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DOCUMENTATION:
A Universal Turing Machine as Self Portrait
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Detail from a series of
Illuminated Universal Turing Machines,
Manchester,
1998. This is one of a series intended to honor A. Turing's work. |
"It is possible to invent a single machine which can be
used to compute any computable number".
Alan Turing (1912-54), Section 6, On
Computable Numbers, 1936.
Turing's
1936 paper outlined a procedure for deciding all "decidable"
statements, in effect a logical method for computing all
"computable" numbers. All general computers are, in principal
"Turing complete', capable of carrying out all decidable statements. This procedure can be formatted as an algorithm
known as a Universal Turing Machine.
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
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Circuit Mind:
Tetra Corporation Memorial, Minneapolis, 1969.
Verostko Center for the Arts,
Latrobe, Pa., USA
Working circuit, test model for
processing information. Hardwired circuit logic originates in
algorithmic procedures for the gating logic embodied in the circuit
board. Software engineers create
circuit diagrams of algorithms that are then hardwired
into the circuit board. 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.
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OPERATION.
Turing's paper outlined a procedure that could be carried out by following an
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. For Turing's theoretical description
of "The universal computing machine" see part 6 of his 1936
paper "On Computable Numbers . . ."
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.
Algorithmic versions 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 marquee 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", 1936.
Convenient PDF download:
On Computable Numbers
Abelard's colorful historic web site:
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 interersting and useful historic 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
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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
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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, pp 71-73,
Note 7, p. 93-96
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