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Abraham, Tara Helen,1969-
Microscopic cybernetics :mathematical logic, automata theory, and the formalization of biological phenomena, 1936-1970.
Ph. D. -- University of Toronto, 2000
Ottawa :National Library of Canada = Bibliothè€que nationale du Canada,[2001]
3 microfiches
Includes bibliographical references.
This thesis highlights the intellectual origins of theoretical studies of biological phenomena based on automata theory and mathematical logic. The study spans the period from the groundbreaking work of mathematician Alan Turing (1912-1954), who in 1936 developed a "logical machine" for the process of mathematical computation, through to the work of Stuart Kauffman (b. 1939), who, circa 1970, developed a model of genetic regulation in cells using mathematical logic. It is argued that automata theory and methods of logic offered a way of simplifying complex biological phenomena into logical, discrete terms, while at the same time characterizing these processes as complex, dynamic, and interactive. Automata theory arose out of the cybernetics movement, which involved making analogies between organisms and machines. "Automata" in with a finite size, a finite number of internal states, and certain specified inputs and outputs. The functioning of an automaton was governed by the rules of mathematical logic, embodied in an "algorithm" or program. The algorithm was rigorous, exhaustive, and unambiguous, and a central point in automata theory was that simple rules could lead to complex behaviour. This thesis demonstrates that the "algorithm" concept proved to be a powerful conceptual tool for many scientists who developed models of complex biological phenomena. It will be shown that these applications of automata theory to biological phenomena were consistent with many of the philosophical assumptions of many theoretical biologists of the period. Chapter One examines Alan Turing's conception of the Turing machine, highlighting the role of mathematical logic in its functioning. Turing presented "computation" as a process that could be carried out in a finite number of logically defined, discrete steps. Chapter Two illustrates that a community of mathematical biologists in Chicago, who formalized biological phenomena, provided an important intellectual space for Warren McCulloch and Walter Pitts, who in 1943 developed a model of neural activity based on the principles of Boolean logic. Chapter Three examines the work of John von Neumann. Influenced by Turing's work and the McCulloch-Pitts model, von Neumann developed a general theory of automata that addressed, in logical terms, the complexity of biological self-reproduction. Chapter Four focuses on the work of Michael Apter, who made strong arguments for the value of automata theory in modeling the process of biological development. Chapter Five further explores the connections between automata theory and theoretical studies of biological phenomena, highlighting the work of Stuart Kauffman, who, in collaboration with Warren McCulloch, developed a logical model of genetic networks.
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