March 2020: In 1999 this was an HTML sort-of rendering of the xeroxed handout for the OUTWEST show. The original was a capture of the ITA2 fixed-width, 72 column output of a 1950's Model 28 teleprinter. Well HTML that "worked" in 1990 doesn't, in 2020, so it is re-rendered below as <pre> preformatted text with a "teletype" font. Good luck with that. The images were intentionally grayed out in low-res for the handout; better images are elsewhere on this site.
As told by the WPS Story Teller System
World Power Systems
1 September, 1999
Publication 45-63A
67 cents
A secret hero of World War Two, his wartime work remained a military secret until 1979. More than any other single person, his work led directly to Germany's defeat.
In 1945 he designed the world's first electronic, stored-program, digital computer, building upon his wartime work, and wrote papers foreseeing future decades of computer development.
By 1950 he was pursuing machine intelligence, and in a brilliant and witty paper defined what is now called the Turing Test for intelligence, which remains basic to artificial intelligence today. He devoted his last years to finding a mathematical basis for morphogenesis, the beginnings of life; his work in this area still considered pioneering.
Alan with friends, 1939.
The Story Teller is a system of obsolete, technological forgeries; leftovers from a Cold War that never, really, existed. It is an open-ended system for telling stories, via printed text, machine-uttered speech, drawings and words on phosphor screens, pen on paper, though only printed text and uttered speech are seen here. The stories are composed ahead of time, and stored as rows of tiny holes in a paper tape, an inch wide and tens or hundreds of feet long; a fabulously tactile, wonderfully obsolete machine-storage medium from another century. The resulting tapes are "played" on the Story Teller, similar to reel to reel magnetic recording tape.
The Model 31 Vocalizer (left)
speaks English phonemes, words, sentences, and programmatic gibberish. In oak, bakelite and brass, it utters speech and sounds in a clear but often unintelligible voice. The sole controls are for volume and speed, the latter controlling how slowly each phoneme is spoken. Glass-jeweled lamps decode each phoneme ("HEH-ELL-OW"); and with the speed control, allow for disturbing deconstruction and destruction of communication.
The Model 3 Tape Reader (right)
plays the perforated tape and sends the information on to other devices that speak or print. A tape is mounted on one side, and spools to the other as it is read. It is a pleasure to use; small, dense, dark oiled oak and bakelite, it makes a soft clucking noise as it reads a tape; you can literally feel the data on your finger tips, as the tape pulls through your fingers.
The Model 28 teletypewriter (left)
made by the Teletype Corporation in 1964, prints inky text onto cheap roll paper, and contains as many moving parts as a modern automobile. "Teletypes" are fantastically reliable and fascinating to watch and hear, a miniature locomotive of the printed word. It contains embedded intelligence to work in the Story Teller system. Teletypes in one form or another were the terminals, as they were called, of the world's original inter-net; telegraphy.
Alan Turing WPS Story Teller August, 1999
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Hyperboloids of wondrous Light
Rolling for aye through Space and Time
Harbour those waves which somehow Might
Play out Gods holy pantomime.
-- in a postcard to Robin Gandy
The world of Alan Turings time didnt know quite what to make
of him; it would be much easier if someone else had done these
things, instead of messy and embarrassing Alan.
Alan was ahead of his time, but trapped in an Edwardian past;
unapologetically homosexual in a world where it was still a crime,
brilliant and sensitive, awkward and clumsy, "a brain" in
school and an Olympic-class runner, Alan just didnt fit in,
anywhere he went.
He was quite conscious of his plight, and lived his life as
he chose, with high standards for himself and the world.
However much of the world, then as now, worried more about
appearance and authority to be anything but embarrassed with
Turing.
In his work, as in his personal life, he chose to be self-
contained, to work things out from the most basic facts,
sometimes to his own detriment.
As it turned out, Turings accomplishments didnt disappear,
despite his indifference to history, a Cold War society unable
to deal with an atheist out-of-the-closet homosexual
mathematician. Even today its hard to grasp the extent of
what he did half a century ago.
I.
--
Alan Mathison Turing was born on 23 June, 1912, in Paddington,
England into a middle class family of marginal success. Neither
he nor his brother John were model boys; bookish and quiet,
and uninterested in toy guns and mock fighting.
As a child Alan was bright and precocious, and would engage
strangers with his high-pitched voice, but he was also willful and
stubborn, and unwilling to follow rules
that "didnt make sense", a trait that Leaving on a trip, his
would follow him through life. mother said to three
year old Alan, "Youll
Not too well off, the Turings could afford be a good boy, wont
one thing for their boys: public school you?" to which Alan
(U.S. translation: private school). replied, "Yes, but
British public school is basic-training sometimes I shall
for the Empire; individuality and forget!"
intelligence rate second place to
tradition, structure and hierarchy. Alan was doomed from the
start.
He found his own solutions to math problems, shunning standard
solutions provided in school books, just as he worked around
school requirements and systems. Reading
Einstein, he identified the crucial point: "He appears self-con-
Einstein doubted the axioms of Newtonian tained and is apt to
physics, just as Alan was now learning to be solitary."
doubt the axioms of normal society. -- SHERBORNE HOUSE-
MASTER
At 15, Alan fell in love with another boy at school, Christopher
Morcom. Alan arranged things to be near him in classes and activities.
As it turned out, Chris was as smart as Alan,
but handsome and confident. Alan "worshipped "I wanted to look
the ground he trod on" and Chris "made everyone at his face, as
seem so ordinary". They had many interests in as I felt so
common; mathematics, astronomy, chemistry, and attracted."
constantly shared ideas and challenged each
other. This was Alans first (unrequited) love, and it was to change
his life forever.
Alans now-year-long friendship with Alans notes on
Chris was starting to show in Einsteins General
improved grooming and penmanship Theory of Relativity:
(the latter bad enough to hurt "Now he has got his
his chances for college). axioms, and is able to
proceed with his
Insecure, Alan tests Chris; walking logic, discarding the
back from the cinema, he hung back old ideas of time,
and was rewarded: "evidently I looked space, etc". 1928,
rather lonely as Chris beckoned to 16 yrs old.
me (mostly I think with his eyes) to
walk beside him. Chris I think knew how well I liked him but
hated me shewing it." Alan never spoke to Christopher of
his love for him, probably realizing it would not be returned.
Alan didnt know that Christophers frequent illnesses had a
cause; as a child he had contracted tuberculosis from the
family cow, and in 1930, when he was 18, Chris died from its
complications. It was a major blow to Alan.
In his last years at Sherborne finally Alan began to gain some
acceptance from his improved confidence and image that showed
in his schoolwork (certainly Chris/s inspiration), and acceptance
for his increasingly obvious brilliance in math. By graduation
he had won substantial scholarships, a medal for math, and
was accepted to Kings College at Cambridge, for the year 1931.
II.
---
Mathematics knows no
races... for
mathematics, the whole
cultural world is a
single country"
--DAVID HILBERT, 1928
Kings College, Cambridge, was an ancient, feudal place, with
an 11pm curfew, gowns after sunset, and an obsession with
social status, gentlemen and servants; but it came with the
freedom to spend time as one chose, very high standards of
learning, and an unprecedented social tolerance.
Alan was amongst the top rank of math students, where status
was gained by accomplishment rather than money or birth; maths
greatest figures, Gauss and Newton, were born farm boys.
It was at this time, 1931, that Hitlers gang was stirring
trouble in Germany, and England talked of war; but with fresh
memories of cynical World War One many Britishers were wary
of another greed-driven war. Alan joined an anti-war council
as did many students, but he did not side with the pro-soviet,
socialist groups; a champion of all that was honest and logical,
he would not go along with dogma of any kind.
In 1933 he met another Cambridge student, James Atkins. They
immediately became friends, and eventually lovers. James
sexuality and self-image was not as
well-developed as Alans; he initially Cambridge was an
made some homophobic rebuffs, but island of sanity
eventually warmed to Alans advances. in an insane world.
Alans sexual openness got him and an unnamed friend some
scurrilous mentions in a school magazines crossword puzzle
hints.
Contemporary ideas on sex were at their most oppressive
throughout most of Alans life, liberation of any kind still
decades away. Utter unmentionability was
still the norm, a hidden horror; the only "I had rather give
mentions were the ancient world, the Oscar a health boy or a
Wilde trial, and rare exceptions like healthy girl a
Havelock Ellis and Edward Carpenter. phial of prussic
Otherwise, there was a complete denial of acid than this
existence of homosexuals. novel." -- SUNDAY
EXPRESS, 1928,
As Alan and his friends studied, people review of "WELL OF
were fleeing the prospect of horror LONELINESS"
growing in Germany, scientists and
mathematicians mainly moving to America
and England; Einstein moved to Princeton "You may call it non-
in 1933. sense if you like,
but Ive heard non-
"A number of mathematicians met recently sense, compared with
at Berlin University to consider the place which that would be
of their science in the Third Reich. It as sensible as a
was stated that...the Germanic intuition dictionary."
which had produced the concept of infinity -- RED QUEEN, in
was superior to...French and Italians... THROUGH THE LOOKING
Mathematics was a heroic science which GLASS
had reduced chaos to order. National
Socialism had the same task and demanded the same qualities..."
-- as reported in THE LONDON TIMES, 10 November, 1933
After attending a course of lectures on the methodology of
science, Alan, skeptical as always, didnt accept the lecturers
explanation of the "normal curve" of statistical science. In
increasingly-typical fashion, Alan set out to find an exact
solution, and from rigorous pure-mathematic principles. In a
vaccuum, Alan re-invented the Central Limit Theorem, already
proven in 1922, because Alan did no research before setting out
on his work.
At age 22, in 1934, Turing was elected to a fellowship. In
addition to his existing scholarships, the post increased
privileges, and included a substantial salary. His re-invention
of the Central Limit Theorem, regardless, was a signifigant
piece of work and showed he was capable of great things.
His work put him at the forefront of the arcane and "useless"
mathematical logic. Hilberts unanswered third question and
Godels Unprovability Theorem, and remarks by Newman about
"mechanical processes" led Alan to write "ON COMPUTABLE NUMBERS
WITH AN APPLICATION TOWARD THE ENTSCHIENDUNGSPROBLEM".
As part of his solution to Hilberts third question, he imagined
an abstract, hypothetical machine, consisting of a table of
instructions and an infinitely long tape upon which it could write
and read symbols. The table would tell the machine what to do
when it examined a square on the tape; move left or right,
read or write a symbol, depending on what was on the tape. With
this hypothetical machine he defined problems that could not
be solved from within mathematics.
Alan had "mechanized" something that was considered innately
human, creating a hypothetical "universal machine", that could
perform the equivalent of human mental activity. While the
immediate subject of the paper remains part of arcane
mathematics, the Universal Machine (today called the "turing
machine") idea was to later start entire new mathematical sciences.
An example UNIVERSAL MACHINE configuration to add two
binary numbers stored on tape as strings of "X"s:
1. The tape.
- ----------------------------------------------------------------- -
1 1 1 1 1 1 1 1 1 1 1
1 1 X 1 X 1 X 1 X 1 1 X 1 X 1 X 1 1
1 1 1 1 1 1 1 1 1 1 1
- ----------------------------------------------------------------- -
A
AAA
AAAAAAA
(scanner)
2. The table of instructions.
if SCANNER reads a ...
BLANK X
------------------------------------------
I II I I
I STATE-1 II MOVE R, I MOVE R, I
I II GO STATE-1 I GO STATE-2 I
I II I I
------------------------------------------
I II WRITE "X", I I
I STATE-2 II MOVE R, I MOVE R, I
I II I I
------------------------------------------
I II I I
I STATE-3 II MOVE L, I MOVE R, I
I II GO STATE-4 I GO STATE-3 I
I II I I
------------------------------------------
I II I ERASE, I
I STATE-4 II NO MOVE, I NO MOVE, I
I II GO STATE-4 I GO STATE-4 I
I II I I
------------------------------------------
III.
----
Alans "COMPUTABLE NUMBERS..." paper, with its "universal
machine" became a quiet revolution in mathematics, and probably
helped him get the fellowship he applied for at Princeton
(USA). Alan left for Princeton in the fall of 1936.
Princeton was quickly becoming the center of the universe of
mathematics and physics; its already substantial local talent
was attracting refugees from Europe.
Einstein, von Neumann, Courant, Hardy, Upon arrival in New
Lefschetz were there; Godel and other York: "...Passing the
notables had visited within the year. This immigration officers
trend was to increase as the war worsened. involved waiting in a
queue for two hours
But Alan was miserable. He pined for his screaming children
sheltered British life, and he wasnt yet round me... I had to
confident enough to be social in an alien go throug the initia-
culture. The culture shock of foreign, tion of being swindled
plain-speaking Americans and open by a taxi driver..."
competition were too much for him.
Adding to his culture-shock was that he was living the charade
of a homosexual in the foreign and sexually more-rigid American
culture. He wrote to James Atkins that he was depressed and
described a complicated way to kill himself with an apple and
electrical wiring.
With his British friend Maurice Pryce, also at Princeton,
Alan visited relatives in rural Rhode Island. His country
cousin put Alan and Maurice in the same bed. Maurice was amazed
at Alans "advance", and Alan apologized -- then lashed out
with a deeply embarrassing outburst of anger and self-pity.
(Cut Alan some slack here; its 1937.)
Alans time at Princeton was hardly wasted however; he attended
lectures by Alonzo Church, John von Neumann, and others, and
in his own way mixed with many
accomplished people. He wrote some minor
papers, one of some note, with von "I think of people as
Neumann, and expanded his thoughts on pink-colored collec-
using his "universal machine" on codes tions of sense data"
and cyphers. Alan built an electric relay Alan once joked.
multiplier, to see if it would work. He
had to make the relays himself, as they were unavailable to him
in wartime. It was utterly unheard of for mathematicians to have
At the end of the school year, spring 1938, Alan headed home
to an increasingly fearful England; Germanys union with Austria
was foreboding, war was in the air, a new kind of war.
Czecho-Slovakia was invaded by Germany, England made a pact
with Poland. War was very close to home.
Cambridge had already extended Alans fellowship, so his academic
future seemed assured, but the war was to change everything.
In 1938, while still at Cambridge, he was recruited by "GC and
CS", the Government Code and Cypher School, should war come
and his be skills needed. That day came on 3 September 1939;
Alan reported to GC & CS the next day, his reservations about
a "selfish" war set aside by the new reality. Alan was assigned
to the Bletchley Park facility.
!!!
IV.
---
Bletchley Park was charged with intercepting and analyzing
enemy communications, mainly radio morse code messages.
Messages were encrypted with a machine called "ENIGMA", commonly
used by banks for financial communications. However the German
military had their own version, with extensive improvements
that made it much more secure. Nearly all German radio
communications used ENIGMA, and the sad state of British
intelligence, its left-over 19th century brain-dead bureaucracies,
incapable of cooperating, utterly without modern technology
(the Admiralty recorded the locations of German ships in huge
centralized notebooks, updated once per month) meant that
England was completely without any sort of intelligence data
on German whereabouts -- none whatsoever.
Not one German message had been decoded for months. Worse,
Commander Denniston, head of GC & CS, was overheard saying to
the Head of the Naval Section, "You know, the Germans dont mean
you to read their stuff, and I dont expect you ever will."
This was the state of affairs when Alan and his fellow
recruitees arrived. Alan volunteered for the hardest and
most important work, the Naval ENIGMA decodes, saying,
"No-one else was doing anything about it and I could have
it to myself."
The only glimmer of hope in this mess was the work of some
brilliant Polish mathematicians who had managed to work out
a scheme for cracking the ENIGMA codes used for a days
encryption (the codes changed daily). It involved making
100,000 cards with holes corresponding to the innards of the
ENIGMA machine, and relied on a particular usage of the ENIGMA.
And they had done so with ENIGMA parts smuggled out of France
in a shockingly complicated scheme. Even more fantastic, the
Poles had created electrical machines, which they called
"BOMBES" (after the ticking noise they made) to run through
the thousands of possible combinations. Even so, it took months
of hand-work to decode a days messages, but it was all they
had.
Alans first contribution, in 1939, was a major one, and typical
of his peculiar mixture of theoretical and practical skills.
With historically "useless" number theory he designed an
electrical machine that exploited weaknesses in the german
ENIGMA crypto machine, building on the work of the Poles
Bombes. His earlier work on the relay multiplier certainly
helped.
When Bletchley Park started on the decrypts in 1939, it took
as long as four months to decode one ENIGMA message; by June
1941, using the new Turing-designed Bombes, they were breaking them
almost as soon as they were received. That same year Churchill
visited Bletchely and met with a very nervous Turing. Churchill
called Bletchley, and Turing, "the goose that laid the golden
eggs and never cackled."
Alan met Joan Clark, a math professor, hired as a lowly
"linguist" by the stodgy civil service (though treated as a
peer in the progressive Cambridge-like atmosphere). After a
few dates they decide to marry (more a social obligation than
a sexual one). He told her bluntly of his homosexuality,
expecting her to call off the marriage; but he underestimated
her, she wanted to continue on.
Bletchley Park found itself overwhelmed with demands for more
and faster decryption, but couldn't get the people and resources
needed to complete the work. Alan, in typical fashion, broke
all the rules of hierarchy, and wrote directly to Churchill,
co-signed by team mates. Churchills reply was immediate, to
his staff:
ACTION THIS DAY: Make sure they have all they
want on extreme priority and report to me that
this had been done.
Eventually Alans inner turmoil over his sexuality and the
marriage to Joan became too much for him, and after much
indecision he calls it off. He quoted Oscar Wildes
closing lines from The Ballad of Reading Gaol:
Yet each man kills the thing he loves,
By each let this be heard,
Some do it with a bitter look,
Some with a flattering word,
The coward does it with a kiss,
The brave man with a sword!
Joan realized that Alan loved her, and that she had not been
rejected as a person. Though they remained friends, things
were somewhat touchy, so they arranged to not work in the same
section.
By early 1942, Bletchley Park was decoding up to 3000 messages
a day. A few months later, the Germans improved their entire
ENIGMA system, by increasing the complexity of the codes by
a factor of millions; Bletchley Parks enormous success ended
over-night. Late in the year however,
some progress was made on the theoretical Alan protected his tea
front, code-named "FISH". Once again the cup, irreplaceable in
most important breakthroughs was from wartime, by chaining
Alan; his coworkers named it it to a radiator; to
"Turingismus". tease him, his friends
picked the lock.
An entirely new type of machine was
designed to handle the fantastic speeds necessary to decrypt
Fish; instead of electrical/mechanical relays, the new machine
would be all electronic. And further, the data that it operated
on was going to be stored electronically, inside the machine.
The new machines were to be called COLOSSUS. While not true
computers, they contained most of the basic concepts of
computers, and in fact a COLOSSUS was later "programmed" for
things far beyond what it was originally designed for. (The
existence of these machines was not known until declassification
in 1978.)
Wartime work was highly compartmentalized; few knew the purpose
of their own work, or of the work of others. Turing was one
of extremely few with overview-access to the entire process;
this would later prove to be an enormous burden in his life.
It also made him the obvious liaison to the U.S. for crypto-
analytic work, not exactly Alans cup of tea, but utterly
necessary. Alan left for the U.S. in the fall of 1942, to visit
the AT&T Bell Laboratories.
There Alan met Claude Shannon, his complement in terms of
brilliance and breadth. Shannon worked on information theory
and communications theory, but gave a lot of thought to logical
machinery, a good match for Alans major interest in math and
mathematical/logical machinery, and his study of information
theory (of which cryptology is a practical aspect).
At Bell Labs Alan was shown the prototype "X system", an
extremely large and complex speech encipherment system,
undergoing tests. After a brief description of a particular
problem, Alan said "That ought to give you 945 codes. Its only
9 X 7 X 5 X 3." They were impressed; it had taken a Bell
Lab technician a week to figure that out.
Shannon was also interested in the idea of a machine emulating
a brain, a thinking machine; a burning interest for Alan. But
Shannon also talked of feeding a "brain" cultural data! Alan
was most impressed.
At lunch in the Bell cafeteria, filled with men in suits
grooming for promotion, Alan blurted out, "No, Im not interested
in developing a powerful brain. All Im after is just a mediocre
brain, something like the President of the American Telephone
and Telegraph Company." The room went silent, while Alan
continued blithely with his story.
After two months in America, Alan returned to England on the
troop transport ship "EMPRESS OF SCOTLAND". He was the only
civilian on the ship. He bought a copy of the RCA RADIO TUBE
MANUAL to read on the trip; he wanted to invent a new, better
way to encipher speech.
V.
--
By 1943 the COLOSSUS machines were in use. Though containing
over 1500 electron tubes, they became more reliable than the
previous electrical machines. Each was the most complex
electronic device ever built. Though they were in part based
on his Turingismus work, Alan wasnt involved in their
construction.
Alan, after getting Bletchley Parks methodologies started,
and after returning from his liaison work in America, found
himself outside of the day to day work. He transferred himself
to Hanslope Park in 1944, another secret GC & CS facility,
where he embarked on a project of his own, a system of speech
encipherment he called Delilah (the biblical "deceiver of men")
after having seen the complicated American "X system" at Bell
Labs.
Working with a young technician, Donald Bayley, Alan designed
a secure speech encryption system that used only 30 electron
tubes, as opposed to the X systems nearly 1000. It fit on a
desk top in a single cabinet, and was mathematically secure.
The British hierarchy showed no interest, sticking with the
American system, and it was never used.
During casual conversation with Donald Bayley, Alan mentioned
his homosexuality. Donald, a rather sheltered young engineer,
was appalled at Alans unapologetic attitude. Worse, rather
than dropping the subject in expected embarrassment, he
continued to argue logically, the argument becoming quite
heated. They eventually reached a mutual agreement, Donald
ultimately chalking it up to yet another
Turing eccentricity, and weighing it Alan told Donald
against NOT working with Turing. It from the start that
almost jeapordized the Delilah project. he wanted to "build a
brain".
Nearly complete, he left the details of
Delilah to Bayley, and started working on his ideas for a
"brain".
Alan assumed that the brain did what it did due to its logical
structure, by the functioning of physics and chemistry; rather
than reducing the brain down to its components, he wanted to
emulate one, to do what a brain does, irregardless of what it
was made of.
And as Turings biographer states so well: "...And thus it was
that in this remote station of the new military intelligence
empire, working with one assistant in a small hut, and thinking
in his spare time, an English homosexual atheist mathematician
had conceived of the computer". The year was 1945.
VI.
---
John von Neumann, and some of the builders of the ENIAC (a
giant American wartime calculator) had come up with the idea
of an automatic computer too, but with vast resources and
far more indirectly; the desire to build fast calculating
machinery to solve mathematical problems.
Throughout the 1940s nearly everyone, except Turing, thought
of the new automatic computers as giant calculators; where
Turing filled his designs with instructions for manipulating
symbols, the Americans machines performed mathematics; where
Turing designed his machines to specifically modify their
own programs as they ran, the Americans ensured that theirs
could NOT "accidentally" modify their instructions (revised,
in a limited fashion, in 1947).
In late 1945, Alan got a phone call from the new Mathematics
division of the National Physical Laboratory. They were looking
into the idea of scientific computing. Alan found himself with
a new job.
But there were problems from the start, of a more typical
bureaucratic kind. The head of the NPL, Sir Charles Darwin, a
descendent of Charles Darwin, was an unimaginative, block-headed
bureaucrat. The Mathematics division head, and Turings boss,
J.R. Womersley, was enlightened, intelligent and a political
player, recruited Alan to write a proposal for a design of an
automatic computer. Alas, Alan hardly helped his own cause,
and managed to clash even with his ally Womersley.
In 1946 Turing produced his report, "Proposed Electronic
Calculator", now called "The ACE report", ACE being the
name Womersley coined for it, the Automatic Computing Engine,
a nod to Babbages work of 100 years earlier. A brilliant
design, it called for a simple "mechanism" and a large memory,
trading off complexity in hardware for
increased complexity in software, exactly It was common for Alan
the opposite of contemporary designs, to bicycle or walk for
essentially the concept as the "RISC" 15 miles at a time. He
designs of the mid-1990s. The ACE REPORT had been running
remains readable today, and its modern- casually for years,
appearing instruction set not too far and recently taken up
removed from today"s, though the long-distance running,
nomenclature may be alien today. as a serious amateur,
running 2 or 3 hours
The "ACE REPORT" goes further, and a day. It also, as his
describes and predicts the entire computer mother put it, "put
environment that would develop in the him in contact with
coming decades: the art of computer men in all walks of
programming, the use of sub-routines and life."
subroutine libraries, floating point
arithmetic libraries. He describes the methodology that people
would use to solve problems on computers; loading standardized
tape, debugging programs, program "checkpointing". He describes
skilled programmers as separate from mathematicians, who would
design algorithms for the programmers to implement. He foresaw
the need for software librarians, and amusingly, that a
"priesthood" of programmers would appear, and resist the later
automation of their arcane programming jobs.
No magic, it was a combination of Alans vision and his vast
experience in setting up similar large organizations at
Bletchley Park, coordinating hundreds of people, complex
machinery producing results requiring intermediate checking,
and an army of thousands to assimilate the information produced;
none of which could be mentioned in the report, due to secrecy.
Wartime secrecy and his innate poor "team player" politics,
did not help him when the report was presented to the NPL;
worse, Darwin was no visionary, and simply never understood
the breadth and profound implications of what he was told, no
matter how much people like Womersley talked it up.
Huskey, the project head, stripped Turings design of all the
logical/symbolic instructions (saying they were "not needed
in most computing programs" -- how could
he know? no one had written any until "...found Turing very
then except Alan Turing.) and cut the opinionated and his
memory to a tenth its proposed size, and ideas widely at
named the machine the "Pilot ACE". variance with what the
main stream of
With diminishing influence on the new computer development
machine, Alan phases himself out of the was going to be."
project, to persue his ideas on machine -- CHARLES DARWIN
intelligence.
Robin Gandy borrowed a book from Alans room, and out flutters
magazine pictures of royal-court page boys; Turing said, "You will
find nice "pages" like that in my books."
One day Alan invited Neville Johnson, a third-year math student,
to tea; he stayed for tea, and indeed stayed many times. Not
a particularly good math student, he was
however Alans "type"; somewhat tough and "Sometimes youre
down to earth. sitting talking to
someone and you know
The NPL "ACE" project now on a path of that in three quarters
its own, Alan quits, and moves to of an hour you will
Manchester University, already at work on either be having a
their own computer, where Alan was made marvelous night or you
Deputy Director of the new Royal Society will be kicked out of
Computing Laboratory, May 1948. the room."
F.C. Williams designed the Manchester computer, "without
stopping to think about it too much", he said. It was a tiny,
minimally functional machine with just over 1000 memory
locations ("bits"), deemed just enough to get the job done;
a race was on to have the first working machine. Turing was
uninvolved in its development; he came too late, and more
aggressively career-driven people like Woodger, F.C. Williams
et al took the project as their own.
The Manchester "baby machine" ran the worlds first working
program on 21 June 1948, factoring integers using brute force
trials, after weeks of errors and problems. Though Alan was
nominally Deputy Director he was so removed from the project
that one of the engineers, G.C. Tootill, mentioned "theres a
chap called Turing coming here, hes written a program".
Alan remained "free-lance" within the NPL, as the resident
programming expert, and he started on the path to becoming a
user of computers. (This may have been his intent in moving
to Manchester, all along.)
Manchester wasnt the comforting intellectual environment of
Cambridge, and was less tolerant of oddness in general. His
schoolboyish appearance, shaggy, messy hair and clothes, stood
out too much. He had little social life at Manchester, and
maintained ties to his friends at Cambridge. He lived in a
lodging house on the edge of town, where he could run in the
country-side and bicycle to work. He never purchased a car saying
dramatically "I might suddenly go mad and crash."
Alan wrote the "PROGRAMMERS HANDBOOK" for the Mark 1, just
as the machine was to go into production in October 1949. It
makes clearer the problems Alan had communicating his
then-far-fetched ideas about computers; while most saw the
contents of programs and memory as "numbers" Alan clearly saw
them as symbols, devoid of inherent meaning, that anyone was
free to employ with any symbolism they wanted. This wasnt
conventionally recognized for decades.
Using a computer in 1948:
"...required considerable physical stamina. Starting in the
machine room you alerted the engineer and then used the
hand switches to bring down and enter the input program.
A bright band on the monitor tube indicated that the
waiting loop had been entered. When this had been achieved,
you ran upstairs and put the tape in the tape reader then
returned to the machine room. If the machine was still
obeying the input loop you called to the engineer to switch
on the writing current, and cleared the accumulator
(allowing the control to emerge from the loop). With
luck, the tape was read. As soon as the pattern on the
monitor showed that the input was ended the engineer
switched off the write current to the drum. Programs which
wrote to the drum during the execution phase were considered
very daring. As every vehicle that drove past was a
potential source of spurious digits, it usually took many
attempts to get a tape in -- each attempt needing another
trip up to the tape room."
-- Cicely Popplewell, 1948
Alan got Geoff Tootill interested in a scheme for computer
character recognition, with a television camera to transfer
an image directly to the program store, but it was too
impractical on the limited machine.
As an example of his advanced thinking, and of his basic social
problems, Alan gave a talk in 1949 titled "Checking a large
routine", and described a sophisticated system of tracking
the contents of memory. But to illustrate, he drew numbers
on the blackboard in base-32 teleprinter code, reversed left
to right as the Manchester computer required, utterly losing
his audience in the mind-boggling details. Wilkes said that
he was certain Alan wasnt trying to be funny, and just couldnt
understand that such a trivial thing could matter.
Back at NPL, the Pilot ACE, based upon a truncated version of
Alans 1946 design, was completed. Though only a shadow of
Turings design, it was the fastest machine in the world, with
its distributed operations (as opposed to the "centralized"
model of the Manchester machine).
Turings old NPL boss Womersley re-wrote the official history
of the ACE project by re-ordering events, such that in Womerleys
history Newman developed the ACE and Turing joined later. By
1950, Turing was already a non-person in the computer
"revolution". It may have ended as Alan wanted; while everyone
was competing to make newer, faster machines, Alan became a
full-time user of computers and persued his machine-intelligence
David Sayre, am American biologist at Manchester to use the
computer, got along unusually well with Turing, and they worked
on a basic X-ray crystallography problem, for a little over
two days:
... before we had finished (Turing) had re-invented by
himself most of the methods which crystallographers, up
to that time, had worked out. He had, for this purpose,
a breadth of knowledge greatly surpassing that of any
crystallographer I have known, and I am certain he would
have advanced the crystallographic situation very decidedly
if he had worked at it seriously for a time. As it was,
he may have had hold of one line which in 1949 had not
yet appeared in crystallography, concerned with establishing
quantitatively how much information is necessary to have
on hand at the outset of a search to ensure that a solution
can be found. -- DAVID SAYRE
Turing continued to write papers and give and attend lectures,
mainly on machine intelligence. He gave a talk titled "Educating
a digital computer" in 1950, attended by influential cybernetic
researchers, including Grey Walters, who made "tortoises" that
recharged themselves when their batteries got low.
Alan was initially interested in Norbert Weiners "cybernetics"
movement, a major fad amongst intelligentsia at the time but
quickly considered the pontificating empire-builder "a
charlatan".
He continued to attend meetings, and found them
entertaining. (Cybernetics faded away when it was clear it
offered no solutions to real problems.)
It was in this environment that Turing wrote "COMPUTING
MACHINERY AND INTELLIGENCE", in the philosophical journal
"MIND", October 1950. In it he laid out his test for machine
(or human) intelligence, now called the "TURING TEST", formulated
as a guessing game.
The point of his game was that there is no way to tell what
other people are thinking -- or that they are thinking at all
-- except by a comparison with themselves, and he saw no reason
to treat machines any differently.
I believe that in about fifty years time it will be
possible to program computers, with a storage capacity of
10 to the 9th, to make them play the imitation game so
well that an average interrogator will not have more than
70 per cent chance of making the right identifications
after five minutes of questioning.
-- from "COMPUTING MACHINERY AND INTELLIGENCE"
It was the end of the "pioneer" period of computers, where people
such as Turing, von Neumann, Shannon and others brought vast
experience and insight, in science and philosophy, to bear on
the basic problems of automated computing. From now on it would be
the era of the machine and empire builders, and the "hardware"
race to build bigger and faster machines.
"COMPUTING MACHINERY AND INTELLIGENCE" is a final landmark in
Alans interest in computing itself. It is still an interesting
read, showing the excitement of the dawn of the computer age,
when accomplishments were limited only by what could be imagined.
Alans hypothetical guessing game, with its human or machine
locked in a room, communicating with the world only via
teleprinter, was an idealized version of the life Alan tried
to live; fully self-contained, dealing with the world only
via rational argument. He was fully conscious of the outside
world, with its rules and codes and ettiquetes, but he chose
to obey few of them, as they all directly threatened his
freedom.
VI.
---
In 1950 Alan bought a house in Wilmslow, 10 miles south of
Manchester. It was furnished in typical Turing style; his
homemade brick pathway incomplete,
experiments in teetering pots on tables, "Brilliant but unsound"
books and papers everywhere. -- Alan's mother
A short walk from his house was the city center, Oxford Street,
where a homosexual culture had flourished since early in the
20th century (and where Wittgenstein had cruised nearly 50 years
before), with its active street, pub and theatre life. It is
almost certain that Alan took part in this clandestine culture.
Alan became fascinated with embryology, an area of biology
where no progress had been made in determining just how one,
two,... many cells differentiated and became an organism.
He wanted to know: just how does a symmetrical sphere of
identical cells suddenly gastrulate, eg. suddenly develop a
groove that becomes the head and tail of an animal? It was
just the sort of clean-slate, "unsolvable" problem Turing liked
(and which caused the likes of the philosopher Michael Polanyi
to declare life to be guided by mysteries outside the human
realm).
Turing wrote a seminal paper, "THE CHEMICAL BASIS
FOR MORPHOGENESIS", applied-mathematics par excellence, and
created a mathematical model for gastrulation; under certain
circumstances waves of chemical molecules would form stationary
... a mathematical model of the growing embryo will be
described. This model will be a simplification and an
idealization, and consequentially a falsification. It is
to be hoped that the features retained for discussion are
those of greatest importance in the present state of
knowledge.
-- from "THE CHEMICAL BASIS FOR MORPHOGENESIS"
At the Manchester computer lab, over the next few years all
that Alan had predicted came true; programmers, support
staff, a library of standard programs. Alan remained
uninvolved with computer development, and stayed with
his fundamental research. It was hard to believe that
in fact he was being paid to "direct" the laboratory.
He was elected a Fellow of the Royal Society, a very high
honor given to those of immense accomplishment. To his friend
(it was) very gratifying to be about to join the Olympians
(referring to other FRS electees). I am delighted to hear
that Maurice Pryce is also in the list...he was quite
my chief flame at one time.
In the letter he included a mathematicians in-joke: "I hope
I am not described as "distinguished for work on unsolvable
problems."
Alan gave a talk about computers on the BBCs "Third Programme"
radio show, on 15 May 1951, titled "Can digital computers
think?", and he talked mainly about the universal machine and
the imitation idea. He ended with this justification:
The whole thinking process is still rather mysterious to
us, but I believe that the attempt to make a thinking
machine will help us greatly in finding out how we think
ourselves.
He was working more or less full-time on his biological problems
now, using the Manchester computer, where he formed the classic
nerd/hacker convention of using a computer; he worked overnight
to have the machine to himself, using the "hooter" to signal
when a new tape or other input was needed, displaying results
on the visible cathode-ray memories, and using the computer
to keep track of his experiments, a novel idea at the time.
Never predictable, Alan wrote a short story, a barely-disguised
story about himself, his work and his sexuality. While it is
fiction, it describes some Manchester street life that strongly
implies he/d taken part in it before. It was never published,
and only a few pages survived in his notebooks.
...
Alec (Alan) had been working rather hard until two or
three weeks before. It was about interplanetary travel.
Alec had always been rather keen on such crackpot problems,
but although he rather liked to let himself go rather
wildly to newspapermen or the Third Programme when he got
the chance, when he wrote for technically trained readers,
his work was quite sound, or had been when he was younger.
This last paper was real good stuff, better than he"d done
since his mod twenties when he had introduced the idea
which is now becoming known as "Pryces buoy". Alec always
felt a glow of pride when this phrase was used. The rather
obvious double-entendre rather pleased him, too.
He always liked to parade his homosexuality, and in suitable
company Alec could pretend the word was spelt without the
"u". It was quite some time now since he had "had" anyone,
in fact not since he hadmet that soldier in Paris last
summer. Now that his paper was finished he might justifiably
consider that he had earned another gay(#) man, and he knew
where he might find one who might be suitable.
...
# Alan Hodges explains: "Was this plain text, or cypher text?
At least since the 1930s in America it had been in use amongst
homosexual men as a code word with plain meaning; from
D.W. Corys 1951 book THE HOMOSEXUAL IN AMERICA: "Needed
for years was an ordinary everyday, matter-of-fact word, that
could express the concept of homosexuality without glorification
or condemnation... Such a word has long been in existence...
That word is GAY.". Alan used the word "homosexual", or amongst
friends, "queer". But he certainly could have know of this
American usage, and would have approved of D.W. Corys
rationale." (Paraphrased for brevity)
VII.
----
In 1951, Alan met Arnold Murray, 19, an unemployed, lower-class
youth, while walking along Oxford Street. Alan asked Arnold
to have lunch, rather than the customary quick tearoom or
alley visit. Each met the others needs in some way; Alan
was someone to look up to, Arnold was full of life with a
good sense of humor, and a lost lamb. After a furtive start
they began an ongoing sexual affair.
Alan continued to work on his biological projects, and again
spoke on the BBC, on whether machines could think, in January,
1952. Alan again argued in his "if it imitates intelligence
we might as well call it intelligent" mode convincingly, if
somewhat far-fetched to a contemporary audience.
Alan and Arnold continued their affair, with many sleep-overs
at Alans; though they had little in common, Arnold picked up
on Alans need to communicate, and so things continued.
There were problems with money, in that Arnold was clearly
broke, and Alan clearly well-off. It came to a head when
Alans house was broken into, and it was determined it was
done by an acquaintance of Arnolds, though Arnold was not
involved.
Alan reported the burglary to the police, who, ever sensitive
to social convention in Cold War England, determined the "true"
crime, that of Alans involvement with
Arnold. When asked what his relationship "When I recall some
was to Arnold, Alan stated bluntly that past epoch, I think
hed had a sexual affair with him. of whoever I was in
love with at the time."
He clearly underestimated the seriousness
of his "offense", and was shocked at how much the police
dwelt upon the sexual aspect rather than the burglary.
Homosexuality brought a penalty of up to two years imprisonment.
Poor Alan; his timing was poor. The tenor of the times was to
change in the coming decade, but not in time for Alan. Over
the previous 20 years, prosecution of homosexuals had increased
five-fold. He became one of those criminals, and was sentenced
to the "modern" "cure" of organotherapy: a years chemical
castration via female hormone injections.
The trial forced Alans life into the public eye. His mother,
brother, all his co-workers past and present found out about
his sexuality, either from him directly or from the papers.
This caused great embarrassment at Manchester University, but
it was generally considered "typical Turing". Most people
simply didnt refer to it; those that avoided him had been
avoiding him anyways. He showed no fear or embarrassment,
and went about his business cheerfully.
He had many strong supporters. Max Newman and others came to
his defense, one even going as far as bringing quotes from
the brand-new "Kinsey Report" to the Vice Chancellor as
argument. Alan kept his job. He did not let it affect his
work; the day after his arrest he spoke at a conference, and
completed papers as scheduled.
For Arnold, the trial was less damaging; he was put on
probation, moved to London, became involved with Colin
Wilson and others in the coffee-bar world there, and
eventually became a muscian.
And some people saw in Alan a new person. Lyn Newman, Max
Newmans wife, found him much more human and interesting, and
started plying him with books such as "ANNA KARENINA" and "WAR
AND PEACE", the latter of which became a major influence on
Alan, seeing himself and his own problems in it.
Despite his fears, the estrogen didnt affect his intellectual
performance, only his sexual. He continued to broaden and
deepen his biological work. His earlier work was starting to
be recognized; the botanist C.W. Wardlaw describing in
biologists words Turings "CHEMICAL BASIS FOR MORPHOGENESIS".
He was becoming quite famous for his 1936 "COMPUTABLE
NUMBERS..." paper; while having lunch with Robin Gandy, Alan
suddenly launched out one door just as a particularly boring
logician was heading for him from another.
While his sentence probably stifled Alans cruising activities
in England, it didnt apply outside the country -- and Alan
took numerous over-seas vacations, notably to Norway, and
learned to speak a little Danish and Norwegian.
On the proto-liberation front, Alan wrote a letter to a titled
politician, arguing for de-criminalizing homosexuality, but
unpoliticly informing them of the homosexuality of the
politicians son. He received only a disclaimer from the
politicians secretary in reply.
Alan started seeing a Jungian psychoanalyst, Franz Greenbaum,
who was comfortable with Alans sexuality. This probably fit
in with his continuing interest in the human brain, and Alan
continued to debate and attend lectures with Manchester
philosophers on the human mind. He filled three notebooks
with dreams.
(An amusing resonance;
Alan wrote a letter to Robin Gandy Alans letter was rendered
using a program he wrote on the on a teleprinter similar
Manchester computer, a fragment of to the one in front of
which is shown here: you, so in fact it looked
exactly as follows.)
....
LD/BE/NO/POSSIBLE/OBJECTION/TO/MAKING/IT/SAY/:FOUR/THIRTY/IF/YOU//
FIND/THIS/MORE/CONVENIENT/HR/IS/PROBABLY/THINKING/OF/YOUR/GETTING/
BACK/THE/SAME/DAY/////////////////IF/YOU/REALLY/ARE/GOING/SKIING/N
O/DOUBT/IT/COULD/BE/DELAYED/TILL/APRIL/OR/MAY//THOUGH/I/MAYBHAVE/F
ORGOTTEN/ABOUT/IT/BY/THEN/MOSTLY////////////////////////////////YO
UR/LAST/LETTER/ARRIVED/INTHE/MIDDLE/OF/A/CRISIS/ABOUT/"DEN//NORSKE
/GUTT"//SO/I/HAVE/NOT/BEEN/ABLE/TO/GIVE/MY/ATTENTION/YET/TOTHE/REA
....
While hard to read it is a sight better than Alans handwriting,
and far easier to read than the computer-edited letter he wrote
to David Champernowne -- delivered on a strip of punched tape
(as used here by the Story Teller). If not the first, these
are certainly amongst the first computer-edited letters.
Alans trips to Norway continued, and from correspondence with
Robin he seemed to have opened up socially. Probably in
connection with his psychotherapy, he apparently decided that
self-exploration and self-revelation were worthy goals, and
pursued them in typical Turing fashion. (Of course seeing a
therapist was another source or social embarrassment to anyone
but Turing. That he was foreign, and Jewish, only made it
worse.)
At the Manchester computer laboratory, a young man Alan found
attractive arrived to use the computer. Alan immediately asked
Tony Brooker "Who is that beautiful young man?", who explained.
In April 1953 his chemical sentence ended; for the final three
months an implant was used, which Alan suspected was designed
to last more than three months; he removed it. At this time
Manchester University created a special "Readership in the
Theory of Computing" post for him, and with it came a pay
raise; his professional future was secure.
That summer, Alan visited the Greek island of Corfu, and
returned with several names and phone numbers; he must have
got more than that, as his biographer wrote of the visit:
"As at school, he made mistakes with the French, but still
did better than with the Greek."
During this period, in spite or because of the Cold War, the
general diversification of culture, and particularly sex, was
changing for the better. Novels with homosexuals of covert
intent were appearing, though mainly of the "tragic ending"
sort; it was becoming obvious that homosexuals muddled through
life just as anyone else.
But just when it seemed Alan was becoming more comfortable in
the world, he killed himself, on 7 June 1954.
VIII.
----
Everyone who knew him was shocked; it seemed so pointless. He
had always been a tense, unhappy person, and the Arnold affair
wold have been a major blow to anyone, but the trial was two
years old, the hormone treatments ended a year before, and he
seemed to rise about it all in his typical fashion.
His housekeeper found him, lying in bed; the coroner determined
he died from cyanide poisoning. A half-eaten apple was by the
side of his bed, and he had jars of potassium cyanide in his
kitchen, for his many experiments. Presumably the cyanide
was on the apple, though it wasnt tested, deemed an obvious
suicide. There was no evidence of any kind to the contrary.
He left no note, and his house was its usual mess of papers
and books; and he had scheduled time on the computers a few days
later. He had however made a new will only months before; his
estate went to his mother and his friends. He had also reached
a peak in much of his current biological work, not exactly
complete, but he had told Robin Gandy that he felt he had gone
as far as he could at the time. He had been working also on
a number of mathematical logic papers and had published small
Alans work (and saw that some of the unfinished work was
published in subsequent work).
-----------------------------------------------------------------------
As Turings biographer Andrew Hodges says, there is amazingly
little information available on such a world-historic person,
and not all of it is due to taboos on homosexuality or state
secrets. Little was saved about the ACE machine, for example,
and most of what exists was saved by participants personally.
A large part of the problem is Turing himself; he didnt live
his life like a "world figure"; he tried to be an ordinary
mathematician, who generally remain obscure. He made no effort
to preserve his work or writing.
Appropriately enough, he achieved a modest immortality in the
expression "turing machine", increasingly used uncapitalized,
a sort of mathematical canonization.
Not until the 1970s was Turings profound understanding of the
capabilities of computers generally appreciated, as machinery
capable of anything that can be expressed symbolically.
Only with the spread of minicomputers, and later microprocessors,
did the world begin to understand the nearly limitless use of
the machines that Alan helped build.
He may be finally, nearly a half-century later, coming into his
own:
# A play entitled "BREAKING THE CODE", by Hugh Whitemore,
opened in London, in 1986. It played in New York in 1987.
I was lucky enough to see it in San Francisco around 1989
or so. See SOURCES for more information.
# A made-for-TV version of the play was first screened in
Canada in 1986 by SHOWCASE TELEVISION.
# And this year (1999) Neal Stephensons novel CRYPTONOMICRON
has a decent rendering of Alan Turing as a fictional
character; a fitting adaptation if his life (though Neal
has him smoking cigarettes.).
# Finally, Andrew Hodges is writing a work of fiction, titled
THE UNWELDING, that has Turing as a fictional character.
-----------------------------------------------------------------------
My interest in Alan Turing began in 1981, while reading "A HISTORY
OF COMPUTING IN THE 20TH CENTURY". I dont recall what I knew
of him at that time, certainly not much, but he came up in
just about every essay in the book, at the most fundamental
level of theory and construction of machines, and seemingly
everywhere in between. And then I.J. Good wrote in his essay
"PIONEERING WORK ON COMPUTERS AT BLETCHLEY":
"It was only after the war that we learned that he was a
homosexual. It was lucky the security people didnt know
about it early on, because if they had known, he might
not have obtained his clearance and we might have lost
the war."
As a young homosexual myself I was instantly fascinated --
but I could turn up no information beyond the most basic
biographical information.
But in 1983 I found the just-released "ALAN TURING: THE ENIGMA",
by Andrew Hodges, a British homosexual mathematician, turned
author, who brought together a phenomenal amount of information
in spite of Turing's indifference to history, wartime secrecy,
and a world unwilling or unable to acknowledge an open
homosexual.
This book was essentially my sole source of information on Turing.
This isn't out of laziness; there simply isn't any other
substantial works; and with a few exceptions, finding Alan's
original work is very difficult.
I strongly recommend Hodges book to anyone at all interested
in Turing or this part of history.
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This paper document is ephemera from the performance of the
"ALAN TURING" story as told by the World Power Systems "STORY
TELLER" system, and stored on approximately 650 feet of punched
tape. It takes about 8 hours to perform, assuming the tape
doesn't break.
A B C D E F G H
I J K L L M N O
P Q R S T U V W
X Y Z 1 2 3 4 5
6 7 8 9 0 - S ,
: ( ) " # ? & .
/ ;
Tom Jennings
19 August, 1999
SOURCES & REFERENCES
--------------------
ALAN TURING: THE ENIGMA by Andrew Hodges, 1983. ISBN 0-671-49207-2, out of print.
A new edition is expected in 2000.
ALAN TURING: THE ENIGMA by Andrew Hodges, 1992. ISBN 0-09-911641-3, UK publication.
Same as above but new preface and documents found since 1983.
A HISTORY OF COMPUTING IN THE 20TH CENTURY, 1980.
ISBN 0-12-491650-3, out of print.
TURING, Andrew Hodges, 1997. ISBN 0-75380-192-2.
Subtitled "A natural philosopher", a brief (60 page) essay on
Turings philosophy of mind, showing more of his wit and
brilliance, and some of the results of his discussions with
Wittgenstein. Obtainable from AMAZON.CO.UK.
ALAN TURING: THE ARCHITECT OF THE COMPUTER AGE, by Ted Gottfried, 1996.
ISBN 0-531-11287-X.
A brief biography intended for young students; what it lacks
in depth is made up for in its frank and enlightened treatment
of Alans sexuality. It does a decent job of explaining Alan"s
work. An excellent stealth book to sneak into libraries.
Gottfried appears to be a prolific writer of biographies.
THE ALAN TURING HOMEPAGE http://www.turing.org.uk/turing/
ANDREW HODGES HOMEPAGE http://www.turing.org.uk/
AMAZON.COM http://www.amazon.com
AMAZON.CO.UK http://www.amazon.co.uk A better source of Hodges work.
Purchase/shipping to the U.S. not a problem with a credit card.
THE INTERNET BOOKSHOP http://www.bookshop.co.uk
Online, overseas ordering not a problem.
BREAKING THE CODE http://www.turing.org.uk/turing/scrapbook/btc.html
A play by Hugh Whitemore, is described here.
THIS DOCUMENT,http://www.sr-ix.com/projects
This document and these URLs can be found on my web page:
All quotations not attributed taken from Hodges book
"ALAN TURING: THE ENIGMA". "Universal machine" table
from Hodges. Otherwise, entire contents copyright
Tom Jennings, 1999.