Four Principles for Unconventional Computing: Continuity, Conservation, Computability and Complementarity

Jonathan W. Mills

Center for Unconventional Computing

Indiana University

Bloomington, Indiana

USA

In 1993, shortly before his death, Lee Rubel wrote his last paper on analog computing. That work, The Extended Analog Computer, gave such a broad and profound insight into the nature of non-digital computation that almost all computer scientists and mathematicians believed that extended analog computers (EACs) could not be built.

In their most general form, EACs cannot be built—which is also true for Turing machines. But in restricted forms, such as reaction-diffusion computers, soap bubble spanning tree computers, and DNA and quantum computers, Rubel’s EAC offers a unifying model based on partial differential equations, one of mathematics’ and physics’ most powerful tools to describe the world about us.

At Indiana University, we have built EACs based on Rubel’s description. These machines have a wide variety of implementations, and an equally wide variety of applications. Learning to understand EACs has been a challenge to my students and myself since the first, crude, operational prototype was breadboarded in 1995.

In this talk we will discuss the four principles that have emerged from our decade-long study of EACs, and show how they relate to the scope of unconventional computing:

Continuity: we will discuss the non-binary numbers and the partial differential equations and continuous logic functions that manipulate them,

Conservation: we will track the spoor of a fundamental principle of physics from Kirchhoff’s current law, across partial differential equations, through a conductive plastic sheet, to its lair in a network of leaky neurons that compute exclusive-OR,

Computability: we will examine a logical, rather than analytical, model of EACs that uses annotated continuous logic, and a work-in-progress proof of the Turing equivalence of EACs that follows from it, and

Complementarity: we will consider an insight recently used to understand this new, non-digital, unconventional paradigm, and integrate it with the current, conventional digital paradigm to the advantage of both.

This talk moves quickly, but summarizes our research in terms that have proved to be understandable to second-year undergraduate students. It has helped us apply a new paradigm of computing by learning to think unconventionally. So, while we will depart from the realm of conventional digital computation, we will follow a path that has been trodden out of a maze of many false starts and dead ends—which are opportunities for future research, and…

You will have an opportunity to use an Internet-accessible EAC after the talk!