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by Roman Verostko, 1998

"It is possible to invent a single machine which can be used to compute any computable sequence. . . ." , Alan Turing  [Note 1]

Replica of the Manchester SSEM (Small Scale Experimental Machine),
Museum of Science & Industry, Castlefield, Manchester.

1998 marked the 50th anniversary of the SSEM. The art works created for this anniversary pay homage to the role of Alan Turing's work underlying this historic moment.

photo credit:  Tom Jeffs

The Project: A family of algorithmic pen plotted drawings, each presented with the binary text for a Universal Turing Machine (UTM), was created for an exhibition at the University of Manchester on the occasion of the Ninth International Symposium on Electronic Art (ISEA 1998).   I created this series as homage to Alan Turing.  The year 1998 marked the 50th Anniversary of  the  Manchester Small-Scale Experimental Machine (SSEM), nicknamed  "Baby" and known also as the "Mark I prototype".  This computer would have been the first "hard wired" computer descended from the logic of a Universal Turing Machine. Built by Frederic C Williams, Tom Kilburn  and Geoff Tootill its first program was run on June 21, 1948.

The circuit logic of the first general computers is viewed as a logic descended from the paper presented by Alan Turing in 1936 where he outlined the procedure for a theoretical tape machine. Yet a historical unfolding of the first general computers would include the work of others including especially Alfonso Church's paper published earlier tyhan Alan Turing's in 1936. [Note 2].  My own work has concentrated on celebrating the emergence of the UTM in the 20th Century as one of the great moments in the history of ideas.

These drawings are intended to be reminiscent of a two page spread of an opened illuminated medieval manuscript. In the examples shown here the algorithm for a Universal Turing Machine is presented in a binary text format as the page to the right (recto) with an algorithmically generated form drawn on the left page (verso).   This series pays homage to Alan Turing by  presenting the UTM code as a valuable precious text of our own time. Executed on hot pressed Arches, each work includes a burnished gold leaf enhancement.

Manchester Illuminated Universal Turing Machine, #23
1998, 30" by 22"
pen plotted drawing with gold leaf

Note: The image links for this specific work lead to high resolution details.
Manchester Illuminated Universal Turing Machine, #24
1998, 30" by 22"
pen plotted drawing with gold leaf
Manchester Illuminated Universal Turing Machine, #20
1998, 30" by 22"
pen plotted drawing 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). In 1928 David Hilbert had posed a problem on the decidability of  whether any statement was provable with the axioms following the rules of Logic.  This "decision problem", known by its German name as the "Entscheidungsproblem", has been of great interest to mathematicians since the time of Wilhelm Leibnitz (1646-1716). The underlying logic for what is now known as a Universal Turing Machine was outlined in Alan Turing's  1936 paper, “On computable numbers, with an application to the Entscheidungsproblem".  Alfonso Church   planted the seminal logical procedure for all general computers.  An algorithm for this procedure, known as

Detail of the UTM binary text with gold leaf. Click here for full text page (719 kb).

The UTM version for these art works is quoted from Roger Penrose’ The Emperor’s New Mind (Chapter 2) and consists of 5,495 binary digits.  These digits represent an algorithm, in expanded binary, for a UTM. In the tradition of illuminated sacred texts this algorithm is presented as a highly treasured text because it played a seminal role in the birth of 20th Century computers.  The form enhancements celebrating the algorithm are generated with the artist’s code

that requires the logic of  a UTM for its execution, thus being a form of  “Turing on Turing”.

Detail shows algorithmically generated pen plotted lines from illumination #23 above.

Procedure. The artistic procedure employs a form-generation method which, by analogy to biological process, may be viewed as epigenetic. The software (code), created by the artist, behaves as genotype capable of generating a distinctive “family of forms” within any given set of parameters.  The hyperspace of all possible forms, based on the specific parameter settings for this Manchester edition, is infinitely vast. This page pictures 5 specific examples from those created for this project. 

Larger image (45 kb)  

Manchester Illuminated Universal Turing Machine, #9
1998, 30" by 22"
pen plotted drawing with gold leaf

Manchester Illuminated Universal Turing Machine, #19
1998, 30" by 22"
pen plotted drawing with gold leaf

Each member of the Manchester series includes a unique pen-drawn form materialized from the vast family of possible forms. The pen-drawn form for each member of the edition is pen plotted using multi-pen plotters driven with original algorithms.  Every line for each work is a unique pen drawn stroke with no repeats. Each finished work, illuminated with an original “code generated” form is signed and identified with its Manchester serial number.  Selection of materials, plotting procedures and the use of gold leaf conspire to achieve a valued object to be treasured.

My essays and notes on UTM's:

    Illuminating  a Universal Turing Machine
The  Cloud of Unknowing revisited: notes on a Universal Turing Machine (UTM) and The Undecidable

Note 1 Turing in Computable Numbers . . .(1936), quoted from Wiki as in Davis 1965:127-128.  See Martin Davis Ed (1965) The Undecidable, Raven Press, Hewlett, NY. Compilation of original papers by Gödel, Church, Kleene, Turing, Rosser, and Post. Republished as Davis, Martin, ed. The Undecidable. Courier Dover Publications. ISBN 978-0-486-43228-1.(2000), Engines of Logic: Mathematicians and the origin of the Computer (1st ed.), New York NY: W. W. Norton & Company, ISBN 0-393-32229-7, (pb.)

Note 2. Entscheidungproblem. Alfonso Church also addressed this problem. His paper was presented to the American Mathematical Society in 1935 and published on April 15 1936. Alan Turing was probably disappointed to learn of Alonzo Church’s proof.  Turing’s paper was not received by the Proceedings of the London Mathematical Society until May 26, 1936 and not published until January 1937. While both of these papers reach the same conclusion Alan Turing's  approach was more applicable as a machine. For clarification of  Entscheidungsproblem, Universal Turing Machine, the Chruch-Turing Thesis and the Church-Turing Theorem readers will find that the Wikipedia provides useful information and sources.


London: Victoria & Albert Museum, Permanent Collection
             Available originals: contact Keith Watson

Germany. Available originals: DAM Gallery, Tucholskystr. 37, 10117 Berlin, Germany, Tel: 0049-30-28098135  Fax: 0049-40-3603753454  Contact:  Wolf Lieser

U.S. Artist's studio by appointment; Tweed Museum, Duluth, MN.

Other Reference:  

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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