Turing’s Vision, The Birth of Computer Science

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Turing’s Vision, The Birth of Computer Science, by Chris Bernhardt, was published by the Massachusetts Institute of Technology in 2016, with the first MIT Press paperback edition published in 2017. Chris Bernhardt is a Professor of Mathematics at Fairfield University, a Catholic University in Fairfield, Connecticut.

Alan Mathison Turing (1912-1954), was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. He emerged into public awareness largely as a result of the 2014 American film, The Imitation Game. The film is based on the biography by Andrew Hodges, Alan Turing: The Enigma, although it is highly dramatized.

Chris Bernhardt’s book is about Turing’s great contribution to theoretical computer science in a paper that Turing wrote in 1936, when he was twenty-four years old. His talents had been recognized and he was then a Fellow at King’s College, Cambridge. The paper is titled On Computable Numbers, with an Application to the Entscheidungsproblem (decision problem). “But don’t be discouraged by the title,” writes Bernhardt, “because it contains a wealth of elegant and powerful results. It also contains some remarkably beautiful truths… This book is for the reader who wants to understand these ideas. We start from the beginning and build carefully. The reader doesn’t have to know much mathematics – high school provides enough – but it does require some mathematical aptitude and also a little work … Turing is not saying trivial things about computation, but saying deep and nonintuitive things. That said, many people find these ideas quite fascinating and the work rewarding.”

The book has a Contents section; a helpful Introduction including paragraphs of information about each of its nine Chapters; a section for Further Reading; Notes for each of the Chapters (e.g., how Boolean algebra works); a Bibliography, and an Index. The Contents section lists all of the topics in each chapter. For example, Chapter 1, Background, includes Mathematical Certainty, Boole’s Logic, Mathematical Logic, Securing the Foundations of Mathematics; Hilbert’s Approach (David Hilbert, German mathematician, 1862-1943); Gödel’s Results (Kurt Gödel, Austrian mathematician, 1906-1978); and Turing’s Results.

From Chapter 1: “Gödel had completely destroyed Hilbert’s program as it stood in 1920. Nevertheless, there was still the Entscheidungsproblem.”

The Entscheidungsproblem is the halting problem – whether the computer program will finish running, i.e., halt, or continue running forever. “Turing would show that there were questions that were beyond the power of algorithms to answer. He would construct a proof … showing that there was no mechanical set of rules for the solutions of all mathematical problems and consequently that our activities as mathematicians would never come to an end.”

“Turing machines are theoretical models of our modern computers. Everything that can be computed on a computer can be computed by a Turing machine, so Turing’s paper is not just of historical interest; it tells us about what can and cannot be computed by any computer. It tells us that there are limitations to computation, and that there are simple questions that at first glance look straightforward, but are beyond the power of any computer to answer correctly … As Marvin Minsky writes: The sheer simplicity of the theory’s foundation and extraordinarily short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory.”

The chapters continue on with explanations of many aspects needed to understand the Turing machine, including diagrams presented as puzzles to be solved. For example, Hilbert’s Hotel: “Hilbert’s hotel is a hotel with an infinite number of rooms…” Skills in algebra will be necessary as well as flexibility in different methods of computation. The Notes section offers additional information, for example, the origins of algorithms. The word algorithm is a Latin translation of Al-Khwarizmi, the name of a Persian mathematician. The author notes however, that the idea has always been a part of mathematics, as far back as Euclid.

Axioms and algorithms are two essentials that those not gifted in mathematics should thoroughly understand, and they will certainly want to read and learn more as they progress in this book.

During World War II, Turing and his mentor, Max Newman (1897-1984), did highly classified work on codebreaking at Bletchley Park, Buckinghamshire, England, specifically the Enigma machine that the Germans were using for encoding their communications. It has been estimated that Turing’s work in cracking the Enigma code shortened the war in Europe by as many as two to four years, and saved millions of lives. Today he is referred to as the father of the modern computer.

Turing’s tragic death in 1954 is described by the author under the heading Downfall in Chapter 9. Through circumstances of a burglary at his house, it was discovered that Turing was homosexual (illegal in England at the time), and he was prosecuted. Instead of serving time in prison, Turing agreed to probation with hormone treatments. About a year after stopping the hormone treatments he died of cyanide poisoning (he had been engaged at times in chemical experiments with cyanide). Bernhardt agrees with Jack B. Copeland, Director of the Turing Archive for the History of Computing, who wrote: “The exact circumstances of Turing’s death may always remain unclear. It should not be stated that he committed suicide – because we just do not know.”  

On December 24, 2013, Turing was granted a royal pardon, and he continues to receive the recognition and the honors that he deserves. – Review by Martha Keltz

References:

https://en.wikipedia.org/wiki/Alan_Turing

There is a Wiki page all about the original Turing Machine, and it has a photo of a model of the original machine, which used tapes: https://simple.m.wikipedia.org/wiki/Alan_Turing

The original enigma machine that was used at Bletchley Park is called the Bombe: https://en.wikipedia.org/wiki/Bombe

Marvin Minsky: https://en.wikipedia.org/wiki/Marvin_Minsky

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