rubel’s Extended Analog Computer model (EAC) is the result of over a decade’s research [1], [2], [3], [9], [34]. Note that the EAC model will be related to the EAC implementation in Sections 11 Implicit and explicit functions, 12 Explicit functions of the EAC model and their EAC implementations, 13 Implicit functions of the EAC model and their EAC implementations after presenting some important concepts; however, the reader may wish to review these sections before continuing.

The EAC board to the left of the laptop computer in Fig. 1(a) was designed in 2005 [5]. It is connected to a digital computer that runs a visual EAC interface (jEAC) [6]. The jEAC interface in Fig. 1(b) is based on a coordinate array, similar to a spreadsheet. By default cells are inactive, that is, the connections to the foam sheet (the EAC’s primary computing element) are in a high-impedance state, effectively disconnected the inputs. The user may individually assign any of the twenty-five cells to perform one (and only one) of these functions at the sheet: a current source, a current sink, or the input to a Lukasiewicz logic function. The voltage gradient generated by current flow through the foam sheet is constantly measured at each of the twenty-five points to produce the output.