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Academician Solomon Marcus (Bucharest, Romania) will give a talk on Monday, 4.6. at 14 in XXIII (University of Turku, Natural Science Building II)
All interested are welcome.
From Turing to von Neumann
Solomon Marcus
Stoilow Institute of Mathematics
Romanian Academy
(Joint work with Sorin Istrail, International Center of Computational Molecular Biology, Brown University, U.S.A.)
They interacted and inspired each other. We focus main attention on their work on the brain and, more generally, on their interest in biology, trying to situate historically and conceptually John von Neumann's unfinished research program towards the unification of discrete and continuous involvement of mathematics in the study of biological systems. Turing was involved in a similar program. An evolutionary trajectory of theories from Leibniz, Boole, Bohr and Turing to Shannon, McCullogh-Pitts, Wiener and von Neumann powered the emergence of the information paradigm. As both Turing and von Neumann were interested in automata, they were deeply challenged by seeing the brain as an automaton. Turing's research was done in the context of the achievements in logic (formalism, intuitionism, logicism, constructivism, Hilbert's, Kleene's and Gödel's work). Turing's 1937 paper, proposing a theoretical machine exclusively built on the paper, has been the preliminary theoretical step towards von Neumann's 1948 programmable electronic computer. John von Neumann's research program is outlined in "The general and logical theory of automata" (1951), "Probabilistic logics and the synthesis of reliable organisms from unreliable components" (1956) and his posthumous book The Computer and the Brain (1958) and in his unfinished book The theory of Self-Reproducing Automata, completed and published by A. Burks (1966).
Inspired by Turing's universal machine, von Neumann described in 1948, i.e., five years before Watson and Crick, the structure of the DNA copying mechanism for biological self-reproduction. A lot of questions and problems appear when confronting these historical facts with the evolution of ideas in the contemporary fields of computational biology and biological computing. Some of them are pointed out in this presentation.