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Math and Art, Febraury 22 to March 30, 2002: an exhibition of works exploring the relationship between art and mathematics.
Selby Gallery, Ringling School of Art and Design
2700 N. Tamiami Trail, Sarasota, FL 34234. Tel: 941/359-7563.
Roman is showing an Illuminated Universal Turing Machine similar to the version shown at SIGGRAPH in 1995.
Illuminated Universal Turing Machine, IV
Algorithmic pen plotted drawing
pen & ink with gold leaf.
What is a Universal Turing Machine? The gating logic for circuit boards in all general computers descends from a logical procedure known as a Universal Turing Machine ("UTM"). The logic for this algorithm by Alan Turing (1912-54) was written in 1936 and published in 1937 in the Proceedings of the London Mathematical Society. This paper, On computable numbers, with an application to the Entscheidungsproblem, planted the seminal idea for all general computers. The term "Turing machine" appeared in print for the first time in the Journal of Symbolic Logic in Alonzo Church's review of the Turing paper. (more)
Illuminated Version. The version shown here is quoted from Roger Penrose The Emperors New Mind (Chapter 2) and consists of 5,495 binary digits. These digits represent an algorithm, in expanded binary, for a "U". In the tradition of illuminated sacred texts this algorithm is presented as a valued authoritative text of our own times. The form enhancements that celebrate the value of the text are generated with the artists code that requires the logic of "U" for its execution, thus being a form of Turing on Turing!
See also a cyberspace version of a UTM as a Self Portrait.
For Verostko's essay on UTM's and Undecidables click here.
For a collection of essays and further reference both general and technical see The Universal Turing Machine: A Half-Century Survey, Edited by Rolf Herken. Springer Verlag 1995, Wien, NY.
Roger Penrose, THE EMPEROR'S NEW MIND: concerning computers, minds and the laws of physics (Oxford University Press, 1989). Chapter two, "Algorithms and Turing machines " provides a detailed presentation of Turing machine logic including step by step procedures for structuring simple machines such as "+1".
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Copyright Roman Verostko, 2002. All rights reserved.