A UNIVERSAL TURING MACHINE
McSorley's Bar, 1912
What is a Universal Turing Machine?
A Turing machine is a logical procedure such as an algorithm for adding numbers. A Universal Turing Machine is a special case of a procedure able to simulate input from all other Turing machines - in effect it would be a general computer able to compute any computable procedure. Such a procedure, "U", was outlined by Alan Turing in his 1936 paper "On computable numbers". The paper proposed a theoretrical method of mechanically carrying out the computation. This paper, published in 1937 in the Proceedings of the London Mathematical Society, planted the seminal idea, the meme, for all general computers.
As an artist, working with algorithmic art, I became aware of the beauty of the concept of a Universal Turing Machine when I came upon a binary version presented by Roger Penrose in The Emperor's New Mind (Chapter II, note 7). The code for a UTM, the meta-algorithm of algorithms, seized my imagination and would not let go. To me it symbolized a historical turning point in the human ability to manage extensive rational procedure. Many are not aware of the time when "computers" referred to humans who did the computing. Businesses required teams of "computers", namely human workers, to do laborious computation that is now done with machines that may be viewed as Universal Turing Machines. Those who recognize the leverage of algorithmic procedure implemented with computers will appreciate the beauty and power of Alan Turing's contribution and recognize its special place in the history of ideas.
Some years ago I learned that McSorley's Bar was one of the favored places for the human "computers" who did the book-keeping work in lower Manhattan's Wall Street sector. This was, of course, well before the time of Alan Turing and the information age revolution. McSorley's had a sawdust floor and was restricted to men only. (This restriction was lifted during the 1960's). In the 19th and early 20th Centuries only men were employed to do the manual book keeping work on Wall Street. Many, who lived in upper Manhattan, would stop at McSorley's for an ale on the way home.
I recall visiting McSorley's in the 1960's as a tribute to John Sloan who was one of my favorite American Painters. And I admired this painting. From my perspective now, knowing that many of these clients at the end of the working day were the "computers" of that time, I view this work with a special appreciation. Comparing these human computers to a electronic Universal Turing Machines makes me pause.
Rationale for this work.
For me, the binary code of a UTM algorithm, like a biblical text in medieval times, radiates an aura of authority even though it is difficult for most of us to comprehend. In the tradition of medieval manuscript illumination I have written algorithms to illuminate the code for a Universal Turing Machine and 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 concept in shaping cultural change in the late 20th century. Like medieval Latin that transcended the vernacular this code speaks a universal tongue. To celebrate it more broadly I have also mounted several UTM versions, with documentation, on my web site as cyberspace illuminations. One version is presented as a “Self Portrait” of the computer with which it is viewed. See: http://www.verostko.com/u.html.
Art & Algorithms.
Detail, illuminated UTM text.
Similar to composers of musical scores, as an algorist, I create “scores” for drawing. The engine for executing my drawing scores, in the most radical sense, is driven by the logic for a UTM. Whence, with a certain wonder and awe, I treasure the UTM texts that I have illuminated to celebrate the treasure we have inherited from those giants who have preceded us.
Roman Verostko, Minneapolis, c.1999
Some documentation and binary versions of UTM's are located on my web site at: http://www.verostko.com/turing-doc.html
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.
Penrose, THE EMPEROR'S NEW MIND:
concerning computers, minds and the laws of physics (Oxford University
Press, 1989). Chapter II,
"Algorithms and Turing Machines " discusses Turing machine