The World of Alan Turing, or

From the Turing machine to the first commercially-available

(general purpose) computer

The paper “On computable numbers…” (1936-7)

• This paper introduced 3 (principal) ideas or concepts – the Turing machine, with its read-write head, 4 basic commands and its tape as the ‘memory’

• The machine description, which Turing refers to as the m-configuration (its collection of – finite – states, thinking in terms of automata)

• The idea of the machine which can read – and operate on – its own description… the universal Turing machine (as a way of tackling the Entscheidungsproblem)

Look first at the Machine and its m-configuration - from Marvin Minsky’s text

“Computation”Turing expresses the m-

configuration as a table in which the rows are ‘action descriptions’, e.g. (A)print 0; move 1 square to the right

(B) Move 1 square to the right(C) Print 1; move 1 square to

the right(D) Move 1 square to the right

and go to (A)Printing 010101…..

Now look at the notion of the Universal (Turing) machine

• This is a machine which can read a series of m-configurations and thus ultimately operate to any specifiable computational sequence (an algorithm)

[ of course, not all such algorithmic operations are deterministic – i.e. produce a defined result, which is repeatable ]

The importance of this notion is its universality – it is a way of ‘interpreting’ any expression of an algorithm (and thus in our terms, any program)

How did Turing become involved in cracking the Enigma code?

• He initially built on the work of the Polish team led by Marian Rejewski, who had catalogued patterns based on the first 6 letters of intercepted messages:-

Enigma messages start with the 3 – letter message key & its repetition, for example the sequence L O K R G M, in which L and R encrypt the same letter, the first in the message-key. This tells us that L and R are related by the initial setting of the Enigma machine

If you have 4 messages, starting with the 6 letters of repeated key -

• If enough messages are received in a day, patterns can be discerned, for example if you have a complete set of 1st and 4th letters –

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z and

F Q H P L W O G B M V R X U Y C Z I T N J E A S D K

Now we see that A is linked to F; look up F on the top row, it is linked to W; look up W on the top row, it is linked to A – which is where we started.

Message 1 - L O K R G MMessage 2 - M V T X Z EMessage 3 - J K T M P EMessage 4 - D V Y P Z X

Now we can see how letters are encoded in these messages –

1st letter ABCDEFGHIJKLMNOP…4th letter P M RX

Think now of how the Enigma machine is constructed -

The Enigma shown has 3 scramblers (rotors)

• If we think of the relations previously described between the 1st and 4th letters, we see a ‘chain’, here - in the simplest case – A->F->W->A (with 3 links)

• It can be shown that the number of links in these (multiple) chains is wholly dependent on the scrambler settings: Rejewski’s team catalogued the chain lengths generated by each of the 105,456 scrambler settings. Now each day messages were received, they could see the first 6 letters and thus identify the chains and the scrambler settings that created them. Thus the scrambler part of the day-key has been separated from the extra encoding performed by the plugboard, which operates as a straightforward substitution (e.g. R may be plugged to L), operating each time a certain letter is encyphered.

When Rejewski’s team met Knox & Turing

In July 1939 in a hut in the Pyry forest outside Warsaw, the French intelligence service arranged a meeting between the British cipher service and the Polish team. This meeting resulted in the handing over of a reconstructed Enigma, a number of bombes of Polish design, and the basis for cracking the Enigma messages using a 3-rotor Enigma.

Issues

While the Poles had devised a method for cracking Enigma, it is perhaps important to note that a major reason for the meeting was an increase in the design complexity of message coding by the Germans –

• 2 more rotors so that 3 were chosen from 5• No. of plugboard cables up from 6 to 10

The Polish methods could not handle these changes!

Start of operations at Bletchley Park (“phoney war”)

When Turing joined Bletchley Park, others like Gordon Welchman had already arrived and were preparing the ground for the codebreaking work. There was a heirarchy being built up to provide support & services to interact with the codebreakers & lots of others, some known to Turing, became involved. Among these were Max Newman, his mentor at Cambridge in much of his work.

Members of the initial heirarchy at Bletchley Park

The different Enigma designs – Abwehr, Kriegsmarine, Luftwaffe

The German army, navy and airforce used Enigma designs of varying complexity –

• The army & airforce used 3 rotors chosen from 5,• The navy 3 or later 4 from a total of 8 The teams at Bletchley were able to develop

techniques in Bombe design & usage to handle army/airforce and navy messages up to the first battle of the Atlantic. However, as U-boat usage of codes and keys became more sophisticated, decoding difficulties were increased and new strategies and techniques were needed.

The problems come to a peak

In 1942 and early 1943, there was an 8 month break in being able to solve Enigma messages from the navy and the U-boats –

• Attacks in the Atlantic were intensifying• 4-rotor Enigmas had been introduced The technique known as ‘gardening’ was the

only real answer Bletchley had. A new strategy was needed. The study of ‘Fish’ was vital.

‘Dilly’ Knox dies, having broken the Abwehr Enigma

• Knox was a scholar & academic, not a mathematician (but he was originally attached to Admiralty room 40). He suffered from cancer and died in Feb. 1943.

• He was determined to create a break into the Abwehr Enigma so that the Double-Cross messages sent via turned German agents could be verified as being ‘believed’ in Berlin. He succeeded in Dec. 1941.

• Once it was known that Double-Cross worked, continuing to read Abwehr Enigma messages became fundamental.

The Lorenz messages (“Tunny”)The German high command centres used

teleprinter-based messaging, not Enigma. Messages were encoded and sent using teleprinter code from 2 centres, on various routes manned by Axis forces. It was these messages that determined the movement and disposition of troops, and following the losses in the Russian and desert campaigns they became vital to intelligence. They were encoded using the Lorenz ciphers.

How was Lorenz different?• There were 3 Lorenz designs, but in general,

Lorenz used twelve wheels or rotors in two groups. 5 were used separately to encode, 5 more could be used either in unison or in tandem to break up the message

• There were 2 motor wheels which controlled the two groups of 5

• The encoding wheels were not connected at every letter and the inter-rotor connecting circuits were varied frequently.

The machines used to break Lorenz ciphers

Initially, there was Heath-Robinson, a machine which read 2 tapes, one the encoded message and the second an example decode based on a chosen setting of the encoding wheels. Because tapes were read at a maximum speed to try and solve the complexity of having to try many wheel settings, this machine had many problems with breaking and tearing tapes.

Enter the Post Office research station team

At Dollis Hill the GPO had an engineering team developing electronics for working on advanced exchange design –

• Valve electronics so reliability issues, but• Circuitry design was advanced and offered complex

functionality Tommy Flowers, head of the Dollis Hill team, was

certain a machine could be designed to overcome the Heath-Robinson problems: Max Newman & Donald Michie are generally credited with the overall Colossus design

Colossus I

• 1500 valves, reads only 1 tape and stores the encoded message within machine ‘memory’

• Uses algorithms to test possible wheel-setting combinations to analyse decodes of the message statistically

• Results can be printed to enable the most likely settings on which to concentrate efforts.

Delivered to Bletchley December 1943.

Colossus II and the timing of efforts• 2500 valves bringing more memory & power• 5 different encodings can be processed

together – stops breaks when no decodes.Combined the advantages of the original design -> The most successful design – eventually 10

were delivered!The new Colossus was first delivered a few days

before D-day and this allowed 2 simultaneous attacks – disinformation and codebreaking.

Colossus design - modular

TOWARDS THE FIRST STORED-PROGRAM COMPUTERS – ON SALE!

War ends – what happened next? Bletchley Park was closed and there was a bonfire to avoid secret information being retained.The computing research efforts continued in 4 or 5 groups, some of which had already started during the War – Radar at Malvern, NPL, Manchester, Cambridge, others

Reviewing the (unfinished) story

Main development groups in 1946• NPL where Turing began initially after the War

– attached to atomic energy research site at Harwell, very bureaucratic, already secretive

• Manchester University where memory advances came together and where Newman started the design lab. – birth of the 3 registers (A, B, and the combined C- PI & program counter). Turing joined him later.

• Cambridge under Hartree and then Wilkes – a pragmatic approach based on human “computers”- produced EDSAC and then LEO.

The different approaches

• NPL was where Turing originated the design for the ACE – not commercially available till after he died

• Manchester was where the first stored-program computer actually ran a program- an advance impossible without perfecting the Williams-Kilburn tube used as a program store

• Cambridge started after the Moore school work and chose a more pragmatic approach

The Manchester “Baby” and the advances that followed there

This basic “fetch cycle” design was varied and improved on several times at Manchester University computing lab. – storage was increased (to 8k words) to provide more flexibility and allow different usage strategies

The Moore school ideas & Maurice Wilke’s work at Cambridge

• Cambridge computing lab. started in 1937 with a differential analyser & desk calculators.

• After the war Wilkes got J. von Neumann’s “Draft report on the EDVAC” and later went to a Moore school course. The Moore school had built ENIAC but it only worked in Nov. ’45.

• Wilkes’ computer- EDSAC - used the same delay-line technology as ENIAC- 4 to 32 delay lines, 3000 valves. Printed a squares table 6 May 1949.

Turing after 1948-49 and his changing interests

• After the practical successes at Manchester in 1948, Turing became a thinker and a documenter again – he created the programming manual for the Manchester Mark 1, later the Ferranti Mark 1

• He moved to thinking about AI and machine learning and how machines, and abstract ‘minds’ might re-design themselves – resulting in the “Turing test” paper of 1950

Source books & papers1. Campbell-Kelly, Martin & Aspray, William, Computer: A History of the

information machine, Basic Books, New York, 19962. B. Jack Copeland & others, Colossus: The Secrets of Bletchley Park’s

Codebreaking Computers, Oxford University Press, 20063. Hinsley, F.H. & Stripp, A., Eds.: Codebreakers: The inside story of Bletchley

Park, OUP, 19934. Lavington, Simon H. Early British Computers: The story of vintage

computers & the people who built them, Manchester University Press 1980; and A History of Manchester Computers, British Computer Society, Swindon, 1998

5. Singh, Simon The Code Book: The Secret History of Codes & Codebreaking, Fourth Estate, London 1999

6. Leavitt, D. The man who knew too much: Alan Turing & the invention of the Computer, Phoenix, London, 2007

7. Smith, Michael, Station X: The Codebreakers of Bletchley Park, Pan Books, London, 2003