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ILLUMINATED UNIVERSAL TURING MACHINES
I remember the first time I viewed the illuminated manuscripts in London's British Museum. Viewing the Lindesfarne Gospels I stood spellbound, trembling and almost in tears. Something of the medieval world flooded from the text and the illuminations. Holy texts underlying a whole way of life were transformed and celebrated. Some years ago, while reading the second chapter in Roger Penrose' volume on the "Emperor's New Mind" (Oxford U Press, 1989), I learned about the underlying logic of a "Universal Turing Machine". The idea tickled my brain. For years I had been deeply immersed in the leverage this idea brought to the world. The binary text for a UTM struck me with profound wonderment. I felt an awesome respect for the idea. I felt privileged to have been living during the time this idea evolved into machines that were changing world culture. Here, I thought, is a text we should celebrate.
ILLUMINATED UNIVERSAL TURING MACHINE, 1998
by Roman Verostko, 1998
Replica of the Manchester SSEM (Small Scale Experimental Machine). Photo credit: Tom Jeff
Museum of Science & Industry, Castlefield, Manchester.
1998 marked the 50th anniversary of the SSEM. The 15 Illuminated Universal Turing Machines created for this anniversary pay homage to the role of Alan Turing's seminal work underlying this historic moment..
Manchester Illuminated Universal Turing Machine, #23, 1998, 30" by 22", pen plotted drawing with gold leaf.
This work was featured in Scientific American, "Art by Numbers" in August 2018 . Private Collection
I viewed my studio as a 20th Century electronic scriptorium and my drawing machines were my scriptors. As I recall, within a few days, I was proof reading code for an illuminated UTM. For me, the text of a UTM like a medieval biblical text, radiates an aura of authority even though difficult to comprehend. I undertook illuminating Universal Turing Machines to celebrate its impact on our culture. These illuminations are works of art and not exercises in computer science. They are intended to celebrate the value and significance of the UTM in shaping cultural change in the late 20th century. Like medieval Latin that transcended the vernacular and was universally understood by those schooled in Latin so also this algorithm speaks a universal tongue understood by those schooled in computer language.
The binary code in the artwork is a "Universal Turing Machine".
The source for the binary code in these illuminations is quoted from Roger Penrose, The Emperors New Mind (Oxford U Press, 1989, Chapter II, Note 7, pp 93-96).
Detail of the UTM binary text with gold leaf. Click here for full text page (719 kb).
Manchester Illuminated Universal Turing Machine, #22, 1998, 30" by 22", pen plotted drawing with gold leaf.
The Project: 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 one page with an algorithmically generated drawing on the other page. The binary numbers are drawn also with the drawing arm of the pen plotter. This series was created for an exhibition at the University of Manchester on the occasion of the Ninth International Symposium on Electronic Art (ISEA 1998). The illuminated UTM's pay homage to Alan Turing whose work played a role in the development of computers. 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". Built by Frederic C Williams, Tom Kilburn and Geoff Tootill its first program was run on June 21, 1948.
"It is possible to invent a single machine which can be used to compute any computable sequence. . . ." - Alan Turing (Note 1)
What is a Universal Turing Machine? In 1928 David Hilbert had posed a mathematical problem on the decidability of whether any statement was provable with axioms following the rules of Logic. This "decision problem", known as the "Entscheidungsproblem", has been of great interest to mathematicians since the time of Wilhelm Leibnitz (1646-1716). Alan Turing's 1936 paper, “On computable numbers . . ."., outlines a mechanical method for addressing the "decision problem". Turing's paper outlined a procedure for deciding all "decidable" statements, in effect a logical method for computing anything that is "computable". This procedure can be formatted as an algorithm known as a Universal Turing Machine. A Universal Turing Machine may be viewed as the ancestral gating logic of today's general computers. We should note however that a UTM can only manage what is computable; it canot decide the "undecidable".
Illuminated UTM , 1995, 40" by 30", pen & ink plotter drawing shown with detail on the right. Click on images for larger image. Tweed Museum Collection, University of Minneosta, Duluth. This is similar to the version shown at the 1995 SIGGRAPH Exhibition in LA.
SOURCES & REFERENCE
The code in these works is quoted from Roger Penrose, The Emperors New Mind (Oxford U Press, 1989, Chapter II, Note 7, pp 3-96).
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.
LOCATION OF ORIGINALS:
London: Victoria & Albert Museum, Permanent Collection
Germany. Available originals: DAM Gallery, Neue Jakobstr. 6, 10179 Berlin, Germany; Email: office(at)dam.org Tel: 0049-30-28098135 Fax: 0049-40-3603753454 Contact: Wolf Lieser
U.S. Artist's studio by appointment; Tweed Museum, Duluth, MN.
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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