
The Lorenz and the Colossus
Although the Enigma was used for all standard German communications, another quite different type of cipher machine the Lorenz, was used at the highest level for strategic commands. See the description by Tony Sale of the Lorenz machine. There is also a picture of the Lorenz machine on the
National Security Agency site.
The Lorenz produced messages which at Bletchley Park were referred to as the 'Fish' ciphertext. These were attacked with increasing success after a young mathematician, W. T. Tutte, brilliantly exploited a dramatic German transmission error of 30 August 1941 and so discovered the basic structure of the cipher machine (which was, in fact, never captured.)
There is an extensive illustrated account of this work in Tony Sale's Virtual Bletchley Park.
Bill Tutte gave a very modest account of this work, Fish and I. It includes the specific method (called 'Turingismus') for breaking Lorenz ciphers that Alan Turing worked out after Tutte's breakthrough.
Turing's contribution to the 'Fish' material also emerges in two wartime reports, now available in a preliminary form on Tony Sale's site. These are the History of the Newmanry and the Special Report on Fish.
The 'Newmanry' took its name from Max Newman (the same Cambridge mathematician who had introduced Turing to logic in 1935) who took charge of this section of Bletchley Park work in 1942. Under his direction, new statistical methods were automated by building new machines with the first largescale use of electronic switching. Later versions of the Bombe used a few electronic valves for fast switching, but the Colossus, started in 1943 for work on 'Fish', used thousands. 
Tony Sale has an illustrated description of his astonishing Rebuilding of the Colossus on his site. The reconstruction is only partially complete, but has gone far enough to demonstrate the brilliance of the original work.
He also has an online Colossus simulator on his Virtual Bletchley Park pages.
A second phase of work is now under way and is intended to result in a complete Mark II Colossus capable of performing its highly sophisticated logical and statistical procedures.
Note: Alan Turing did not become the chief figure in the Fish work, and in particular did not design or build the Colossus, as is so often incorrectly stated. Note also that the Colossus did not work on the Enigma ciphers! However, it depended on the statistical theory that Alan Turing had developed for breaking the naval Enigma. It was also very important that Turing knew all about the success of the Colossus, because this was the first largescale application of digital electronics, and showed that this technology was reliable and practical. Turing's acquaintance with this work allowed him to plan with confidence for the computer of the future.

The electronic Colossus, working in time for DDay, 6 June 1944.

What if...
Here is a transcript of a muchquoted 1993
talk by Sir Harry Hinsley on the significance of work done at Bletchley Park. During the Second World War Hinsley worked on interpreting the naval messages that were decrypted by Turing's group. In the 1970s he become the official historian of the whole operation.
Hinsley went into the question of what would have happened if the Enigma had not been broken. He speaks of an invasion of Europe taking place in 1946 or 1947: a mere deferment of the inevitable. But a continuation of the war after 1945 would have been very different. The Allies were all prepared to infect Germany with anthrax, and after July 1945, American atomic bombs would have become available at the rate of one a month, presumably annihilating German cities or Uboat bases one by one. Would these measures have induced German surrender, or led to protracted guerrilla war? Would there have been chemical or biological retaliation on Britain? Where would this have left the Soviet Union?

The secrets of Hanslope Park 19445
After March 1944 Turing was overall consultant for the work at Bletchley Park. But after August 1944, with the invasion of Europe secure, he spent more time with his hands on electronics, preparing himself for the design of an electronic computer. He did this at the MI6 base at Hanslope Park, Buckinghamshire. With the assistance of Donald Bayley, a young electronic engineer, he built an advanced speech scrambler of his own elegant design.

They called it the Delilah.
This was at the suggestion of the young Cambridge mathematician Robin Gandy,
who was also working there.
After 1948 Robin Gandy became Alan Turing's student, colleague and close friend. 
Alan Turing was particular open about his being gay while working with Donald Bayley. The young engineer was amazed at meeting someone who was open and 'almost proud' of it. He also told me how in 1944 he left this as a private matter, but that if such a thing had happened after 1948 when new 'security' rules came into force, he would have had to report it. Donald Bayley spoke further of this on the television programme made in 1992, The Strange Life and Death of Dr Turing, and said how by 1952 homosexuality was 'beyond the pale' and disqualified anyone from secret work.
Alan Turing's colleague Jack Good, however, said on the same television programme that if the security authorities had known about Alan Turing's homosexuality from the beginning, 'we might have lost the war.'
The author Arthur C. Clarke made a similar claim in a foreword to a book on Artificial Intelligence: 'How ironic that Alan Turing, who perhaps contributed more than any other individual to the Allied victory, would never have been allowed into Bletchley under normal security regulations.'
In a subsequent interview, Donald Michie has pointed out that the 'security' authorities did not appear to worry about various other gay men at the Bletchley Park establishment, thus confirming that such vetting only started after the Second World War.

Alan Turing enjoyed a pleasant life at the secret Hanslope base, in those innocent preVetting days. He delighted in going running, and finding mushrooms in the countryside. Once he found the deadly Amanita Phalloides or Death Cap.
 

Alan Turing at VE Day
In 1995, at the occasion of the fiftieth anniversary of Allied victory over Nazi Germany, I wrote an account of Alan Turing's situation at that moment for the London Sunday Times.
Online now:
Alan Turing at VE Day

The image of fireworks at Bletchley Park is used by Sir Eduardo Paolozzi in the last of his Turing Collection of screenprints See my talk about this print and its images.

The secret mushroom cloud
The atomic bomb was soon to be open knowledge. This other application of leading mathematics and science, equally central to the Second World War and its aftermath, remained a closed book.
Everything about Bletchley Park had been borrowed from twenty years ahead of its time. The mathematical methods, the electronic technology, the informal organisation and breaking of barriers, the social and sexual liberalism, giving women and young people a vital place. To defeat Nazi Germany, the future was borrowed — though hardly anyone knew what had happened. Alan Turing was one of a tiny few with any understanding of the overall picture, and everyone maintained total secrecy about it for thirty years.
 The door out of Bletchley Park 
Alan Turing at the end of the war
Of all those who worked at Bletchley Park, the closest to Alan Turing's mathematical work was probably Jack Good. Here is Good's closing comment, from the summary he wrote in Codebreakers, about the work they did: ...the success of our efforts during the war, and the feeling that we were helping substantially, and perhaps critically, to save much of the world (including Germany) from heinous tyranny, was a hard act to follow.
A hard act to follow... but in 1945 Alan Turing was very confident about his future plans. His handson work on electronics was practice for the construction of a Universal Turing Machine — the computer of the future.

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