Alan Turing
“Sometimes it is the people no one can imagine anything of who do the things no one can imagine.” ~ Alan Turing
“Those who can imagine anything, can create the impossible.” ~ Alan Turing
‘Science is a differential equation. Religion is a boundary condition.’
~Alan Turing
‘We can only see a short distance ahead, but we can see plenty there that needs to be done.’ ~ Alan Turing
“The isolated man does not develop any intellectual power. It is necessary for him to be immersed in an environment of other men, whose techniques he absorbs during the first twenty years of his life. He may then perhaps do a little research of his own and make a very few discoveries which are passed on to other men. From this point of view the search for new techniques must be regarded as carried out by the human community, rather than by individuals.”
~ Alan Turing
This essay will focus on the life and works of Alan Turing.
Alan Mathison Turing (23/06/1912–07/06/1954), was a British Mathematician and Logician. who had profound impact on the fields of Mathematics, Cryptanalysis, Logic, Philalosophy, and Mathematical Biology. He is the father of Artificial Intelligence and Artificial Life.
In 1936 Turing published his seminal paper “On Computable Numbers, with an Application to the Entscheidungsproblem [Decision Problem] link to his paper → (On Computable Numbers, with an Application to the Entscheidungsproblem — Turing — 1937 — Proceedings of the London Mathematical Society — Wiley Online Library). Upon submitting his paper An American Mathematician called Alonzo Church had published a paper arriving at same conclusion as Turing but, via a different method. Turing paper had an impact on computer science but, not so much's Churches. Later he moved to Princeton University under the direction of Chruch and completed his PHD — “Systems of Logic Based on Ordinals”
The Entscheidungsproblem sought out to find the correct algorithm to solve a particular mathematical problem, during Turning’s time clerks completed them. In 1936 Turing and Church independently showed that, in general, the Entscheidungsproblem problem has no resolution, proving that no consistent formal system of arithmetic has an effective decision method in fact, Turing and Church showed that even some purely logical systems, weaker than arithmetic, have no effective decision method. This result and others — notably mathematician-logician Kurt Gödel’s 28/04/ 1906–14/01/1978. who is a significant figure in field of logic -> he created the technique now known as Gödel numbering, which codes formal expressions as natural numbers.
He also contributed to proof thoery which helped to clairfy the connection between
- > Classical logic ->> Aristotle’s logic the original first order.
Gottlob Frege (8/ 11/ 1848–26 /7/1925) (Begriffsschrift )being one of the modern pioneers within this field. Frege, who is considered the founder of Analytic Philosophy, invented it to show all of mathematics was derivable from logic, and make arithmetic rigorous as David Hilbert (23/ 01/ 1862–14/ 02/ 1943) had done for geometry, the doctrine is known as logicism in the foundations of mathematics. The notation Frege used never caught on much.
-> Intuitionistic logic ->> also known as constructive logic refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof Systems of intuitionistic logic do not include the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic.
Formalized intuitionistic logic was originally developed by Arend Heyting (9 /5/ 1898–9/071980) to provide a formal basis for L. E. J. Brouwer’s (27/02/ 1881–2/12/ 1966) program of intuitionism.
Several systems of semantics for intuitionistic logic have been studied. One of these semantics' mirrors classical Boolean-valued semantics but uses Heyting algebras in place of Boolean Algebras. Another semantics uses Kripke models. These, however, are technical means for studying Heyting’s deductive system rather than formalizations of Brouwer’s original informal semantic intuitions. Semantical systems claim to capture such intuitions, due to offering meaningful concepts of constructive truth.
-> Modal logic ->> A collection of formal systems developed to represent statements about necessity and possibility. It plays a key role in philosophy of language, Epistemology, Metaphysics, and Natural language semantics.
incomplete results — dashed the hopes, held by some mathematicians, of discovering a formal system that would reduce the whole of mathematics to methods that (human) computers could carry out. It was in the course of his work on the Entscheidungsproblem that Turing invented the universal Turing machine, an abstract computing machine that encapsulates the fundamental logical principles of the digital computer.
The term “Entscheidunsproblem” was renamed to “Chruch-Turning Thesis”. Turner stated that everything a Human can do, the Turner Machine could do, Church in his work used instead the thesis that all human-computable functions are identical to what he called lambda-definable functions (functions on the positive integers whose values can be calculated by a process of repeated substitution). Turing showed in 1936 that Church’s thesis was equivalent to his own, by proving that every lambda-definable function is computable by the universal Turing machine and vice versa. In a review of Turing’s work, Church acknowledged the superiority of Turing’s formulation of the thesis over his own (which made no reference to computing machinery), saying that the concept of computability by a Turing machine “has the advantage of making the identification with effectiveness…evident immediately.”
Code Breaker — Breaking the Enigma Cipher.
BOMBE -> polish for ICE Cream, was the name of an Electro-Machine developed by Alan Turing and Gordan Welchman (15/ 06/ 1906–8/10/1985) whilst working with Computer Engineer's at Bletcher Park. It was used to help breaking the German Enigma codes and was (partly) based on the so-called BOMBA, an earlier machine developed by Polish mathematicians in 1938. From 1943 onwards, an improved version of the British BOMBE was built in the US by the US Navy and — independently — by the US Army.
The polish where the first to break the miliary variant of Enigma in 1932. A young Polish mathematician Marian Rejewski (16/ 08/1905 –13 /02/ 1980) had recovered the wiring of the military Enigma machine. Later joined with Henryk Zygalski (15/07/1908– 30 /08/ 1978) and Jerzy Rózyk (24/ 07/1909 — 9/ 01/ 1942) their success was based on information from a German spy by the name of Hans-Thilo Schmidt (codename Asche), and a commercial Enigma intercepted in the Polish mail. They then bought a commercial Enigma and used the gathered information to convert it into a military one. This converted machine is commonly known as the Polish Enigma.
“The Polish code breakers had no way out except with the mission. Vera had three: Marian Rejewski, Jerzy Rozycki, and Henryk Zygalski. Jerzy was with his wife, who had been advised along the way to strangle their baby because of German atrocities. She chose to care for the infant and urged Jerzy to go. He would never see his wife or child again.”
~ William Stevenson (Spymistress: The True Story of the Greatest Female Secret Agent of World War II)
From 1930 onwards, the Germans had been using a remarkably simple key management scheme, in which the randomly chosen message key was sent twice in encrypted form at the beginning of each message. This allowed the daily key to be recovered easily with hand methods. (A form of Hashing)
On 1 October 1936, the Germans stopped using six and started using five to eight of them. This defeated the hand methods and the Poles thought out a catalog attack based on the cycle length of the indicator permutations. Rejewski subsequently developed a machine to assist in building the catalog: the Cyclometer.
Building the catalog took well over a year, but when it was ready, it allowed the message key to be recovered in about 15 minutes.
On 1 November 1937, the Germans replaced the existing reflector (UKW A) for a new one (UKW B), and the Poles had to build a completely new catalog, which would take another year.
Then, on 15 September 1938, the Germans entirely changed the procedure for enciphering the message keys, and the catalog method had become completely useless. This prompted the Poles to produce new solutions, such as the Zygalski Sheets and the Bomba Kryptologiczna (cryptologic bomb), often abbreviated to Bomba.
Bomba is based on the principle that the random 3-letter message key is sent twice at the beginning of each message and that every now and then, a particular plaintext letter yields the same ciphertext letter three positions further on.
Although all Bomby were destroyed by the Poles in 1939, just before the German Army invaded Poland, Rejewski made a sketch based on his memories many years later. This sketch appeared in Brian Johnson’s book The Secret War in 1978. An improved version of this sketch appeared in a report of 1979, written by Marian Rejewski himself. This report was provided as an appendix to Władysław Kozaczuk’s book W kręgu Enigmy and was translated into English in 1984 ( Enigma : how the German machine cipher was broken, and how it was read by the Allies in World War Two : Kozaczuk, Władysław : Free Download, Borrow, and Streaming : Internet Archive)
Although the exact operation of the Bomba is still unknown, many have tried to explain its principle by reconstructing a theoretical model. A plausible attempt was made by David Link in Cryptologia in 2009.
Based on the information presented by the Poles Alan Turing developed a machine that could recover the key settings even if the Germans would drop the double encryption of the message key at the beginning of each message. The machine was called Bombe (later: Turing-Welchman Bombe) and was built by the British Tabulating Machine Company (BTM) in Letchworth, Hertfordshire (UK) under supervision of Harold Keen (1894–1973) nickname Doc.
Although the Bomba concept was known to Bletchley Park, Turing took a different approach. When the Germans had discovered the weakness, they gave up the double encipherment of the message indicator on most radio networks on 1 May 1940 1 rendering the Bomba useless
Turing designed the British Bombe in 1939. Compared to the Polish Bomba, it used a completely different approach. It assumed that a known (or guessed) plaintext, a so-called crib, is present at a certain position in the message. The bombs were built by the British Tabulating Company (BTM, later: ICL) at Letchworth (UK) under the supervision of Harold ‘Doc’ Keen The first machine, called ‘Victory’, was delivered at Bletchley Park on 18 March 1940.
Shortly afterwards, the Bombe was improved by adding the so-called diagonal board — an invention of fellow codebreaker Gordon Welchman which reduced the number of steps needed for the codebreaking effort. A second Bombe, with Welchman’s diagonal board present, was installed on 8 August 1940. The first machine (Victory) was later modified with a diagonal board as well.
During the war, over two hundred Turing-Welchman Bombes were built. To avoid the risk of losing them in case of a bomb attack, they were spread between Bletchley Park and its so-called Outstations in Wavendon, Adstock, Gayhurst, Eastcote and Stanmore, where WRNS, RAF-technicians and civilian personnel operated them.
Like the German Army, The Airforce and the Navy used a three-wheel Enigma machine with Steckerbrett (plug-board). The Navy called it the M3. Unlike the Army and the Navy however, the Navy used additional codebooks for shortening their messages. The shorter their radio broadcasts, the smaller the risk of Direction Finding (DF).
Because the head of the U-Boat section of the German Navy had his doubts, three extra wheels were introduced (VI, VII and VIII), exclusively for the Navy. But that wasn’t all he had changed. On 2 February 1942, completely unexpected, the German Navy introduced the Enigma M4, a four-wheel machine, exclusively for U-Boat communication. At the same time, they changed their codebooks, leaving the codebreakers at Bletchley Park in the dark.
The Enigma M4 had an extra rotor inserted between the third wheel and reflector As the Bombe was built specifically for breaking three-wheel Enigma traffic, it was not suitable for attacking the new M4 machine.
The code was changed overnight, and the rest of the Navy was still using the 3-wheel machine, Turing figured that the machines were somehow compatible.
Brition had a shortage of everything. It Took nine months to create M4.
Ever since their involvement in the war in 1942, the Americans had been pushing the Brits to share their knowledge about the Bombe and allow them to copy its design. Finally, in late 1942, when the British 4-wheel Bombe was facing production problems and the daily losses in the Battle of the Atlantic were accumulating, the Brits gave in, and allowed the US to build its own Bombe.
The US-Bombe was built by the National Cash Registers (NCR) in Dayton (Ohio, USA), where Joe Desch (23 /05/ 1907–03/ 08/ 1987) helped develop it.
Towards the end of 1942, Desch proposed a less elegant but more realistic approch: an electromechanical machine — like the UK Bombe — but much faster and more reliable as well. The US Navy immediately approved the project.
Desch set out to build the machine and had the first prototypes running by mid-1943. Although the initial design faced reliability problems, he managed to improve it. In the end, the US Bombe turned out to be reliable, fast, and effective. By December 1943, 120 machines had been installed. For the remainder of the war, the US managed the breaking of most of the German Naval Enigma traffic and in particular the messages of the dreaded German U-Boats.
After the war, it became clear that the US Bombe had helped to save thousands of lives.
After the war, all US Bombes were destroyed, except for one unit which has since become a permanent exhibit a the National Cryptologic Museum (NCM) in the USA.
None of the buildings at the former NCR site in Dayton (Ohio, US) have survived. They were taken down just before NCR moved its head office to Atlanta in 2009. All that reminds us of the highly secret work that was carried out in Building 26 by Joe Desch and his team.
In the UK, all British Bombes were destroyed or dismantled once the war was over. Not a single machine has survived. This has triggered a group of enthusiasts — led by John Harper — to start a rebuilding project in the mid-1990s. The aim of the project was to recreate a fully functional replica of a war-time Bombe machine, which was completed in 2007
The completed machine was on public display for many years at the Bletchley Park Museum as part of the permanent exhibition was relocated in 2018 to The National Museum of Computing (TNMOC) which is also located at Bletchley Park. It is demonstrated on a regular basis and can break real wartime messages.
Different versions of the Bombe exist.
Enigma was broken with help from Colossus, the first valve-based electronic digital computer, which was developed at Bletchley Park during WWII. It is even claimed in some books and TV documentaries. This claim is not correct however, as Colossus was used to break the far more advanced Lorenz SZ-40/42 cipher machine, which was used by OKW, Hitler’s High Command.
When the war was over Turing was recruited to the National Physical Laboratory (NPL) in London to create an electronic computer. His design for the Automatic Computing Engine (ACE) was the first complete specification of an electronic stored-program all-purpose digital computer. The Pilot Model ACE (1950) was built under Turing’s supervision ( The version that was created was not his original designs as the engineer's thought it too hard, hence creating a small version)
NPL lost the race to build the world’s first working electronic stored-program digital computer — an honor that went to the Royal Society Computing Machine Laboratory at the University of Manchester in June 1948. Discouraged by the delays at NPL, Turing took up the deputy directorship of the Computing Machine Laboratory in that year. His earlier theoretical concept of a universal Turing machine had been a fundamental influence on the Manchester computer project from the beginning. After Turing’s arrival at Manchester, his main contributions to the computer’s development were to design an input-output system — using Bletchley Park technology — and to design its programming system. He also wrote the first-ever programming manual, and his programming system was used in the Ferranti Mark I, the first marketable electronic digital computer (1951).
Turing was a founding father of artificial intelligence and of modern Cognitive Science, and he was a leading early exponent of the hypothesis that the human brain is in large part a digital computing machine.
Turing was elected a fellow of the Royal Society of London in March 1951, a High Honor. During this time, he was working on Artificial life. He published “The Chemical Basis of Morphogenesis” describing aspects of his research on the development of form and pattern in living organisms. Turing used Manchester’s Ferranti Mark I computer to model his hypothesized chemical mechanism for the generation of anatomical structure in animals and plants.
In the midst of this groundbreaking work, Turing was discovered dead in his bed, poisoned by cyanide. The official verdict was suicide, but no motive was established at the 1954 inquest. His death is often attributed to the hormone “treatment” he received at the hands of the authorities following his trial for being gay. Yet he died more than a year after the hormone doses had ended, and, in any case, the resilient Turing had borne that cruel treatment with what his close friend Peter Hilton called “amused fortitude.”
No conclusion is needed as his story continues with all the amazing stuff that is happening in AI.
