Course Description

How do we make circuits (physics) compute and provide answers to human defined problems? The answer to this question consists of two parts: (1) transforming our ideas expressed in natural languages (our common sense) to calculus, and (2) mapping of the calculus to physics, namely, facilitating the implementation of the ideas in physical substrates. This course explains the key concepts at the foundations of computing with physical substrates. It also describes recent developments related to biological computing, including:

• Motivation: Biology is magical
• Context: The power of languages
• The evolution of languages for quantities
• Number systems and algorithms: Syntax manipulation
• Leibniz: Computing with syntax boxes and the binary system
• Boole: The mappings of syllogisms to algebra
• Boolean algebra as an axiomatic system
• Boolean functions and their representations
• Syntax boxes and Boolean functions
• Shannon: the mappings of algebra to physics
• Computing Boolean functions with relay circuits
• Computing with DNA strands: Probabilistic relay circuits
• Biologically inspired computing: Neural networks
• Computing with And Or and Not (AON) gates
• Associative memories: Convergence properties of neural networks
• Computing with state machines