The nature of the Extended Analog Computer

This paper defines the relationship between Rubel's Extended Analog Computer (EAC) model and Indiana University's implementation of it, a fundamental distinction that is necessary to understand the design, implementation, operation, and applications of the EAC. Beginning with the detailed structure of the current EAC, its method of computing is illustrated with diagrams and three applications. Next, the Δ-digraph, a labeled directed graph, is introduced to show how unconventional and conventional computers relate nature, mathematics and computer architecture. The Δ-digraph defines the paradigms of analogy and algorithm, illustrates how applications for the EAC are analogies developed by choosing the semantics for a machine configuration, and suggests how partial differential equations might be compiled to EAC configurations (a difficult problem compared to compiling a digital computer program, and one that is still not solved). The Δ-digraph also distinguishes between the EAC's explicit functions (whose operation is defined in the structure of its components) and implicit functions (whose operation is inherent in the properties of matter and energy). Brief case studies show how industry and academia are adopting the EAC. The paper closes with topics and open questions for future research.