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Alan Turing
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Alan Turing

TORIma Academy — Mathematician / Computer Scientist

Alan Turing

Alan Turing

Alan Mathison Turing ( ; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical…

Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English polymath, excelling as a mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. His contributions were profoundly influential in the development of theoretical computer science, particularly through his formalization of the concepts of algorithm and computation with the Turing machine, which is considered a foundational model of a general-purpose computer. Turing is widely recognized as the father of theoretical computer science.

Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science.

Turing, born in London, spent his formative years in southern England. He completed his undergraduate studies at King's College, Cambridge, and subsequently obtained a doctorate from Princeton University in 1938. During World War II, Turing was employed by the Government Code and Cypher School at Bletchley Park, the United Kingdom's primary codebreaking facility, where he contributed to the generation of Ultra intelligence. He directed Hut 8, the unit tasked with German naval cryptanalysis. Turing developed innovative techniques to accelerate the decryption of German ciphers, notably enhancing the pre-war Polish bomba method, an electromechanical device designed to ascertain Enigma machine settings. His efforts were instrumental in deciphering intercepted communications, which significantly aided the Allied forces in overcoming the Axis powers during the Battle of the Atlantic and other critical conflicts.

Post-war, Turing was affiliated with the National Physical Laboratory, where he conceived the Automatic Computing Engine, a pioneering design for a stored-program computer. In 1948, Turing transitioned to Max Newman's Computing Machine Laboratory at the University of Manchester, contributing to the advancement of early Manchester computers and cultivating an interest in mathematical biology. His research included theoretical work on the chemical underpinnings of morphogenesis and predictions of oscillating chemical reactions, exemplified by the Belousov–Zhabotinsky reaction, which was empirically observed in the 1960s. Notwithstanding these significant achievements, his contributions remained largely unacknowledged during his lifetime, primarily due to the classification of much of his work under the Official Secrets Act.

In 1952, Turing faced prosecution for homosexual acts. He opted for hormone treatment, a process colloquially termed chemical castration, as an alternative to incarceration. Turing passed away on 7 June 1954, at the age of 41, due to cyanide poisoning. While an inquest concluded his death was a suicide, the available evidence also aligns with the possibility of accidental poisoning. Subsequent to a public campaign in 2009, then-British Prime Minister Gordon Brown issued an official public apology for "the appalling way [Turing] was treated". Queen Elizabeth II granted him a posthumous pardon in 2013. Informally, the term "Alan Turing law" designates a 2017 UK statute that retroactively pardoned individuals cautioned or convicted under historical legislation criminalizing homosexual acts.

Turing bequeathed a substantial legacy in mathematics and computing, which is now broadly acknowledged through various tributes, including statues, numerous dedications, and an annual award recognizing innovation in computing. His likeness is featured on the Bank of England £50 note, initially issued on 23 June 2021, coinciding with his birthday. In a 2019 BBC series, an audience poll designated Turing as the greatest scientist of the 20th century.

Cognitive scientist Douglas Hofstadter asserts: "Atheist, homosexual, eccentric, marathon-running mathematician, A. M. Turing was in large part responsible not only for the concept of computers, incisive theorems about their powers, and a clear vision of the possibility of computer minds, but also for the cracking of German ciphers during the Second World War. It is fair to say we owe much to Alan Turing for the fact that we are not under Nazi rule today."

Early Life and Education

Family

Alan Turing's birth occurred in Maida Vale, London, during a period when his father, Julius Mathison Turing, was on leave from his duties with the Indian Civil Service (ICS) under the British Raj administration. His father's posting was in Chatrapur, then part of the Madras Presidency and now located in Odisha state, India. Julius Mathison Turing was the son of the Reverend John Robert Turing, originating from a Scottish mercantile family with historical ties to the Netherlands, which also included a baronetcy. Turing's mother, Ethel Sara Turing (née Stoney), was the daughter of Edward Waller Stoney, who served as the chief engineer for the Madras Railways. The Stoney family constituted a Protestant Anglo-Irish gentry, with roots in both County Tipperary and County Longford; Ethel herself spent a significant portion of her early life in County Clare. Julius and Ethel formalized their union on October 1, 1907, at St. Bartholomew's Church of Ireland, situated on Clyde Road in Ballsbridge, Dublin.

Julius Turing's professional commitments with the ICS necessitated the family's relocation to British India, a region where his own grandfather had previously held the rank of general in the Bengal Army. Nevertheless, both Julius and Ethel expressed a strong desire for their children to be raised in Britain. Consequently, they established residence in Maida Vale, London, where Alan Turing was born on June 23, 1912. This birthplace is commemorated by a blue plaque affixed to the exterior of the building, which subsequently became the Colonnade Hotel. Turing's elder brother was John Ferrier Turing, who later became the father of Dermot Turing, the 12th Baronet of the Turing lineage. In 1922, Turing encountered Edwin Tenney Brewster's work, Natural Wonders Every Child Should Know, which he later attributed as a pivotal influence that ignited his interest in scientific inquiry.

Throughout Turing's early life, his father's civil service commission remained active, leading his parents to frequently commute between Hastings in the United Kingdom and India. During these periods, their two sons were entrusted to the care of a retired Army couple. In Hastings, Turing resided at Baston Lodge, located on Upper Maze Hill, St Leonards-on-Sea, a site now distinguished by a blue plaque. This commemorative plaque was unveiled on June 23, 2012, coinciding with the centenary of Turing's birth.

In 1927, Turing's parents acquired a residence in Guildford, which served as Turing's home during school holiday periods. This location is similarly commemorated with a blue plaque.

Educational Background

Turing's parents enrolled him in St Michael's, a primary institution situated at 20 Charles Road, St Leonards-on-Sea, where he attended from the age of six to nine. The headmistress of the school notably recognized his exceptional aptitude, remarking that while she had "clever boys and hardworking boys, Alan is a genius."

From January 1922 to 1926, Turing received his education at Hazelhurst Preparatory School, an independent institution located in the village of Frant, then in Sussex (now East Sussex). In 1926, at the age of 13, he matriculated at Sherborne School, an independent boarding school situated in the market town of Sherborne, Dorset, where he resided in Westcott House. The commencement of his first term coincided with the 1926 General Strike in Britain; however, Turing's resolve to attend was such that he undertook an unaccompanied 60-mile (97 km) bicycle journey from Southampton to Sherborne, pausing for an overnight stay at an inn.

Turing's inherent aptitude for mathematics and scientific disciplines was not universally appreciated by certain educators at Sherborne, whose pedagogical philosophy prioritized classical studies. The headmaster communicated to Turing's parents, expressing concern: "I hope he will not fall between two stools. If he is to stay at public school, he must aim at becoming educated. If he is to be solely a Scientific Specialist, he is wasting his time at a public school." Notwithstanding this perspective, Turing consistently demonstrated exceptional proficiency in his preferred subjects, successfully resolving advanced mathematical problems in 1927 without prior instruction in elementary calculus. By 1928, at the age of 16, Turing engaged with the works of Albert Einstein; he not only comprehended the material but potentially inferred Einstein's challenges to Newtonian mechanics from a text where such critiques were not explicitly stated.

Christopher Morcom

During his time at Sherborne, Turing developed a profound friendship with a peer, Christopher Collan Morcom (born July 13, 1911; died February 13, 1930), a relationship often characterized as Turing's inaugural romantic attachment. This connection served as a source of inspiration for Turing's subsequent pursuits; however, it was tragically terminated by Morcom's demise in February 1930. His death resulted from complications arising from bovine tuberculosis, which he had contracted several years prior through the consumption of infected cow's milk.

This incident profoundly affected Turing, who channeled his grief into intensified academic pursuits, focusing on the scientific and mathematical subjects he had explored with Morcom. In a letter addressed to Morcom's mother, Frances Isobel Morcom (née Swan), Turing articulated:

I am sure I could not have found anywhere another companion so brilliant and yet so charming and unconceited. I regarded my interest in my work, and in such things as astronomy (to which he introduced me) as something to be shared with him and I think he felt a little the same about me ... I know I must put as much energy if not as much interest into my work as if he were alive, because that is what he would like me to do.

Turing maintained a relationship with Morcom's mother for an extended period following Morcom's death, characterized by an exchange of correspondence and gifts, often coinciding with Morcom's birthday. On February 13, 1933, a day prior to the third anniversary of Morcom's passing, Turing wrote to Mrs. Morcom:

I expect you will be thinking of Chris when this reaches you. I shall too, and this letter is just to tell you that I shall be thinking of Chris and of you tomorrow. I am sure that he is as happy now as he was when he was here. Your affectionate Alan.

It has been posited by some scholars that Morcom's death contributed to the development of Turing's atheism and materialism. Evidently, during this period, he still adhered to beliefs in concepts such as a spirit, distinct from the physical body and capable of surviving death. In a subsequent letter, also addressed to Morcom's mother, Turing expressed:

Personally, I believe that spirit is really eternally connected with matter but certainly not by the same kind of body ... as regards the actual connection between spirit and body I consider that the body can hold on to a 'spirit', whilst the body is alive and awake the two are firmly connected. When the body is asleep I cannot guess what happens but when the body dies, the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.

University Education and Early Work on Computability

Following his graduation from Sherborne, Turing sought scholarships from various Cambridge colleges, including Trinity and King's, ultimately securing an £80 per annum scholarship (approximately £4,300 in 2023 equivalent) to attend King's College. There, he pursued his undergraduate studies in Schedule B from February 1931 to November 1934, graduating with first-class honours in mathematics. His senior-year dissertation, On the Gaussian error function, submitted in November 1934, demonstrated a variant of the central limit theorem and was formally accepted on March 16, 1935. In the spring of that year, Turing commenced his master's course (Part III), which he concluded in 1937. Concurrently, he published his inaugural academic paper, a one-page article titled Equivalence of left and right almost periodicity (submitted on April 23), which appeared in the tenth volume of the Journal of the London Mathematical Society. Subsequently, based on the merit of his dissertation, Turing was elected a Fellow of King's College, where he also served as a lecturer. Unbeknownst to Turing, however, the specific iteration of the theorem he had proven had previously been established by Jarl Waldemar Lindeberg in 1922. Nevertheless, the committee recognized the originality of Turing's methodology, deeming his work meritorious for the fellowship. Abram Besicovitch's committee report even asserted that had Turing's work been published prior to Lindeberg's, it would have constituted "an important event in the mathematical literature of that year".

From spring 1935 to spring 1936, Turing, concurrently with Alonzo Church, investigated the decidability of problems, building upon Gödel's incompleteness theorems. By mid-April 1936, Turing had submitted the initial draft of his research to Max Newman. During the same month, Church published his paper, An Unsolvable Problem of Elementary Number Theory, which presented conclusions analogous to Turing's then-unpublished findings. Subsequently, on May 28 of the same year, Turing completed and submitted his 36-page manuscript, titled "On Computable Numbers, with an Application to the Entscheidungsproblem," for publication. This seminal work appeared in the Proceedings of the London Mathematical Society journal, released in two segments: the first on November 30 and the second on December 23. Within this publication, Turing re-conceptualized Kurt Gödel's 1931 findings concerning the inherent limitations of proof and computation. He achieved this by substituting Gödel's universal arithmetic-based formal language with a set of formal, simplified hypothetical mechanisms, which subsequently gained recognition as Turing machines. The Entscheidungsproblem, or decision problem, was initially formulated by the German mathematician David Hilbert in 1928. Turing demonstrated that his "universal computing machine" possessed the capacity to execute any imaginable mathematical computation, provided it could be expressed algorithmically. Furthermore, he established the insolvability of the decision problem by initially proving the undecidability of the halting problem for Turing machines, meaning no algorithm can determine if a Turing machine will eventually cease operation. This particular paper has been acclaimed as "easily the most influential mathematics paper in history."

While Turing's proof appeared soon after Church's analogous demonstration, which utilized lambda calculus, Turing's methodology is notably more comprehensible and intuitive. His work also introduced the concept of a 'Universal Machine' (presently termed a universal Turing machine), positing that such a device could emulate the functions of any other computational apparatus (a capability also inherent in Church's lambda calculus). In accordance with the Church–Turing thesis, both Turing machines and lambda calculus are theoretically capable of performing any computable function. John von Neumann recognized Turing's paper as the foundational source for the core concept of the modern computer. Currently, Turing machines remain a fundamental subject of inquiry within the theory of computation.

Between September 1936 and July 1938, Turing primarily pursued his studies under Church at Princeton University, serving as a Jane Eliza Procter Visiting Fellow during his second year. Beyond his strictly mathematical endeavors, he engaged in cryptology research and constructed three out of four stages of an electro-mechanical binary multiplier. In June 1938, he earned his PhD from Princeton's Department of Mathematics; his doctoral dissertation, Systems of Logic Based on Ordinals, presented the concept of ordinal logic and the idea of relative computing, wherein Turing machines are enhanced with "oracles" to facilitate the investigation of problems intractable for standard Turing machines. Although von Neumann sought to employ him as a postdoctoral assistant, Turing opted to return to the United Kingdom.

Professional Trajectory and Research Contributions

Upon his return to Cambridge, Turing attended a series of lectures delivered in 1939 by Ludwig Wittgenstein, focusing on the foundational principles of mathematics. These lectures have been meticulously reconstructed verbatim from student notes, incorporating interjections from Turing and other attendees. Turing and Wittgenstein engaged in significant debate and disagreement, with Turing advocating for formalism while Wittgenstein asserted that mathematics invents truths rather than discovering absolute ones.

Cryptanalytic Operations

Throughout the Second World War, Turing played a pivotal role in the decryption of German ciphers at Bletchley Park. According to historian and wartime codebreaker Asa Briggs, "Exceptional talent, indeed genius, was required at Bletchley, and Turing possessed that genius."

From September 1938, Turing commenced part-time employment with the Government Code and Cypher School (GC&CS), the United Kingdom's primary codebreaking agency. His primary focus, alongside Dilly Knox, a senior GC&CS cryptanalyst, was the cryptanalysis of the Enigma cipher machine employed by Nazi Germany. Following a July 1939 conference near Warsaw, where the Polish Cipher Bureau disclosed the Enigma machine's rotor wiring and decryption methodology to British and French representatives, Turing and Knox devised a more comprehensive solution. The Polish technique, however, depended on an insecure indicator procedure that the Germans subsequently altered in May 1940. Turing's methodology was more universally applicable, employing crib-based decryption, and he subsequently developed the functional specifications for the bombe, an enhanced version of the Polish Bomba.

On September 4, 1939, the day following the United Kingdom's declaration of war against Germany, Turing reported for duty at Bletchley Park, which served as the wartime operational headquarters for GC&CS. Consistent with all personnel assigned to Bletchley, he was mandated to sign the Official Secrets Act, thereby committing to absolute confidentiality regarding his work at the facility, with explicit provisions for severe legal repercussions in the event of non-compliance.

The design specification of the bombe represented the initial achievement among five significant cryptanalytical breakthroughs attributed to Turing during the conflict. His subsequent contributions included: deciphering the indicator procedure utilized by the German navy; formulating a statistical methodology, designated Banburismus, to enhance the operational efficiency of the bombes; devising a process, termed Turingery, for determining the cam configurations of the Lorenz SZ 40/42 (Tunny) cipher machine's wheels; and, nearing the war's conclusion, the creation of a portable secure voice scrambler, codenamed Delilah, at Hanslope Park.

Turing significantly advanced cryptology through his innovative application of statistical techniques to optimize the evaluation of various possibilities within the code-breaking paradigm. He authored two seminal papers exploring mathematical methodologies, entitled The Applications of Probability to Cryptography and Paper on Statistics of Repetitions. These documents held such profound importance for GC&CS and its successor organization, GCHQ, that they remained classified and were not declassified for public release to the UK National Archives until April 2012, coinciding with the eve of his birth centenary. A GCHQ mathematician, identified solely as "Richard," commented at the time that the seventy-year restriction of these contents under the Official Secrets Act underscored their critical significance and enduring relevance to post-war cryptanalysis.

He stated that the prolonged restriction of these contents "demonstrates their immense foundational importance to our field." The documents elucidated the application of "mathematical analysis to ascertain the most probable settings, thereby facilitating their rapid testing." Richard further indicated that GCHQ had thoroughly extracted all pertinent information from the two papers and was consequently "content for their release into the public domain."

At Bletchley Park, Turing was widely recognized for his eccentricities. His colleagues commonly referred to him as "Prof," and his authoritative work on the Enigma machine was colloquially termed the "Prof's Book." Historian Ronald Lewin documented the observations of Jack Good, a fellow cryptanalyst who collaborated with Turing, regarding his colleague:

Annually, during the initial week of June, he experienced severe hay fever, prompting him to cycle to his office while wearing a service gas mask to mitigate pollen exposure. His bicycle was afflicted by a recurring mechanical issue: the chain frequently disengaged. Rather than seeking repair, he meticulously counted pedal rotations, dismounting preemptively to manually readjust the chain. A further manifestation of his eccentric behavior involved chaining his personal mug to radiator pipes to deter theft.

Peter Hilton documented his professional interactions with Turing within Hut 8 in his publication, "Reminiscences of Bletchley Park," which is featured in A Century of Mathematics in America:

Encountering a true genius is an infrequent occurrence. Within academic circles, scholars frequently experience the intellectual stimulation provided by gifted peers. While their contributions are admirable and their origins often discernible, one might even perceive the potential to have independently conceived similar ideas. In contrast, engaging with the intellect of a genius evokes a distinct sensation, characterized by profound wonder and excitement, stemming from the recognition of an intelligence and sensibility of unparalleled depth and innovation. Alan Turing exemplified such genius; individuals, including the author, who had the extraordinary and unforeseen opportunity, born from the unique demands of the Second World War, to collaborate with and befriend Turing, attest to an unforgettable and immensely beneficial experience.

During his tenure at Bletchley, Turing, an accomplished long-distance runner, would sometimes run the 40 miles (64 km) to London for meetings, demonstrating a capacity for world-class marathon performance. He attempted to qualify for the 1948 British Olympic team but was impeded by an injury. Notably, his marathon trial time was merely 11 minutes slower than the 2 hours 35 minutes achieved by British Olympic silver medallist Thomas Richards. His exceptional ability was evident when he, running solo, overtook the Walton Athletic Club group, revealing him to be their premier runner. When questioned about the intensity of his training regimen, he responded:

My profession is so demanding that vigorous running serves as the sole means to alleviate mental strain and achieve a sense of liberation.

Ascertaining the precise impact of Ultra intelligence on the war is inherently difficult, given the complexities of counterfactual history and the speculative nature of determining alternative outcomes had specific historical events unfolded differently. Nevertheless, official war historian Harry Hinsley posited that these efforts curtailed the conflict in Europe by over two years. He qualified this assessment by noting that it did not incorporate the influence of the atomic bomb or other potential developments.

Upon the cessation of hostilities, a memorandum was disseminated to all Bletchley Park personnel, reiterating that the Official Secrets Act's mandate for silence extended indefinitely beyond the war's conclusion. Consequently, despite Turing's appointment as an Officer of the Order of the British Empire (OBE) by King George VI in 1946 for his wartime contributions, his specific work remained classified for an extended period.

Bombe

Shortly after his arrival at Bletchley Park, Turing designed an electromechanical device named the bombe, which proved more effective at deciphering Enigma messages than the Polish bomba kryptologiczna, the source of its nomenclature. Augmented by an improvement proposed by mathematician Gordon Welchman, the bombe emerged as a principal, and the foremost automated, instrument for decrypting Enigma-enciphered communications.

The bombe systematically sought potential correct settings for an Enigma message, encompassing rotor order, rotor settings, and plugboard configurations, by utilizing a suitable crib, defined as a segment of probable plaintext. For every conceivable rotor setting—ranging from approximately 1019 states to 1022 states for the four-rotor U-boat variant—the bombe executed an electromechanically implemented sequence of logical deductions derived from the crib.

The bombe was designed to identify contradictions, thereby eliminating incorrect settings and proceeding to the subsequent possibility. The majority of potential settings generated contradictions and were consequently discarded, leaving a limited number for thorough examination. A contradiction manifested when an enciphered character was decrypted back into its original plaintext form, an outcome rendered impossible by the Enigma's design. The inaugural bombe was operationalized on March 18, 1940.

Action This Day

By late 1941, Turing and his colleagues, cryptanalysts Welchman, Hugh Alexander, and Stuart Milner-Barry, experienced frustration. Despite establishing an effective system for decrypting Enigma signals, which built upon Polish foundational work, their operational capacity was constrained by insufficient personnel and a limited number of bombes, preventing the translation of all intercepted communications. During the summer, significant progress was achieved, leading to a reduction in shipping losses to below 100,000 tons monthly; however, a critical need for Previous attempts to secure increased staffing and funding for more bombes through official channels had proven unsuccessful.

On October 28, the group, with Turing listed first, directly petitioned Winston Churchill, detailing their operational challenges. Their correspondence highlighted the modest scale of their requirements relative to the substantial military expenditures in personnel and finances, and in contrast to the significant support they could provide to the armed forces. Andrew Hodges, Turing's biographer, subsequently noted that "This letter had an electric effect." Churchill responded by issuing a memorandum to General Ismay, stating: "ACTION THIS DAY. Make sure they have all they want on extreme priority and report to me that this has been done." By November 18, the head of the secret service confirmed that all necessary actions were being implemented. Although the Bletchley Park cryptographers remained unaware of the Prime Minister's direct intervention, Milner-Barry later recounted, "All that we did notice was that almost from that day the rough ways began miraculously to be made smooth." Ultimately, over two hundred bombes were operational by the conclusion of the war.

Hut 8 and the Naval Enigma

Turing undertook the challenging task of decrypting the German naval Enigma, motivated by the lack of other dedicated efforts in this area, which allowed him exclusive focus. By December 1939, he successfully resolved the critical component of the naval indicator system, a system notably more intricate than those employed by other military branches.

Concurrently, he conceptualized Banburismus, a sequential statistical methodology—later termed sequential analysis by Abraham Wald—designed to facilitate the decryption of naval Enigma. Turing expressed initial uncertainty regarding its practical efficacy, stating, "though I was not sure that it would work in practice, and was not, in fact, sure until some days had actually broken." For this technique, he devised a metric for the weight of evidence, which he designated as the ban. Banburismus enabled the elimination of specific Enigma rotor sequences, thereby significantly decreasing the time required for testing settings on the bombes. Subsequently, this sequential accumulation of evidence, utilizing decibans (one-tenth of a ban), was applied in the cryptanalysis of the Lorenz cipher.

In November 1942, Turing traveled to the United States, where he collaborated with US Navy cryptanalysts in Washington on naval Enigma decryption and bombe development. His itinerary also included a

Turing's assessment of the American bombe design was notably unenthusiastic, as evidenced by his remarks:

The American Bombe programme was to produce 336 Bombes, one for each wheel order. I used to smile inwardly at the conception of Bombe hut routine implied by this programme, but thought that no particular purpose would be served by pointing out that we would not really use them in that way. Their test (of commutators) can hardly be considered conclusive as they were not testing for the bounce with electronic stop finding devices. Nobody seems to be told about rods or offiziers or banburismus unless they are really going to do something about it.

During this visit, Turing also contributed to the development of secure speech devices at Bell Labs. He subsequently returned to Bletchley Park in March 1943. In his absence, Hugh Alexander had formally taken over as the head of Hut 8, a role he had occupied de facto for a considerable period, given Turing's limited engagement in the section's daily operations. Upon his return, Turing transitioned into a general consultancy role for cryptanalysis at Bletchley Park.

Alexander documented Turing's contributions as follows:

It is unequivocally established that Turing's contributions were the most significant determinant of Hut 8's success. In the initial phases, he was the sole cryptographer to recognize the problem's solvability and undertake its resolution. He was not only principally accountable for the foundational theoretical advancements within the Hut but also shared primary recognition with Welchman and Keen for the bombe's development. While absolute indispensability is rarely asserted, Turing's role in Hut 8 was demonstrably critical. Pioneering efforts often recede from collective memory as subsequent experience and established routines simplify complex tasks, and numerous personnel within Hut 8 perceived that the profound impact of Turing's contributions remained largely unappreciated externally.

Turingery

In July 1942, Turing developed a methodology designated as Turingery (or colloquially Turingismus) for use against Lorenz cipher messages generated by the German Geheimschreiber (secret writer) machine. This device was a teleprinter rotor cipher attachment, internally designated Tunny at Bletchley Park. Turingery constituted a wheel-breaking technique, specifically a procedure for determining the cam configurations of Tunny's rotors. Turing additionally facilitated the introduction of Tommy Flowers to the Tunny team; Flowers, under Max Newman's direction, subsequently constructed the Colossus computer. This machine, recognized as the world's inaugural programmable digital electronic computer, superseded the less sophisticated Heath Robinson and enabled the effective application of statistical decryption methods due to its enhanced processing speed. It has been erroneously asserted that Turing played a pivotal role in the Colossus computer's design. While Turingery and the statistical methodology of Banburismus undeniably influenced the cryptanalytic strategies for the Lorenz cipher, Turing himself was not directly engaged in the Colossus's development.

Delilah

Subsequent to his engagement at Bell Labs in the United States, Turing investigated the concept of electronically encrypting speech within telephonic networks. During the latter stages of the conflict, he transferred to the Secret Service's Radio Security Service (subsequently HMGCC) at Hanslope Park. At this location, he advanced his expertise in electronics, aided by REME officer Donald Bayley. Collaboratively, they commenced the design and fabrication of a portable secure voice communication device, designated Delilah. Although conceived for diverse applications, the machine proved unsuitable for long-distance radio transmission. Ultimately, Delilah's completion occurred too late for wartime deployment. Despite the system's full functionality, evidenced by Turing's demonstration to officials involving the encryption and decryption of a Winston Churchill speech recording, Delilah was not formally adopted. Turing additionally provided consultancy to Bell Labs regarding the development of SIGSALY, a secure voice system implemented during the concluding years of the war.

Early computers and the Turing test

From 1945 to 1947, Turing resided in Hampton, London, concurrently engaged in the design of the Automatic Computing Engine (ACE) at the National Physical Laboratory (NPL). On February 19, 1946, he presented a seminal paper outlining the first comprehensive design for a stored-program computer. While von Neumann's unfinished First Draft of a Report on the EDVAC preceded Turing's publication, it offered considerably less detail. John R. Womersley, Superintendent of the NPL Mathematics Division, noted that it "contains a number of ideas which are Dr. Turing's own".

Despite ACE's conceptual viability, the constraints imposed by the Official Secrets Act, pertaining to his wartime activities at Bletchley Park, precluded Turing from elucidating the foundational principles of his analysis concerning the operation of a computer system integrating human operators. Consequently, the project's initiation was delayed, leading to his disillusionment. In late 1947, he commenced a sabbatical year at Cambridge, during which he authored a foundational treatise titled Intelligent Machinery, which remained unpublished until after his death. Concurrently with his Cambridge sabbatical, the Pilot ACE was constructed in his absence. This prototype executed its inaugural program on May 10, 1950, and significantly influenced numerous subsequent global computer designs, notably the English Electric DEUCE and the American Bendix G-15. The complete iteration of Turing's ACE was not realized until post-mortem.

The memoirs of German computer pioneer Heinz Billing, from the Max Planck Institute for Physics and published by Genscher, Düsseldorf, document a meeting between Turing and Konrad Zuse. This encounter occurred in Göttingen in 1947, structured as a colloquium. Attendees included Womersley, Turing, and Porter representing England, alongside German researchers such as Zuse, Walther, and Billing. Additional details are provided in Herbert Bruderer's Konrad Zuse und die Schweiz.

In 1948, Turing received an appointment as a reader within the Mathematics Department at the University of Manchester. His residence was located at "Copper Folly," 43 Adlington Road, Wilmslow. The following year, he assumed the role of deputy director at the Computing Machine Laboratory, contributing to the software development for the Manchester Mark 1, one of the pioneering stored-program computers. Turing authored the initial version of the Programmer's Manual for this machine, gained election to the Manchester Literary and Philosophical Society, and was engaged by Ferranti as a consultant for the development of their commercialized Ferranti Mark 1 machine. Ferranti continued to remunerate him for his consultancy services until his demise. Concurrently, he pursued more abstract mathematical research, and in his seminal paper "Computing Machinery and Intelligence," Turing explored the challenge of artificial intelligence, proposing an experiment subsequently termed the Turing test, which aimed to establish a criterion for machine intelligence. The core concept posited that a computer could be deemed capable of "thinking" if a human interlocutor, through conversational interaction, could not distinguish it from a human. Within the same publication, Turing advocated for developing a simpler program to emulate a child's mind, which could then undergo an educational process, rather than attempting to simulate an adult mind directly. A reverse application of the Turing test is extensively employed on the Internet through CAPTCHA tests, designed to ascertain whether a user is human or a computer.

In 1948, Turing collaborated with his former undergraduate colleague, D.G. Champernowne, to commence the development of a chess program intended for a hypothetical computer. The program, completed by 1950, was christened Turochamp. An attempt to implement it on a Ferranti Mark 1 in 1952 proved unsuccessful, as the computer lacked the requisite processing power to execute the program. Consequently, Turing manually "executed" the program by following the algorithmic instructions page by page and performing the moves on a chessboard, with each move requiring approximately thirty minutes. This game was documented. Garry Kasparov noted that Turing's program exhibited a "recognizable game of chess." While the program was defeated by Turing's colleague Alick Glennie, anecdotal accounts suggest it secured a victory against Champernowne's wife, Isabel.

The Turing test stands as a significant, characteristically provocative, and enduring contribution to the ongoing discourse surrounding artificial intelligence, a debate that has persisted for over half a century.

Pattern Formation and Mathematical Biology

In 1951, at the age of 39, Turing shifted his focus to mathematical biology, culminating in the publication of his seminal work, "The Chemical Basis of Morphogenesis," in January 1952. His research centered on morphogenesis, the biological process governing the formation of patterns and structures in living organisms. Turing posited that a reaction–diffusion system, involving chemicals reacting and diffusing spatially, could elucidate the primary mechanisms of morphogenesis. He employed systems of partial differential equations to model catalytic chemical reactions. For instance, an autocatalytic reaction, where a catalyst A is essential for a reaction that subsequently generates more of catalyst A, exhibits positive feedback amenable to modeling with nonlinear differential equations. Turing demonstrated that distinct patterns could emerge if the chemical reaction not only generated catalyst A but also an inhibitor B, which decelerated A's production. If A and B then diffused at disparate rates within a medium, this differential diffusion could establish regions where either A or B predominated. Determining the precise extent of these patterns would have necessitated substantial computational power, which was not readily accessible in 1951; consequently, Turing relied on linear approximations to manually solve the equations. These manual computations yielded qualitatively accurate results, predicting, for example, a homogeneous mixture exhibiting regularly spaced, fixed red spots. Concurrently, Russian biochemist Boris Belousov conducted experiments yielding comparable outcomes; however, his findings faced publication barriers due to prevailing biases suggesting such phenomena contravened the second law of thermodynamics. Belousov remained unaware of Turing's publication in the Philosophical Transactions of the Royal Society.

Despite preceding the elucidation of DNA's structure and function, Turing's research on morphogenesis retains contemporary significance and is recognized as a foundational contribution to mathematical biology. A portion of this research sought to comprehend plant phyllotaxy, particularly the formation of plant primordia in a ring around the apical meristem during growth and development, which often follows Fibonacci sequences. An early practical application of Turing's theory was James Murray's explanation for the characteristic spot and stripe patterns observed on the fur of various feline species. Subsequent investigations indicate that Turing's framework can partially account for the development of structures such as "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that positions the heart on the left side of the chest". In 2012, Sheth et al. demonstrated that in mice, the deletion of Hox genes leads to an increased number of digits without altering overall limb size, implying that Hox genes regulate digit formation by modulating the wavelength of a Turing-type mechanism. Additional papers related to this work became accessible only upon the publication of the Collected Works of A. M. Turing in 1992.

In 2023, a study presented by the American Physical Society experimentally validated Turing's mathematical model hypothesis. The experiment involved cultivating chia seeds in uniform layers within trays, subsequently manipulating moisture availability. Researchers systematically adjusted parameters corresponding to those in Turing's equations, which resulted in the emergence of patterns analogous to those observed in natural ecosystems. This investigation is considered the inaugural instance where experiments utilizing living vegetation have empirically confirmed Turing's mathematical insights.

Personal Life

Hidden Valuables

During the 1940s, concerns regarding the potential loss of his assets amidst a German invasion prompted Turing to secure his savings. To safeguard these funds, he acquired two silver bars, totaling 3,200 oz (90 kg) and valued at £250 (equivalent to £8,000 adjusted for inflation or £48,000 at spot price in 2022), which he subsequently interred in a wooded area adjacent to Bletchley Park. Upon his return to retrieve the silver, Turing discovered he could not decipher his own cryptographic notes detailing the precise location of the hidden valuables. This inability, compounded by subsequent renovations in the area, resulted in his permanent inability to recover the silver.

Engagement

In 1941, Turing proposed marriage to Joan Clarke, a fellow mathematician and cryptanalyst with whom he collaborated in Hut 8; however, their engagement was brief. Following his disclosure of his homosexuality to Clarke, who reportedly remained "unfazed" by the revelation, Turing concluded that he could not proceed with the marriage.

Chess

Turing devised a hybrid chess variant, predating chess boxing, known as round-the-house chess. This game involved one player executing a chess move, then physically running around the house, while the opponent was required to complete their move before the first player's return.

Conviction for Homosexuality and Gross Indecency

In December 1951, Turing encountered Arnold Murray, an unemployed 19-year-old, on Manchester's Oxford Road, near the Regal Cinema, and subsequently invited him to lunch. Their subsequent meetings led to the initiation of an intimate relationship in January 1952. On January 23, Turing's residence in Wilmslow was burgled. Murray informed Turing of his acquaintance with the burglar, prompting Turing to report the incident to the police. During the ensuing investigation, Turing disclosed his sexual relationship with Murray. Given that homosexual acts constituted criminal offenses in the United Kingdom at that time, both individuals faced charges of "gross indecency" under Section 11 of the Criminal Law Amendment Act 1885. Preliminary committal proceedings for the trial occurred on February 27, during which Turing's solicitor "reserved his defence," meaning no arguments or evidence were presented to counter the allegations. These proceedings took place at the Sessions House in Knutsford.

Following counsel from his brother and solicitor, Turing subsequently entered a plea of guilty. The case, formally titled Regina v. Turing and Murray, proceeded to trial on March 31, 1952. Turing received a conviction and was presented with an alternative between incarceration and probation. The terms of his probation stipulated his consent to undergo hormonal interventions intended to diminish libido, commonly referred to as "chemical castration." He opted for injections of stilboestrol, then known as diethylstilbestrol (DES), a synthetic estrogen. This feminizing treatment was administered for a period of one year, resulting in impotence and the development of breast tissue. Turing articulated in a letter, "no doubt I shall emerge from it all a different man, but quite who I've not found out." Murray, conversely, received a conditional discharge.

Turing's conviction resulted in the revocation of his security clearance, thereby precluding his continued cryptographic consultancy for GCHQ, the British signals intelligence agency established in 1946 as a successor to GC&CS. Despite this, he retained his academic position. The trial occurred merely months after the defection of Guy Burgess and Donald Maclean to the Soviet Union in summer 1951, an event that prompted the Foreign Office to classify individuals known to be homosexual as potential security risks.

Subsequent to his 1952 conviction, Turing was denied entry to the United States, although he retained the freedom to travel to other European nations. During the summer of 1952, he traveled to Norway, a country exhibiting greater tolerance towards homosexual individuals. Among the acquaintances he made there was Kjell Carlson. Carlson's intention to Concurrently, Turing commenced consultations with psychiatrist Franz Greenbaum, with whom he developed a positive rapport, and who subsequently became a family friend.

Demise

On June 8, 1954, Turing's housekeeper discovered him deceased at his residence on 43 Adlington Road, Wilmslow. A post-mortem examination conducted that evening concluded that he had died the preceding day at the age of 41, with cyanide poisoning identified as the cause of death. Upon the discovery of his body, a half-eaten apple was found beside his bed. Although the apple was not subjected to cyanide testing, it was hypothesized to be the vehicle through which Turing ingested a lethal dose.

John, Turing's brother, identified the body the subsequent day and, following Franz Greenbaum's counsel, accepted the inquest's verdict due to the minimal likelihood of proving the death accidental. The inquest, conducted the next day, concluded that suicide was the cause of death. However, his nephew, author Dermot Turing, disputes any connection between Turing's conviction or hormone treatment and his demise. He highlights that the conviction concluded in 1952 and the treatment ceased the subsequent year. Moreover, no physiological evidence indicated that the treatment adversely affected his uncle's mental state, and Turing had recently compiled a list of professional tasks to address upon returning to his office after a public holiday. An alternative hypothesis suggests Turing might have accidentally inhaled cyanide fumes from an electroplating experiment conducted in his spare room, noting his habit of consuming an apple before bed and often leaving it partially eaten.

Turing's cremation occurred at Woking Crematorium on 12 June 1954, merely two days after his death. Only his mother, brother, and Lyn Newman were present, and his ashes were dispersed within the crematorium gardens, mirroring the disposition of his father's remains. Turing's mother, who was vacationing in Italy at the time of his passing, returned home following the inquest. She consistently rejected the official suicide verdict.

Philosopher Jack Copeland has raised doubts regarding several elements of the coroner's original verdict. He proposed an alternative explanation for Turing's death: the inadvertent inhalation of cyanide fumes originating from an apparatus employed for electroplating gold onto spoons, where potassium cyanide served as the gold solvent. Turing maintained such equipment in his small spare room. Copeland observed that the autopsy results aligned more closely with cyanide inhalation than with its ingestion. Additionally, Turing routinely consumed an apple before retiring, frequently leaving it partially eaten. Moreover, Turing reportedly endured his legal challenges and hormone therapy (which had ceased a year prior) "with good humour" and exhibited no indications of despondency before his passing. He had even documented a list of responsibilities he intended to fulfill upon his return to the office after the holiday weekend. Turing's mother maintained that the ingestion was accidental, stemming from her son's imprudent storage of laboratory chemicals. Andrew Hodges, Turing's biographer, posited that Turing intentionally orchestrated his death to appear accidental, thereby protecting his mother from the truth of his suicide.

Further skepticism regarding the suicide hypothesis has been introduced by John W. Dawson Jr., who, in his critique of Hodges' biography, referenced "Turing's vulnerable position in the Cold War political climate." Dawson highlighted that Turing was discovered deceased by a maid, "lying neatly in his bed"—a posture inconsistent with the struggle typically associated with cyanide-induced suffocation. Furthermore, Turing had not communicated any suicidal intentions to his acquaintances nor had he taken steps to organize his personal affairs.

Both Hodges and subsequent biographer David Leavitt have theorized that Turing may have been re-enacting a scene from the 1937 Walt Disney film Snow White and the Seven Dwarfs, which was his preferred fairy tale. Both scholars observed that Turing, as Leavitt articulated, derived "an especially keen pleasure in the scene where the Wicked Queen immerses her apple in the poisonous brew."

Another hypothesis posits that Turing's inclination towards fortune-telling might have contributed to a depressed state. In his youth, a fortune-teller had predicted his genius. In mid-May 1954, shortly preceding his death, Turing chose to consult a fortune-teller once more during an excursion to St Annes-on-Sea with the Greenbaum family. Barbara, the Greenbaums' daughter, recounted the event:

The day was described as pleasantly sunny, with Alan exhibiting a cheerful disposition as they embarked on their outing. Subsequently, he proposed visiting the Pleasure Beach at Blackpool. Upon locating a fortune-teller's tent, Alan expressed a desire to enter, prompting the group to await his return. However, his previously bright and cheerful demeanor had transformed into a pale, trembling, and horror-stricken expression. Although the specific content of the fortune-teller's pronouncement remained unknown, it was evident that he was profoundly distressed. This encounter was likely the final occasion they saw him before learning of his suicide.

Government Apology and Pardon

In August 2009, British programmer John Graham-Cumming initiated a petition advocating for an official apology from the British government regarding Alan Turing's prosecution for homosexuality. This petition garnered over 30,000 signatures, prompting Prime Minister Gordon Brown to issue a statement on September 10, 2009, in which he formally apologized and characterized Turing's treatment as "appalling."

Numerous individuals have collectively sought justice for Alan Turing and acknowledgment of the egregious manner in which he was treated. Although Turing's case was processed according to the prevailing laws of that era, and historical events cannot be reversed, his treatment was undeniably unjust. I am therefore gratified to express the profound regret felt by myself and the entire nation for the events that transpired. Consequently, on behalf of the British government and all those who enjoy freedom due to Alan's contributions, I am immensely proud to declare: we offer our apologies; you merited significantly better treatment.

In December 2011, William Jones, alongside his Member of Parliament, John Leech, launched an e-petition advocating for a posthumous pardon from the British government for Alan Turing's conviction of "gross indecency."

This petition formally requests that His Majesty's Government grant a pardon to Alan Turing for his conviction of "gross indecency." In 1952, Turing was found guilty of "gross indecency" with another man, subsequently being compelled to undergo "organo-therapy," a form of chemical castration. Tragically, two years later, at the age of 41, he died by suicide from cyanide poisoning. Alan Turing's profound despair and premature demise were consequences of actions by the very nation he had significantly contributed to safeguarding. This historical episode continues to represent a blemish on the British government and its national history. A pardon could contribute substantially to rectifying this injustice and serve as an implicit apology to numerous other gay men, less prominent than Alan Turing, who were similarly subjected to these discriminatory statutes.

The petition accumulated more than 37,000 signatures and was subsequently presented to Parliament by John Leech, the Member of Parliament for Manchester. However, the request for a pardon was met with discouragement from Justice Minister Lord McNally, who articulated the following position:

A posthumous pardon was deemed unsuitable because Alan Turing had been duly convicted of an act that constituted a criminal offense under the prevailing laws of the era. It was presumed that he would have been aware that his actions contravened the law and would lead to prosecution. While it is tragic that Alan Turing was convicted of an offense now perceived as both cruel and absurd—a sentiment particularly intensified by his exceptional contributions to the war effort—the legal framework at the time necessitated such a prosecution. Consequently, established policy dictates the acceptance of such historical convictions, prioritizing the prevention of future similar injustices over attempts to retrospectively alter historical contexts or rectify what is inherently unchangeable.

John Leech, who served as the Member of Parliament for Manchester Withington from 2005 to 2015, initiated multiple legislative proposals and spearheaded a prominent campaign to secure a pardon for Alan Turing. Within the House of Commons, Leech argued that Turing's pivotal contributions during the war established him as a national hero, rendering the persistence of his conviction "ultimately just embarrassing." Leech persistently advanced the bill through Parliament and campaigned for several years, garnering significant public endorsement from numerous distinguished scientists, notably the physicist Stephen Hawking.

On July 26, 2012, a legislative bill was introduced in the House of Lords, proposing a statutory pardon for Alan Turing concerning offenses under Section 11 of the Criminal Law Amendment Act 1885, for which he had been convicted on March 31, 1952. Later that year, in a letter published in The Daily Telegraph, Stephen Hawking and ten other prominent signatories—including the Astronomer Royal Lord Rees, the President of the Royal Society Sir Paul Nurse, Lady Trumpington (who had collaborated with Turing during the war), and Lord Sharkey (the bill's sponsor)—collectively urged Prime Minister David Cameron to address the pardon request. The government subsequently signaled its support for the bill, which successfully completed its third reading in the House of Lords in October.

During the second reading of the proposed legislation in the House of Commons on November 29, 2013, Conservative Member of Parliament Christopher Chope raised an objection, thereby impeding its progression. Although the bill was scheduled for further deliberation in the House of Commons on February 28, 2014, the government opted to invoke the royal prerogative of mercy prior to any subsequent parliamentary debate. Consequently, on December 24, 2013, Queen Elizabeth II formally issued a pardon for Turing's conviction of "gross indecency," which became effective immediately. In his announcement of the pardon, Lord Chancellor Chris Grayling asserted that Turing merited recognition for his exceptional contributions to the war effort, rather than being defined by his subsequent criminal conviction. The Queen officially declared Turing pardoned in August 2014. This pardon represented only the fourth instance of royal clemency granted since the cessation of the Second World War. Typically, pardons are extended exclusively when the individual is demonstrably innocent and a formal request has been submitted by family members or other relevant stakeholders; however, neither of these prerequisites was satisfied concerning Turing's conviction.

In September 2016, the government declared its intent to extend this retroactive exoneration to other individuals convicted of comparable historical indecency offenses, a measure colloquially termed the "Alan Turing law." This "Alan Turing law" now informally refers to the legislation within the United Kingdom's Policing and Crime Act 2017, which functions as an amnesty, retroactively pardoning men who received cautions or convictions under historical statutes criminalizing homosexual acts. This legislation is applicable within England and Wales. Owing to his persistent advocacy on this matter, Leech is frequently recognized as the principal architect of Turing's pardon and, subsequently, the Alan Turing Law, which ultimately facilitated pardons for an additional 75,000 individuals. During the British premiere of The Imitation Game, a film chronicling Turing's life, the producers publicly acknowledged Leech for his role in raising public awareness and securing Turing's pardon.

On July 19, 2023, subsequent to an apology issued by the UK Government to LGBT veterans, Defence Secretary Ben Wallace proposed that Turing be commemorated with a permanent statue on the fourth plinth of Trafalgar Square. Wallace characterized Turing as "arguably the preeminent war hero of the Second World War," whose accomplishments "shortened the war, saved thousands of lives, [and] helped defeat the Nazis," further noting that "his story is a poignant reflection of societal treatment."

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About Alan Turing

A short guide to Alan Turing's life, research, discoveries and scientific influence.

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