Alan Turing: influences, peers and legacy

Every connection with its receipt

Turing's mind was formed less by mathematics alone than by a collision of logic, boys' science books, and morphology. This mix traces the Hilbert-Gödel problem that produced the Turing machine, the obscure childhood and Cambridge readings that pushed him toward machines that think and chemicals that pattern, and the Bletchley and Manchester circles he worked within. It ends with the writers and scientists who made him a founding myth of the computer age.

The Kynda mix for Alan Turing

• Key Influence · On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel (1931). Turing's 1936 paper is a direct answer to the unfinished business of Gödel's incompleteness theorem: Gödel showed arithmetic could not prove its own consistency, leaving Hilbert's decision problem open. Turing learned of both through Max Newman's Cambridge lectures on the foundations of mathematics in 1935, and built his machine specifically to give 'effective calculability' a mechanical definition Gödel himself later praised as the correct one.'
• Influencia Obscura · Natural Wonders Every Child Should Know by Edwin Tenney Brewster (1912). A forgotten children's science book given to Turing around age ten, and arguably the most consequential text he ever read. Brewster describes the body as a machine — 'a sort of engine' running on food — a frankly mechanistic account of life that Turing's biographers identify as the seed of both his machine intelligence work and his later chemical theory of growth. Cheap popular science that set a lifetime's research program.
• Local Roots · Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939 by Ludwig Wittgenstein (1939). Turing sat in the same small Cambridge room as Wittgenstein in 1939 and argued with him directly; Cora Diamond's edition of the student notes preserves their exchanges over contradiction in formal systems, with Turing defending the mathematician's worry that a contradiction could make a bridge fall down. It is the best surviving record of Turing talking philosophy aloud, in the scene that produced both men's work.
• Beyond the Medium · Erewhon by Samuel Butler (1872). Butler's Victorian satire contains 'The Book of the Machines,' which argues machines are evolving consciousness and should be destroyed before they surpass us. Turing names Butler in 'Computing Machinery and Intelligence' when handling theological and 'heads in the sand' objections to thinking machines — a novelist's joke promoted into a serious philosophical adversary, and one of the earliest statements of the argument Turing set out to dismantle.
• Peer · A Mathematical Theory of Communication by Claude Shannon (1948). Shannon and Turing met over lunch at Bell Labs in early 1943, while Turing was consulting on speech encipherment and Shannon on cryptography; they discussed machine intelligence and Turing's 1936 paper, which Shannon had read. Shannon's information theory did for communication what Turing had done for computation, and the two men's wartime secrecy meant they could only trade ideas about thinking machines, not codes.
• From the Canon · On Computable Numbers, with an Application to the Entscheidungsproblem by Alan Turing (1936). The founding document of computer science, written at twenty-three. Turing imagines a clerk with a paper tape, reduces calculation to reading, writing and moving, and proves no machine can decide whether an arbitrary machine halts — settling Hilbert's problem. The universal machine he sketches, able to simulate any other, is the stored-program computer in theory a decade before one existed in metal.
• Key Collaborator · Elements of the Topology of Plane Sets of Points by M. H. A. Newman (1939). Max Newman taught the 1935 Cambridge course that handed Turing the Entscheidungsproblem, then sponsored the publication of 'On Computable Numbers' and vouched for him at Princeton. At Bletchley he ran the Newmanry, whose Colossus machines broke Lorenz, and afterwards he brought Turing to Manchester to work on the first stored-program computers. This topology monograph shows the pure mathematician behind that career-long patronage.
• Legacy · Alan Turing: The Enigma by Andrew Hodges (1983). Hodges, a mathematician and gay rights activist, wrote the biography that rescued Turing from footnote status, reconstructing the logic, the Bletchley work and the 1952 prosecution for gross indecency with equal seriousness. It drove the campaign for the 2009 apology and 2013 royal pardon, and supplied the source for the stage and screen versions — the single book most responsible for Turing as a public figure.

What influenced Alan Turing

• Snow White and the Seven Dwarfs by Walt Disney Productions (1937). The article reports a speculative connection between Turing’s death and a film scene he liked. “‘He used to go over the scene in detail, dwelling on the ambiguity of the apple, red on one side, green on the other, one of which gave death.’” (Alan Turing: the Enigma — Update for Part 7)
• Alonzo Church. Turing studied under Church at Princeton. (also via The Calculi of Lambda-Conversion) “From September 1936 to July 1938, Turing spent most of his time studying under Church at Princeton University , [ 5 ] in the second year as a Jane Eliza Procter Visiting Fellow .” (Wikipedia)
• Ada Lovelace (1815). Turing named a concept in his paper after Lovelace's objection. (also via Computing Machinery and Intelligence, Sketch of the Analytical Engine, with Notes by the Translator) “Note G also contains what came to be known as "Lady Lovelace's Objection" to the concept of artificial intelligence, so named by Alan Turing in his paper "Computing Machinery and Intelligence" The objection is Lovelace's statement that: …” (en.wikipedia.org)
• Natural Wonders Every Child Should Know by Edwin Tenney Brewster (1912). Natural Wonders Every Child Should Know (Edwin Tenney Brewster) — ghost for Alan Turing “In 1922, he discovered Natural Wonders Every Child Should Know by Edwin Tenney Brewster . He credited it with opening his eyes to science.” (Wikipedia)
• Grundzüge der theoretischen Logik by David Hilbert (1928). Grundzüge der theoretischen Logik (David Hilbert) — titan for Alan Turing “The Entscheidungsproblem (decision problem) was originally posed by German mathematician David Hilbert in 1928, and consists of seeking a computational procedure for proving or disproving theorems in the logical calculus employed by Hilb…” (en.wikipedia.org)
• On Growth and Form by D'Arcy Wentworth Thompson (1917). On Growth and Form (D'Arcy Wentworth Thompson) — ghost for Alan Turing “Waddington, Alan Turing, René Thom, Claude Lévi-Strauss, Eduardo Paolozzi, Le Corbusier, Christopher Alexander and Mies van der Rohe.” (en.wikipedia.org)
• The Nature of the Physical World by Arthur Stanley Eddington (1928). The Nature of the Physical World (Arthur Stanley Eddington) — ghost for Alan Turing (openlibrary.org)
• Principia Mathematica by Alfred North Whitehead (1910). Principia Mathematica (Alfred North Whitehead) — titan for Alan Turing (openlibrary.org)
• Sketch of the Analytical Engine, with Notes by the Translator by Ada Lovelace (1843). Sketch of the Analytical Engine, with Notes by the Translator (Ada Lovelace) — culture for Alan Turing “Note G also contains what came to be known as "Lady Lovelace's Objection" to the concept of artificial intelligence, so named by Alan Turing in his paper "Computing Machinery and Intelligence" The objection is Lovelace's statement that: …” (en.wikipedia.org)
• On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel (1931). On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Kurt Gödel) — titan for Alan Turing (openlibrary.org)
• Erewhon by Samuel Butler (1872). Erewhon (Samuel Butler) — culture for Alan Turing (openlibrary.org)
• Snow White and the Seven Dwarfs by Walt Disney (1937). Snow White and the Seven Dwarfs (Walt Disney) — culture for Alan Turing

Peers and kindred spirits

• Gordon Welchman. Welchman contributed an enhancement to the bombe specified by Turing. (also via The Hut Six Story) “was incredulous at first, as I had been, but when he had studied my diagram he agreed that the idea would work, and became as excited about it as I was.” (The National Museum of Computing)
• University of Manchester. Turing held a reader appointment at the University of Manchester. “Turing joined the Department of Mathematics as a Reader in September 1948, with the nominal title of "Deputy Director of the Royal Society Computing Machine Laboratory".” (The University of Manchester)
• Bell Labs. Turing consulted with Bell Labs on SIGSALY. “I had been intending to report to Potter at Bell Laboratories without any more formality than a preliminary phone call. This was apparently all wrong.” (Alan Turing: The Enigma)
• Ratio Club by John Bates. Turing accepted an invitation to join the Ratio Club. “At the first meeting on 4 September 1949 it was agreed to invite Turing to join. He accepted, giving his introductory talk at the 21 April 1950 meeting.” (Wikipedia)
• Donald Bayley. Turing and Bayley designed and constructed Delilah together. “The papers of Alan Turing and Donald Bayley relating to the Delilah project, a wartime collaboration seeking to develop a speech encryption system” (Bonhams)
• Dilly Knox. Turing and Knox worked together on Enigma cryptanalysis. “He brought back the information from the Polish Cipher Bureau and handed it to Alan Turing, a Cambridge mathematician. Turing’s task was to find a way into Enigma” (The National Museum of Computing)
• Manchester Literary and Philosophical Society. Turing was elected to membership of the society. “Alan Turing was an exceptional computer scientist, codebreaker, mathematician, and member of the Literary and Philosophical Society.” (Manchester Literary and Philosophical Society)
• Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939 by Ludwig Wittgenstein (1939). Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge 1939 (Ludwig Wittgenstein) — geography for Alan Turing “His thesis was republished in the journal Proceedings of the London Mathematical Society in 1939, == Career and research == When Turing returned to Cambridge, he attended lectures given in 1939 by Ludwig Wittgenstein about the foundation…” (en.wikipedia.org)
• D. G. Champernowne. Turing and Champernowne began writing a chess program together. “In 1948, Turing, working with his former undergraduate colleague, D.G. Champernowne , began writing a chess program for a computer that did not yet exist.” (Wikipedia)
• The Calculi of Lambda-Conversion by Alonzo Church (1941). The Calculi of Lambda-Conversion (Alonzo Church) — collaborator for Alan Turing “Between the springs of 1935 and 1936, at the same time as Alonzo Church, Turing worked on the decidability of problems, starting from Gödel's incompleteness theorems.” (en.wikipedia.org)
• Stuart Milner-Barry. Milner-Barry is identified as one of Turing’s fellow cryptanalysts. “By late 1941, Turing and his fellow cryptanalysts Welchman, Hugh Alexander and Stuart Milner-Barry were frustrated.” (Wikipedia)
• Cicely Popplewell. Napper describes Popplewell working with Turing on early Manchester Mark 1 software. “he worked on providing the early software requirements for the Manchester Mark 1, with the full time help of Cicely Popplewell , and wrote the first programming manual for the Ferranti Mark 1.” (The University of Manchester)
• Max Newman. Napper identifies Newman as Turing’s collaborator on Mersenne-prime investigations. “As soon as the Manchester Mark 1 was generally available for use in April 1949, he enthusiastically set about using it, especially to investigate Mersenne Primes , in collaboration with Newman.” (The University of Manchester)
• King's College, Cambridge. Turing served as a lecturer at King’s College. “Later that year, Turing was elected a Fellow of King's College on the strength of his dissertation [ 59 ] where he served as a lecturer.” (Wikipedia)
• Robin Gandy. The catalog describes Gandy helping organize Turing’s wartime mathematics lectures. “Bayley, Gandy and Alan Wesley commandeered a '...singularly cold classroom...' (Hodges, p.352) at Hanslope and organised evening lectures on mathematical methods given by Turing” (Bonhams)
• The Hut Six Story by Gordon Welchman (1982). The Hut Six Story (Gordon Welchman) — geography for Alan Turing “The bombe, with an enhancement suggested by mathematician Gordon Welchman, became one of the primary tools, and the major automated one, used to attack Enigma-enciphered messages.” (en.wikipedia.org)
• Hugh Alexander. Alexander is identified as one of Turing’s fellow cryptanalysts. “By late 1941, Turing and his fellow cryptanalysts Welchman, Hugh Alexander and Stuart Milner-Barry were frustrated.” (Wikipedia)
• cybernetics. Computing Machinery and Intelligence (Alan Turing) — peer for cybernetics (via Computing Machinery and Intelligence) “=== Ratio Club and other cybernetics contacts === The Ratio Club was a London dining club for researchers (mostly biologists) with interests in cybernetics (which encompassed neuroscience, artificial intelligence and computing), "undoubt…” (en.wikipedia.org)
• Formal Reductions of the General Combinatorial Decision Problem by Emil Post (1943). Formal Reductions of the General Combinatorial Decision Problem (Emil Post) — peer for Alan Turing (wikidata.org)
• Probability and the Weighing of Evidence by I. J. Good (1950). Probability and the Weighing of Evidence (I. J. Good) — collaborator for Alan Turing “Irving John Good (9 December 1916 – 5 April 2009) was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing.” (en.wikipedia.org)
• Elements of the Topology of Plane Sets of Points by M. H. A. Newman (1939). Elements of the Topology of Plane Sets of Points (M. H. A. Newman) — collaborator for Alan Turing (openlibrary.org)
• A Mathematical Theory of Communication by Claude Shannon (1948). A Mathematical Theory of Communication (Claude Shannon) — peer for Alan Turing (wikidata.org)
• Cybernetics: Or Control and Communication in the Animal and the Machine by Norbert Wiener. Cybernetics: Or Control and Communication in the Animal and the Machine (Norbert Wiener) — peer for Alan Turing (wikidata.org)
• Geoffrey Hinton. Computing Machinery and Intelligence (Alan Turing) — geography for Geoffrey Hinton (via Computing Machinery and Intelligence) (wikidata.org)
• Faster Than Thought: A Symposium on Digital Computing Machines by B. V. Bowden (1953). Faster Than Thought: A Symposium on Digital Computing Machines (B. V. Bowden) — geography for Alan Turing
• AlphaFold. Computing Machinery and Intelligence (Alan Turing) — geography for AlphaFold (via Computing Machinery and Intelligence)

Who Alan Turing influenced

• First Draft of a Report on the EDVAC. Womersley attributed some ideas in von Neumann’s report to Turing. “Von Neumann 's incomplete First Draft of a Report on the EDVAC had predated Turing's paper, but it was much less detailed and, according to John R. Womersley , Superintendent of the NPL Mathematics Division, it "contains a number of idea…” (Wikipedia)
• Alan Turing: The Enigma by Andrew Hodges (1983). Alan Turing: The Enigma (Andrew Hodges) — legacy for Alan Turing “As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect." Churchill wrote a memo to General Ismay, which read: "ACTION THIS DAY.” (en.wikipedia.org)
• Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter (1979). Gödel, Escher, Bach: An Eternal Golden Braid (Douglas Hofstadter) — legacy for Alan Turing “The cognitive scientist Douglas Hofstadter writes: Atheist, homosexual, eccentric, marathon-running mathematician, A.” (en.wikipedia.org)
• Breaking the Code by Hugh Whitemore (1986). Breaking the Code (Hugh Whitemore) — legacy for Alan Turing “This 1986 Hugh Whitemore play tells the story of Turing's life and death.” (en.wikipedia.org)
• James Murray. Murray applied Turing’s paper in work on animal coat patterns. (via The Chemical Basis of Morphogenesis) “One of the early applications of Turing's paper was the work by James Murray explaining spots and stripes on the fur of cats, large and small.” (Wikipedia)
• Demis Hassabis. Computing Machinery and Intelligence (Alan Turing) — titan for Demis Hassabis (via Computing Machinery and Intelligence) (wikidata.org)
• Grace Hopper. On Computable Numbers, with an Application to the Entscheidungsproblem (Alan Turing) — titan for Grace Hopper (via On Computable Numbers, with an Application to the Entscheidungsproblem) (wikidata.org)