1.Copeland, B. J. “Alan Turing | Biography, Facts, Computer, Machine, Education, and Death.” Encyclopedia Britannica, 12 Feb. 2024, www.britannica.com/biography/Alan-Turing.
2. The Church-Turing Thesis (Stanford Encyclopedia of Philosophy). 18 Dec. 2023, plato.stanford.edu/entries/church-turing.
3. Dimri , Bipin. “History Archives - Historic Mysteries.” Ultra: How Did the Allied Codebreakers Crack the German Codes?, Ultra, 16 Aug. 2022, www.historicmysteries.com/history/ultra-codebreakers/26279/.
4.Be Smart. “The Mathematical Code Hidden in Nature.” YouTube, 22 Sept. 2021, www.youtube.com/watch?v=JLkCaBwRrVo.
Introduction
Alan Turing was a British mathematician and logician who primarily contributed to fields of cryptanalysis, mathematics, philosophy and logic. Despite being known as the father of computer science, his work became prominent in areas including cognitive science and artificial intelligence (AI) in later years, he also invented rather interesting theories in the field of biology!
Education
Born on June 23, 1912 in London, he received his education at top private schools, including a degree in mathematics from University of Cambridge in 1934 and his research in probability theory made him a fellowship at King’s College.
In 1936, he wrote a paper “On Computable Numbers, with an Application to the Entscheidungsproblem” (Decision problem) investigating the truth or falsity of any mathematical statement seeking an algorithmic method. (1)
His paper was eventually recommended by Alonzo Church for publication, as he also reached the same conclusion with a different method. Both papers were extremely significant for the development of computer science establishing the theoretical basis of computability, namely the concept of a universal computing machine known as the Turing machine. (2)
WW2 and the Turing machine
During World War II, Turing played an important role by applying his knowledge in cryptanalysis in codebreaking. Whilst working at the Bletchley Park, the codebreaking centre established by the British government, he broke German codes with the Enigma cipher used by the German military.
Along with Gordon Welchman, they developed what they called bombs, which were electromechanical devices assisting in breaking the Enigma-encrypted messages being a predecessor of electronic computers.
The Allies were now able to decrypt German communications providing essential strategic intelligence, as they understood the German military plans and predicted troop movements and naval operations. By deploying their naval forces to counter the German U-boat movements, they also reduced the implications of the German submarine attacks on Allied shipments, designed to fight off the Axis powers. Alan Turing, because of his substantial contributions shortening the war by two to four years, he’s an internationally known war hero. (3)
Mathematical biology and Turing patterns
Biology usually isn’t a subject of expertise for most mathematicians, although there was one, namely Alan Turing, that worked in mathematical biology using theoretical frameworks to explain the wonders of life, from spots to stripes on their animals using codes; not of DNA but rather a mathematical language. (4)
One of his other substantial papers written in 1952 explains the diffusion-reaction theory, often nicknamed the “Turing patterns”. In his paper, he explains the behaviour of a system containing two substances that would diffuse
Biology usually isn’t a subject of expertise for most mathematicians, although there was one, namely Alan Turing, that worked in mathematical biology using theoretical frameworks to explain the wonders of life, from spots to stripes on their animals using codes; not of DNA but rather a mathematical language.
One of his other substantial papers written in 1952 explains the diffusion-reaction theory, often nicknamed the “Turing patterns”. In his paper, he explains the behaviour of a system containing two substances that would diffuse
containing two substances that would diffuse and interact with each other, and he discovered that through such a system has the capability to generate spatially periodic patterns, even when starting from a random or nearly uniform initial state known as a homogeneous system when an organism is subjected to certain conditions exhibiting spatially heterogeneous patterns.
At a fundamental level, a reaction-diffusion system model involves two processes: reaction and diffusion. The reaction is the biochemical reactions happening within a system, whilst the diffusion describes the diffusion of a chemical through space or its distribution. The interactions between these components leads to the formation of patterns.
When two or more substances interact they are known as morphogens, and they diffuse through space and react with each other for the inhibition of their own production. The diffusion or localised reactions depend on the concentrations of the morphogens causing the emergence of distinctive patterns. (5)
Furthermore, there are activators and inhibitors. The activators foster their own production whilst attempting to induce the production of other morphones. Inhibitors on the other hand suppress their own production and inhibit the production of other morphogens. The interactions between activators and inhibitors, combined with diffusion, stabilise the patterns being formed.
Turing studied various biological systems, such as fish and bird pigmentation, animal coat markings, bacterial colonies and even embryonic development!
When describing the models using mathematics, they often involved partial differential equations to represent the dynamics of morphogen concentrations changing over space and time.
Overall, Turing patterns are essential as they help explain various developmental processes, morphogenesis, and the importance of chemical signals in the formation of biological patterns. (6)
Tragic personal life
Alan Turing, despite being a brilliant mathematician was persecuted for his sexuality. One of the most significant and influential figures in his life was Christopher Morcom, a close friend and a young love interest of his. From their common interest in science and mathematics, they had a profound relationship. Unfortunately, in 1930 at the age of 19 Christopher passed away due to Bovine tuberculosis, a bacterial disease that affects both cattle and humans. His death greatly affected Turing as he was devastated by the loss of his close friend or even lover.
Homosexuality though was criminalised in the United Kingdom, and in 1952, he was prosecuted for “gross indecency” and was proposed either imprisonment or chemical castration. Turing opted for chemical sterilisation, which are hormonal treatments that reduce or suppress sexual desire and function. Two years later, at the age of 41, he died likely because of suicide from cyanide poisoning. The reasons for his death remain unclear, although the medication at that time affected both his emotional and physical state. The British government never officially apologised until 2009, more than half a century after his tragic death. (7)
Conclusion
In the end, Alan Turing will always be remembered for being a mathematician, logician, computer scientist, and a war hero. His work in both the early field of computer science and mathematical biology have shaped our modern society, helping us develop new technological innovations applying his theoretical frameworks and discover mathematical patterns in living organisms.
5.Kondo, Shigeru, and Takashi Miura. “Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation.” Science, vol. 1616–1620, no. 5999, 24 Sept. 2010, https://doi.org/10.1126/science.1179047.
6.Nakao, Hiroya, and Alexander S. Mikhailov. “Turing Patterns in Network-organized Activator–inhibitor Systems.” Nature Physics, vol. 544–550, no. 7, 25 Apr. 2010, https://doi.org/10.1038/nphys1651.
7. Engelbrecht, Lezette. “The Man Behind the Enigma.” ITWeb, 28 Mar. 2024, www.itweb.co.za/article/the-man-behind-the-enigma/YKzQenqjj9oqZd2r.