Alan Turing: Revision Pack for Mastermind

Introduction

Alan Turing was a pioneering British mathematician, logician, and computer scientist who is widely considered one of the fathers of modern computing and artificial intelligence. His work on breaking the German Enigma code during World War II is credited with helping to shorten the war, and his theoretical contributions laid the foundation for computer science. This revision pack will cover the key events in Turing’s life, his major contributions to mathematics, computing, and cryptography, as well as his legacy and posthumous recognition.

Early Life and Education

Born: 23rd June 1912, London, England
Died: 7th June 1954, Wilmslow, Cheshire, England
  • Family Background:
    • Alan Mathison Turing was born to Julius Mathison Turing, a civil servant in the Indian Civil Service, and Ethel Sara Stoney.
    • Turing showed early signs of genius, with a natural aptitude for mathematics and science. His interest in solving complex problems developed from a young age.
  • Education:
    • Turing attended Sherborne School, a prestigious boarding school, where his fascination with mathematics blossomed despite struggling in more classical subjects.
    • He went on to study mathematics at King’s College, Cambridge (1931–1934), where he excelled in mathematical logic and graduated with first-class honours.
    • In 1936, Turing moved to Princeton University in the United States, where he studied under Alonzo Church and earned a PhD in mathematics in 1938.

Key Contributions and AchievementsTuring Machine (1936)
  • Definition: The Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a set of rules. It is a theoretical model for computation, helping to define the limits of what can be computed.
  • Key Concept:
    • Turing’s 1936 paper, "On Computable Numbers, with an Application to the Entscheidungsproblem", introduced the concept of a universal machine (later called the Turing machine), which could simulate the logic of any other machine.
    • The Turing machine became the foundation for the development of computer science, as it formalised the concept of an algorithm and computation.
  • Significance:
    • Turing’s work laid the groundwork for the development of modern computers, as it proved that any computational task could be performed by a machine given enough time and memory.

The Entscheidungsproblem and Computability
  • Context: The Entscheidungsproblem (German for "decision problem") was a challenge posed by the mathematician David Hilbert, asking whether a general algorithm could be found to determine the truth or falsity of every mathematical statement.
  • Turing’s Contribution:
    • Turing proved that no such algorithm could exist, effectively solving Hilbert’s problem by showing that there are some questions in mathematics that are undecidable — meaning no algorithm can solve them.
    • This work was crucial in establishing the limits of computation and was a cornerstone of theoretical computer science.

World War II and Enigma Codebreaking
  1. Bletchley Park:
    • During World War II, Turing worked at Bletchley Park, the British government’s codebreaking centre. He played a central role in breaking the German Enigma code, which the Nazis used to encrypt their military communications.
  2. The Bombe Machine:
    • Turing designed an electromechanical machine called the Bombe, which was used to help decipher Enigma-encrypted messages. The Bombe automated much of the codebreaking process and enabled the Allied forces to read vast amounts of enemy communication.
    • By 1940, Turing and his colleagues were regularly decrypting German naval messages, giving the Allies a significant advantage in the Battle of the Atlantic.
  3. Impact of Codebreaking:
    • Historians estimate that Turing’s work on breaking the Enigma code helped shorten the war by at least two years, potentially saving millions of lives.
    • His contribution remained classified for decades after the war, meaning Turing’s key role in the Allied victory was not widely recognised during his lifetime.

Post-War Work and Artificial Intelligence
  1. The Turing Test (1950):
    • In his 1950 paper, "Computing Machinery and Intelligence," Turing posed the question, "Can machines think?" He introduced what is now known as the Turing Test, a test of a machine’s ability to exhibit intelligent behaviour indistinguishable from that of a human.
    • The test involved a human evaluator interacting with both a machine and a human, without knowing which was which. If the evaluator could not reliably distinguish the machine from the human, the machine would be considered to have passed the test.
    • The Turing Test remains a fundamental concept in discussions about artificial intelligence (AI) and the philosophy of mind.
  2. Automatic Computing Engine (ACE):
    • After the war, Turing worked on the design of an automatic computing machine at the National Physical Laboratory (NPL). His design for the Automatic Computing Engine (ACE) was one of the first detailed plans for a stored-program computer.
    • Though his full vision for the ACE was never realised, it influenced the development of the first computers in the UK.
  3. Work on Morphogenesis:
    • In the early 1950s, Turing turned his attention to biology, focusing on morphogenesis, the process that causes organisms to develop their shapes.
    • In 1952, he published a paper titled "The Chemical Basis of Morphogenesis," where he used mathematical equations to describe how biological patterns (such as the stripes on a zebra or the arrangement of leaves on a plant) could emerge from simple chemical reactions.
    • This work, though underappreciated at the time, has since become influential in the fields of developmental biology and pattern formation.

Persecution and Death
  1. Conviction for Homosexuality (1952):
    • In 1952, Turing was convicted of "gross indecency" after admitting to a homosexual relationship, which was illegal in the UK at the time.
    • As part of his sentence, Turing was subjected to chemical castration (hormonal treatment), which had a devastating impact on his physical and mental health.
  2. Death:
    • On 7th June 1954, Turing was found dead from cyanide poisoning in his home in Wilmslow, Cheshire. His death was ruled a suicide, though there has been some speculation that it may have been accidental.
    • Turing’s tragic death highlighted the harsh treatment of LGBTQ+ individuals during that period, and it cast a shadow over his incredible achievements.

Legacy and Posthumous Recognition
  1. Posthumous Pardon (2013):
    • In 2013, Queen Elizabeth II granted Turing a royal pardon, formally absolving him of the criminal conviction that led to his persecution. This followed decades of campaigning by human rights activists, scientists, and the LGBTQ+ community.
  2. The Alan Turing Law (2017):
    • The "Alan Turing Law" was passed in the UK in 2017, granting posthumous pardons to thousands of men who had been convicted under historical laws banning homosexuality, in recognition of the unjust treatment of LGBTQ+ individuals.
  3. Turing Award:
    • The Turing Award, established in 1966 by the Association for Computing Machinery (ACM), is often referred to as the "Nobel Prize of Computing." It honours individuals who have made significant contributions to the field of computer science.
  4. Depictions in Popular Culture:
    • Turing’s life and achievements have been the subject of numerous books, films, and plays, the most famous being the 2014 film "The Imitation Game," starring Benedict Cumberbatch, which brought his story to a wider audience.
  5. £50 Banknote:
    • In 2021, Turing was honoured by being featured on the UK’s £50 note, symbolising his lasting impact on science and society.

Terminology and Key Concepts
  1. Turing Machine: A theoretical device that can simulate any computer algorithm, serving as a fundamental model for understanding computation.
  2. Enigma Code: The encryption system used by Nazi Germany during World War II to secure military communications. Turing’s work at Bletchley Park was key in breaking this code.
  3. Bombe Machine: An electromechanical device designed by Turing and used by British codebreakers to decrypt Enigma-encoded messages during the war.
  4. Turing Test: A test of a machine’s ability to exhibit intelligent behaviour equivalent to, or indistinguishable from, that of a human.
  5. Artificial Intelligence (AI): The simulation of human intelligence by machines, particularly computer systems, which is a field that Turing helped pioneer.

Practice Questions for Mastermind
  1. What was the primary purpose of the Bombe machine designed by Alan Turing during World War II?
  2. What is the Turing Test, and why is it significant in the field of artificial intelligence?
  3. Which mathematical problem did Alan Turing solve with his work on computability and the Entscheidungsproblem?
  4. In what year was Alan Turing granted a royal pardon for his conviction for "gross indecency"?
  5. What was the significance of Turing’s 1952 paper on morphogenesis, and how has it influenced modern science?

Conclusion
​Alan Turing’s contributions to mathematics, computer science, and cryptography have had a profound and lasting impact on modern technology and society. Despite facing personal persecution during his lifetime, his legacy has only grown stronger, and he is now widely recognised as one of the most brilliant minds of the 20th century. As you revise for your Mastermind quiz, focus on understanding Turing’s major works, his role during World War II, and the impact of his ideas on computing and artificial intelligence.