self portrait menu  |  main menu | site map | copyright
 

 
 

DOCUMENTATION:
A Universal Turing Machine as Self Portrait

Detail from a series of Illuminated Universal Turing Machines, Manchester, 1998. This is one of a series intended to honor A. Turing's work.

The operating system of a general computer may be viewed also as a Universal Turing Machine (UTM) because general computers are, in principal,  capable of computing all numbers that are computable. It was Alan Turing (1912-54) who outlined such a universal function  in his 1936 paper on "Computable numbers. . ."  published by the London Mathematical Society.    This paper addressed a logical problem known as the "Decision Problem", whether there is an algorithm (a step by step procedure) for deciding the truth of all arithmetic statements.  Turing's negative solution  demonstrated that  there is no algorithm that could, in principle, decide the truth of all arithmetic statements. By showing  what was not computable  it  pointed  to the  procedure for computing  all that is computable. When a  general computer displays a version of a UTM it displays the ancestral logic for  its own operational self, a "Self Portrait"

Rationale for a "Universal Turing Machine Self Portrait"

For me, the text of a UTM algorithm, like a medieval biblical text, radiates an aura of authority even though difficult to comprehend.  As an artist I have written algorithms for illuminating a Universal Turing Machine (UTM) 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  in shaping  cultural change in the late 20th century.  To honor the UTM text more broadly the "Self Portrait"   version on this web site is presented as a cyberspace typographic illumination. 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 science.    

Sources &  Binary Texts                   

  F0.UTM     Self Portrait display version by Steven Gunhouse
  B0.UTM
    Leanest version by Steven Gunhouse
  U.UTM       Roger Penrose Version, (from The Emperor's New Mind)
  Reference   
  Precursor Memes

Circuit Man: Tetra Corporation Memorial, Minneapolis, 1969.

Working circuit, test model for processing information. Hardwired circuit logic originates in algorithmic procedures for the gating logic. Software, as an algorithmic procedure, becomes "hardware" when it is translated into a hard wired circuit.

The term "software" did not exist in  the early days of computing. While its first usage remains uncertain it is John Tukey (1915-2000) who is credited with coining the term "software" for its use in print in 1958.

 

OPERATION.  Turing's paper outlined a procedure that could be carried out by following a simple instruction, one step at a time.  Because the instruction path could be implemented mechanically it was theoretically possible to make a machine to carry out the operation. When Turing published his paper the term  "computer" referred to humans who performed computation. During World War II hundreds of  "computers" (humans) were employed for the immense calculating tasks required for breaking codes and creating accurate targeting tables for artillery. Even with advanced calculating machines these human computers were too slow and inadequate for the complex calculations required.   The  development of  universal  computing machines with stored programs & memories emerged after World War II.  In his book on Turing's Cathedral George Dyson identifies the role of Turing's thesis in that emergence.  Today, the computers we use for everything from our social networks and banking to email and gaming are general computers.  Turing's procedure for a "U" outlined the logic that underlies the operation of general computers.  

THE SELF PORTRAIT, HISTORY.  As an algorist, working with algorithmic art, I became aware of the beauty of the UTM procedure when I came upon "U", an expanded binary version presented by Roger Penrose in The Emperor's New Mind. The "text" 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 human "computers" to do laborious computation that is now done with machines.  Imagine the  many millions of  human "computers" the world would require if we had to use human computers to manage data for today's  finance, communications, and food supplies!  Those who recognize the power 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.

FORMAT CONSIDERATIONS.  Several versions  of a  UTM are documented below. The Gunhouse version, employed in the self portrait display,  employs  cyberspace typography and is organized with Fibonacci numbering.  The movement of the binary digits is intended to suggest the movement of the tape in Alan Turing's original conception. The scrolling feature allows the full text to be virtually present within the physical limits of the window frame .  The marque movement displays all the text flowing back & forth from left to right. The complete text is present in the HTML source code and in the documentation below for F0.UTM.

Top of page


UTM Text sources:

B0.UTM and F0.UTM. Text quoted from correspondence with the author, Steven V. Gunhouse.

U,  see Note 7, page 71, Roger Penrose, The Emperor's New Mind. . .( Oxford University Press,  1989).

Reference & Links:

Alan Turing’s thesis "On Computable Numbers, with an application to the Entscheidungsproblem" is availabale at:  http://www.abelard.org/turpap2/tp2-ie.asp

George Dyson, Turing's Cathedral: The Origins of the Digital Universe, 2012, Pantheon.

Wikipedia entries for "Entscheidungsproblem" and "Universal Turing Machine" provide a good brief intro to the subject.

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.

WWW:  See the Alan Turing Homepage maintained by Andrew Hodges. His scrapbook page on Turing Machines includes useful material.

For a discussion of the Golden Section (phi) in art and geometry see: H.E.Huntley, The Divine Proportion (Dover, 1970); Matila Ghyka, The Geometry of Art and Life (Sheed & Ward, 1946).

The Manchester Illuminated Turing Machine, pen plotted works on paper, Verostko, 1998.

A Turing Machine in Conway's Game of Life, extendable to a Universal Turing Machine   Turing Machines in Conway's Game of Life

http://www.alanturing.net Turing Archive for the History of Computing

http://www.turingarchive.org  Turing Digital Archive


PRECURSOR MEMES
FROM GEORGE BOOLE  (1815-64)

NOTE 1: George Boole's classic work on the investigation of the laws of thought (1854) identified the Aristotelian principle of contradiction as the ancestral logic for Boolean operators that have played a central role in both hardware and software gating logic.

PROPOSITION I. To deduce the laws of the symbols of Logic from a consideration of those operations of the mind which are implied in the strict use of language as an instrument of reasoning. . . The literal symbols of Logic are universally subject to the law whose expression is X2=X. Of the symbols of Number there are two only, 0 and 1, which satisfy this law.

PROPOSITION IV. That axiom of metaphysicians which is termed the principle of contradiction, and which affirms that it is impossible for any being to possess a quality, and at the same time not to possess it, is a consequence of the fundamental law of thought, whose expression is X2=X .

SOURCE: The texts above are quoted from  George Boole in An investigation of  THE LAWS OF THOUGHT. . . (Macmillan 1854)

TRIBUTE TO GEORGE BOOLE:  verostko.com/boole.html 


F0, Universal Turing Machine

F0.UTM  was written by Steven Gunhouse with aesthetic considerations in mind as he employed Fibonacci numbers as a basis for its organization. It is believed that Alan Turing had a special interest in Fibonacci numbers in relation to biomorphic structures. The author feels that a version organized with Fibonacci numbering would be especially appropriate for an illuminated UTM.  Fibonacci numbers hold a venerable place in the history of art. As the numbering increases,  the sequential ratio grows ever nearer to "phi", the golden section, a proportion commonly found in art and nature. The text color was chosen to signify "golden".  Author: Steven V. Gunhouse

F0.UTM=1010010010010111010011101010010100010111010000000101011101
00010001010110100010010110100000000001011010100111010010010000101
11010000011010100000010101101001001110100001001001110100001000011
10101110100000011101000000101010111010001001101000001010010110100
10001101000010010010110101000011101000010101010111010101001110100
01000010101110100000001101000100100010110100010000101110100001010
11101000100011010000110100010011010010001011010010000000111010010
10101101010100010011101010000101101001010000010111010100101011101
00101010001011101010100101110100000010010111010100000001101010000
10101101000010100101101010010101011101000001010110101000100011010
10010001101000101001110101000101010111010010000011101010010000101
11010010010011101010000010011101001010001101010100000101101010000
00110101000010010110100001001011101000001011101001000110101001001
01101000010110101010001011010101001001011101010000000101110100101
01001011101000000001011101000101010101110100000010101110100010100
00111010000010001110101010100001110101000100111010010100000110100
10000110100010000011101001000010011101000101001011010001001010111
01000000010011010001010010110100100010101110100100000101110100100
10010111010100100010111010010010001110101001000011101000001010011
10100101000101101000000000011010010101010111010000010001110101000
00010110101000010011010000010011010100010010110101001001011010010
00100111010011101010100010111010101010001110100000001011101010100
00101110100010000110101010010101110100100101011101010101001011101
00010001011010001000101101010000101110100001011010100011101001000
01001011001110100000100010110101000101110101010101011101000000101
10100001000010110100101011101010000101010111010001011010000101001
01101001110100010000010110100001000101011010001001001011010000001
00010110100100100010110110111010000100000110101001001010111010101
01010111010000010101011101000010100110100000000010110100001000101
10101001001110100101000011010101000111010101000010111010000100111
01000010101011010010000110100010010011101001110100100000111010100
01000101110101001001110101010101010111010010010101110101001010010
11101010000001101000100000101101000101001110100000000110100010100
11101000010010110100100000111010000100011010101000011010000000101
10100101001011010100000101101001010001101000010101110100101001110
10100101110101000101011101010101011101000001010110101010111010101
00011101010011101000100101101000000001010110100010010110100100010
01011010000101011101001000011010100011101001000100010110100000011
10100000100001011101000000111010000010010101110100000011101001010
01010111010001001101000010000010110100010011010001010000101100111
01000101001010110100100011010000101000101101001000110100100010101
01101010000111010001000000101110101000011101000101010010111010101
00111010001000100101110101010011101001000000010111010000000110100
01001010101101000000011010010000010101101000100110100000100010110
01110100100000101110101000011101010100101011101010100111010010101
01011101000000011010000100100111010100011101001010101101010001110
10100010101110100100011010100001011010100111010010010010101110101
00111010010010100101110101001110100100101010111010000110100101000
10101110100001101001010010010111010000110101000100101011101000110
10010101010101110100011010100000000101110100011010100010100101110
10000011010100000100101101000001101010000100010110100000110101001
00000101101001010111010100010000101110100101011101010010001010111
01000011010000000010111010001101000000101011101001010111010000001
00101101001010111010100101010111010001110100011010011101010010101
0101110100111010101000000101110100111010000000100101

Top of page


B0, Universal Turing Machine

This version was written by Steven V. Gunhouse in 1987.  The shortest of  the Gunhouse versions, B0.UTM consists of 136 states compared to 201 states in Penrose' "U".  This work by Gunhouse allows us to savor the human spirit at its best,  seeking clarity, brevity, and universality. Author: Steven V. Gunhouse

B0.UTM=1000000101110100000001010110100000010010110100001010110100000100
01011010100111010000010101011101000011101000010010101110100100110100001
01001011010100011010001000101011010101001110100101010100101110100000111
01000000000111010000001010110100000100101101001000110100010101001011010
01000100011010010101000111010100001110100101001001011101001000100101101
01000101001110100100000011101010100101110100100101001110101010101011101
00000011101001010101010111010000100110100011010001010000110100000101110
10100101000101110100010101011101001000011010101001010010110101001011010
01001010110101000101011010010100101110101010000100111010010101010111010
00101010011101010000101101010010001101010001010110100010000101110101001
01101001001001101010010101011010010010001011101010100010111010101010001
10101010010101101001000101101010101001011001110100010010111010010000011
10100010001011101001000110100000101011010010010010011101000010010110100
10011010000101010110101001001011101001101000000011101000100101011010010
00101011101000101001011101010010001011101001000010111010010100010101110
10100100010111010010010010111010010100010111010010010001110100101000011
10100010001101001010010011101001000100111010000111010010100111010100100
11101001010011101001010101110100000011101010001000101110101000101001011
10101000001011101001000001110101000010101101000100110101000100101110101
00100111010100101011101001010100101011101010001001010111010101010001011
10101001001010111010000101011010101000101011001110101010101010010110100
01010110101010000101110101010010010110101000000111010001000001110100010
00111010000111010101010010101110101000001001110100101000001110100001110
10101001011101001000001011101000000001101001001101000010101010110101000
00010110100001010101101000100110100001000011010001010110100000100110101
00111010000001010101110100101101000010001011010000111010101001010101110
10010011010101010101010110100100110100010010101101001001010111010101011
10101000110101010001010101101010000100101101010100101110100000001110100
01010010101101001000010011101000101000101101000000011101000101001011101
00100011010001010101010110100100011010010001010101101000100001101010101
01000111010101010100100111010010000100111010000001001101000001000110100
10001101000010010110100010101110101001001001110101000001110101110101010
10101010101101001001010101011010100001001101000101001110101010100001110
10101010100001110100001001011101010001011101010000111010010100101010111
01010000111010010101000101110101000011101010001001011101000100010111010
10101011101010100111010010101010101011101010100111010100001010101110100
00000011010000000101101010000100011010100000001101000100100011010001001
00101101010100111010101000010111010000001110101001000010111010100000011
10101001001010101110100011010100010101010111010001101010010001010111010
00000111010101000001011101000110101001001001011101000110101010101011101
00010100111010100111010011010100101001010111010011010100101010010111010
01101010010101010101110100110100101010101110100101000111010010011010001
00101101010100010010111010101001001101010010100110101000110101010010001
01101010001101010100100101011010000101110101001010101011010010000110101
01001010101011010010000110101010100001011010010000110100000000011101000
01011101010101001001011101000010111010101010010101011101000010111010010
01000101110101000001010111010010100001011101101110011101010000101100111
01010101010101101000010111010101010001010111010000010101101010110100010
01010101101001001010010110101001110100000100101011101000010101101010010
100101101010011101000001010010111010101000101110100001

Top of page


U, Universal Turing Machine

This binary version is quoted from Roger Penrose in 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 a simple machine. As an artist and non-mathematician  I  found this chapter very helpful.

Source: Roger Penrose, The Emperor's New Mind, Oxford University Press, 1989.  See Chapter 2, Algorithms & Turing Machines, Note 7, pp 71-73  

U=1000000001011101001101000100101010110100011010001010000011010100110100010101 001011010000110100010100101011010010011101001010010010111010100011101010100100 101011101010100110100010100010101101000001101001000001010110100010011101001010 000101011101001000111010010101000010111010010100110100001000011101010000111010 100001001001110100010101011010100101011010000011010101001011010010010001101000 000001101000000111010100101010101110100001001110100101010101010101110100001010 101110100001010001011101000101001101001000010100110100101001001101001000101101 010001011101001001010111010010100011101010010100100111010101010000110100101010 101110101001000101101010000101101010001001101010101010001011010010101001001011 010100100101110101010010101110101001010011010101000011101000100100101011101010 100101011101010100000111010100100000110101010100101110101001010110100010010001 110100000001110100101001010101011101001010010010101110100000101011101000010001 110100000101010011101000010100111010000010001011101000100001110100001001010011 101000100001011010001010010111010001010010110100100000101101000101010010011010 001010101011101001000001110100100101010101110101010100110100100010101101001001 001011010000000101101000001000110100000100101101000000000110100101000101110100 101010001101001010010101101000001001110100101010010110100100111010100000010101 110101000000110101010001010101101001010101101010000101011101010010010101110101 000100101101010010000101110100000011101010010001011010100101001101010100010111 010100101001011101010100000101110101010000010111010000001110101010000101011101 001010101101010100001011101010001010101110101010010010111010101010000111010100 000001110100100100001101001001000101101010101010011101000000001011010010000110 101010101001011101001000011010010001010101110100001000111010001000011101000011 010000000101101000001001011101010100101010110100010001001011101000001001110101 010011010000010101011010000100001110100100001000111010101010101001110100001001 001110100010010000111010000101001011010000101000011101010101010101110100010010 011010001001001101010010100101110100010001010111010000000111010001001001011101 001101001001000010110101010100110100010100010111010000110101000010001011010100 110101010010100101101010100110100100101011101001101001000001011010001010101000 111010010000101011010000001001101001000100101110100100001101010000010010111010 010010100110100100101010110100110100100101001011010011010010100000101101001000 001110101001001101010101000010111010010100001011101001010101011101010001001011 010010011101001010100010111010001001110101000010110100100111010010101010101110 100100011101001010101001011101001000111010100000101010111001101010000010110100 100111010100000010111010010110101000001010110100101001011101010000100101110100 001101010001000010110101001101010001000101101010101001011101010001010010110100 010101010111010010000101011010100010111010100100101010111010101001001011101010 001110101000111010100100100101110101000111010100101000101110101000101110101000 010010111010100011101000101000101110100101001011101010010101001011101001010101 010101101010000101010101101000010011101000010101010101110101010001010111010101 000101011101000000111010101000100101110100000011101010100100010111010100000011 010100001011010000001110100100000010111010100011101010010001010111010100110101 010100010101101000001101010101001010101101000000100110101010100100111010100110 101010100100101101010011010010010011101000001101010101010010101101010001001101 000101001010101110100000110101010101010010110100010001110100010101010101011010 001000111010000101011101000100100001110100110100000001001110100000010010111010 001000101001110100000010010111010010101010100101101000010101010111010001001010 010111010000010001011101010100101101000100010011101000001001010111010000001010 101101000010001110011110100001000001110100001001001110100000101001011101000001 010010110100001000101011101000010001001101000100001110101111010000100100101110 100001001001011101000000010101110100001010100011010001001011101000010000011101 000010011101000100000101110101010010110100010000010111010000101010101110100000 010101011101000100001010111010001000010101110100100000111010100100100110100000 010101110100010001001011101010100001110101001010110100101010100001101000001010 011010000000111010000010010011101001011010010001010010110101010011010001010010 010110101010011010001010100010110011010100100101110101010011010001010101010110 011010100010101011001101001000101010101110100010001110100100101010101011010010 100101000110100100000010111010000011010101001010101011010010101011010010001000 101110100010101011010100000101011010001000001101001000101011010000100111010100 101010101011101001011010010010001010110011010010010010101011101001101001001001 010110100101101001001001001011010010110100100101000101100110100100101001010111 010001010111010010010111001101001001010100101110011010010100010101011101000100 011101000010100101101001010001011101001010001010110100010011101001010001001011 101000100111010010100100010111001101001000100011101000100111010010100101010111 001101001010000011100110101010101011010000000111010010101001010101110100100011 101001010100101011100110100001010010011001101010000011010000000111010010101010 010101110011010100010000110100000001110100010010101010111010001000111010101010 101010101101000010011101001000100101011101001010100010011010100000001011010010 011101010000101011101001000011010100000001011010010001110101001001011101000011 010100001010101101010001011101010000101001011101010001011101010001010101011100
1101010001010110100001101010001001010

 

 
 

top of page | self portrait menu  |  main menu | site map | copyright