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13th International Conference on Membrane Computing - MTA Sztaki

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Sorin Istrail, Solom<strong>on</strong> Marcus<br />

probability theory. In 1937 at age 25 he published his seminal paper “On Computable<br />

Numbers, with an Applicati<strong>on</strong> to the Entscheidungsproblem,” solving <strong>on</strong>e of the most<br />

famous problems in mathematics proposed by Hilbert. This paper, with negative and<br />

positive results of greatest depth, defining the Turing machine, and inspiring the<br />

designers of electr<strong>on</strong>ic computers in England and United States -- v<strong>on</strong> Neumann, in<br />

particular, in such a decisive way -- is without questi<strong>on</strong> the most important and<br />

influential paper in computer science, <strong>on</strong>e offering proof positive that the new field<br />

had emerged.<br />

2. From Leibniz, Boole, Bohr and Turing to Shann<strong>on</strong>,<br />

McCullogh-Pitts and v<strong>on</strong> Neumann and the emergence of<br />

the Informati<strong>on</strong> Paradigm<br />

The middle of the past century has been very hot, characterized by the appearance of<br />

the new fields defining the move from the dominati<strong>on</strong> of the energy paradigm,<br />

characterizing the sec<strong>on</strong>d half of the 19 th century and the first half of the 20 th century,<br />

to the dominati<strong>on</strong> of the informati<strong>on</strong>-communicati<strong>on</strong>-computati<strong>on</strong> paradigms,<br />

appearing at the crossroad of the first and the sec<strong>on</strong>d halves of the 20 th century. So,<br />

John v<strong>on</strong> Neumann’s reflecti<strong>on</strong>, by which he became a pi<strong>on</strong>eer of the new era,<br />

developed in the c<strong>on</strong>text of c<strong>on</strong>comitant emergence in the fifth and the sixth decades<br />

of the 20 th century of theory of algorithms (A.A. Markov), simply typed lambda<br />

calculus (Al<strong>on</strong>zo Church), game theory (v<strong>on</strong> Neumann and Oskar Morgenstern),<br />

computer science (Turing and v<strong>on</strong> Neumann), cybernetics (Norbert Wiener),<br />

informati<strong>on</strong> theory (Claude Shann<strong>on</strong>), molecular genetics (Francis Crick, James<br />

Wats<strong>on</strong>, Maurice Wilkins, am<strong>on</strong>g others), coding theory (R. W. Hamming), system<br />

theory (L. van Bertalanfy), c<strong>on</strong>trol theory, complexity theory, and generative<br />

grammars (Noam Chomsky). Many of these lines of development were no l<strong>on</strong>ger<br />

available to v<strong>on</strong> Neumann and we are in the situati<strong>on</strong> to questi<strong>on</strong> the c<strong>on</strong>sequences of<br />

this fact.<br />

V<strong>on</strong> Neumann was impressed by Warren McCullogh and Walter Pitts’s result<br />

c<strong>on</strong>necting logic, language and neural networks. [“A logical calculus of the ideas<br />

imminent in nervous activity”, Bull. Math. Biophysics 5, 1943, 115-133] In v<strong>on</strong><br />

Neumann’s formulati<strong>on</strong>, this result shows “that anything that can be exhaustively and<br />

unambiguously described, anything that can be completely and unambiguously put<br />

into words, is ipso facto realizable by a suitable finite neural network. Three things<br />

deserve to be brought into attenti<strong>on</strong> in this respect: a) In the 19 th century, George<br />

Boole’s project to unify logic, language, thought and algebra (c<strong>on</strong>tinuing Leibniz’s<br />

dream in this respect) was <strong>on</strong>ly partially realized (An investigati<strong>on</strong> in the laws of<br />

thought, <strong>on</strong> which are founded the mathematical theories of logic and probabilities,<br />

1854) and it prepared the way for similar projects in the 20 th century; b) Claude<br />

Shann<strong>on</strong>, in his master’s thesis (A symbolic analysis of relay and switching circuits)<br />

submitted in 1937, <strong>on</strong>ly <strong>on</strong>e year after Turing published his famous N<strong>on</strong>-computable…,<br />

proved the isomorphism between logic and electrical circuits; c) Niels Bohr, in his<br />

philosophical writings, developed the idea according to which the sphere of<br />

competence of the human language is limited to the macroscopic universe; see, in this<br />

respect, David Favrholdt’s ‘Niels Bohr’s views c<strong>on</strong>cerning language’ in Semiotica 94,<br />

1993, 1/2. Putting together all these facts, we get an image of the str<strong>on</strong>g limitati<strong>on</strong>s<br />

that our sensati<strong>on</strong>s, our intuiti<strong>on</strong>s, our logic and our language have to obey. We can<br />

40

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