# The Turing Guide

Jack Copeland is a professor at the University of Canterbury, NZ, director of the Turing Archive for the History of Computing, co-director of the Turing Center of the ETH Zürich, and he has written or edited several books about Turing and his work. So he seems to be also the driving force behind this new collection of papers devoted to the life and the legacy of Alan Turing. Only four authors are explicitly mentioned on the cover of this book, but the collection contains 42 papers authored by 33 persons with very diverse backgrounds. Fifteen of the 42 papers were (co)authored by Copeland. Four of the papers by older authors (three of them have known or collaborated with Turing) are published posthumously.

Alan Turing (1912-1954) hardly needs any introduction. Most people will know him as a codebreaker of the German Enigma at Bletchley Park during the second World War. They probably also have heard of his tragic death covered by a veil of uncertainty: was it an accident or suicide. He was convicted in 1952 to chemical castration for having a gay relationship. Only in 2013 he was rehabilitated by a royal pardon. Some may also have an idea of what a Turing Test is. A mathematician or a computer scientist will almost certainly also know that he proved independently but almost simultaneously with Alonso Church that Hilbert's *Entscheidungsproblem* was unsolvable. Turing proved it by reducing it to a halting problem which is undecidable on a universal Turing Machine. Many books and even films tell the story of Turing and of all the activities at Bletchley Park. The Turing Centenary Year 2012 which triggered the publication of many more and the recent (loosely biographical) film *The Imitation Game* (2014) have spread the knowledge about Turing in a broader audience. Bletchley Park may now be a major tourist attraction park, but the confidentiality that was kept by the British authorities about what was developed there during the war concerning cryptanalysis and the early digital computers has delayed the historical disclosure of the role played by Turing and other scientists in that period. Somewhat less known, but very familiar to biologists is Turing's work on morphogenesis which he developed during a later stage in his life. The book has eight parts that cluster papers about eight different aspects of Turing's life and legacy.

Thus Turing was much more than just a codebreaker. His universal machine was an essential theoretical model in proving results about the foundations of mathematics, logic, and computer science. Because of his work at Bletchley Park while the first digital computing machines were being assembled during and just after the war, he was intensively involved in writing original software, a user's manual, and he has even contributed to the design of circuits and hardware. The introduction of machines that could be instructed to perform less trivial tasks raised concern about the future of Artificial Intelligence and Turing contributed with several variants of his Turing test in an attempt to define what intelligence really meant. He called his ultimate version of 1950 the 'imitation game'.

It should not be forgotten, that, even though his scientific interest and contributions are broad, Turing was fundamentally a mathematician. It is less known that his Kings College Fellow Dissertation (1935) involved a proof of the Central Limit Theorem. It was little known that this was proved already in 1920 by Jarl Lindeberg and so Turing's result was never published. He also worked on group theory, in particular the word problem, on number theory (the Riemann hypothesis and normal numbers) and of course the code breaking involved statistical analysis and hypothesis testing. Turing exploited these statistics in his algorithms Banburismus and later Turingery. After the war he was also doing numerical analysis (LU decomposition, error analysis,...). His work on morphogenesis was also mathematical and involved diffusion equations that model the random behaviour of the morphogenes.

This collection of papers is produced for an interested but general audience. Formulas are kept to a minimum and technical discussion is maintained at an accessible level. It may not be the best choice to read as a first introduction to Turing and his work. Better introductions that are less chopped up in different papers are available. On the other hand, if you have read already several books about Turing and his work, I am sure you will find here some anecdotes and historical facts that you did not know yet in each of the eight parts of the book.

A first part is biographical. The timeline by Copeland is useful to place everything in a proper historical sequence. There is a testimony of Sir John Dermot Turing, Alan's nephew, and another by the late Peter Hilton an Oxford professor who worked with Turing at Bletchley Park.

Part two is more history in which Copeland explains about the Universal Turing Machine conceived by Turing to solve the Entscheidungsproblem. It has also a noteworthy contribution by Stephen Wolfram, the creator Mathematica and Wolfram-alpha, who praises Turing for initiating computer science.

The third part is the most extensive one and puts the codebreaking and Bletchley Park in the spotlight. Some of the texts are by people who worked there and who give an account of how everyday life was during the war, other papers are explaining how the Enigma machine worked and how it could be broken.

In part four the first computers as they developed after the war are in the focus. The Colossus machines were computers that were used since 1943 for codebreaking, These facts were only declassified in 2000 so that one got the impression that the original ideas and prototypes came from von Neumann at Princeton who developed the ENIAC and the EDVAC. However, the University of Manchester had a small scale computer *Baby* (1948) that was running a few months before the ENIAC and Turing at the National Physical Laboratory developed the Automatic Computing Engine (ACE) that was operational in 1950. Turing even wrote a manual on how to program the machine to play musical notes.

The fifth part is about computers and the mind: chess computers, neural computing, and the working of the human brain. It also has a remarkable text by novelist David Leavitt about Turing and the paranormal.

The next two parts are about Turing's biological (morphogenesis) and mathematical (cf. supra) contributions. The final part has two papers contemplating the Turing thesis (1936) which claims that a Turing machine can do any task a human computer can do. Similar claims were made by Zuse and Church, but whether the whole universe can be seen as a computer, obviously depends on what you call a computer.

In the last chapter about Turing's legacy in different disciplines we find many references to books and other media that can be consulted for further information.

The remaining pages offer a short biography of the contributors, references to some books about Turing, and a list of published papers by Turing. The many references and notes from the contributions are also gathered at the end. The book ends with a very detailed index, which is of course very welcome and obviously non-trivial with that many different authors.

In summary, this is a welcome addition to the existing generally accessible literature that gives additional testimony of the brilliant mind of Alan Turing. There is historical as well as technical material that will be appreciated also by specialists whatever their discipline: history, mathematics, biology, computer science, or philosophy.

**Submitted by Adhemar Bultheel |

**13 / Mar / 2018