##
**Alan Turing: The Enigma.**
*(English)*
Zbl 0541.68001

New York: Simon and Schuster, Inc. XII, 587 p. $ 22.50 (1983).

Alan Mathison Turing (1912-1954) was a poser lurking within an enigma concealed behind a paradox. About twenty years before his tragic death in early June, 1954, apparently by suicide, this seminal genius has introduced a fairly practical model of computing into mathematics and engineering. Few people today realize the courage and innovation it took in 1935 to talk publicly about paper tapes and patterns punched into them in a mathematical world where G. H. Hardy ruled nearly supreme. On the one hand, he had a brilliant mind whose product, the Universal (Turing) Machine, could imitate, for Churchill’s benefit, any of the so-called Enigma Machines which carried the vital combat communications directly from Hitler to the Nazi Armed Forces. On the other hand, he had a childlike mind that closely followed ”Toytown”, a child’s program about Larry the Lamb broadcast by BBC, discussing each detail of the story with his mother by telephone. This natural childlike attitude allowed him to conceive essentially new approaches to difficult problems but may have had the collateral consequence of permitting frequent formal errors to occur in his results. However, his life ended in ruin more than thirty years ago of cyanide poisoning, probably self-administered on an apple.

The book under review is a thorough-going biography of Turing including his family background, interactions with many other scholars and his technical contributions. It goes far beyond the biography published by his mother in 1959. The discussions of Turing’s technical contributions on computable numbers, machinery and intelligence, ordinal logics and even the Riemann Hypothesis provide much technical detail worthy of use in undergraduate engineering and mathematics classes today. Indeed, the presentations on the important role of Hilbert’s Program on Turing’s development and on elementary Turing machine theory are clearer and closer to this reviewer’s approach than those in J. E. Hopcroft’s recent paper ”Turing machines” [Scientific American, May, 1984, 86-98], where, e.g., Hilbert’s 23rd problem is badly misidentified. There are numerous conversations with many of the pundits: Von Neumann, Wittgenstein, Ashby, Shannon, Church, Hardy, and Wiener. Some of Turing’s impressions are not laudatory! The story of Turing reads like a sympathetically composed Shakespearean tragedy with all the contradictions that coexist between the worlds of knowledge and power.

The book, with its punning title, is divided into two major parts: The Logical (5 chapters) and The Physical (4 chapters). For some enigmatic reason the chapter entitled ”Bridge Passage” i not numbered. The author is a historical journalist with formal training in mathematical physics and a deep knowledge of the British academic establishment and class structure. The book contains detailed technical workings of Enigma Machines.

Early in 1935, Turing moved rapidly and creatively toward the far frontiers of logic and its applications by tackling the last of three difficult problems posed by Hilbert in 1928: (1) Is mathematics complete?; (2) Is mathematics consistent?; and (3) Is mathematics decidable? The Late Gödel had settled (1) and (2), in 1931, with his two incompleteness theorems. Turing’s achievement was to settle (3), negatively and independently of Church, using the new idea of a ”mechanical process” in the form of a (Turing) machine, a sort of super typewriter. A useful and classroom adaptable discussion of Turing machines is given in the last 15 pages of chapter 2.

Only later did Turing worry about actually building a machine that could simulate any human computer. The capabilities of such a machine for breaking the super complex Enigma ciphers of the Nazi Armed Forces further supported the requirement for the construction of a suitable special-purpose machine at some later time. Indeed, by pushing to its limits the capabilities of his universal machine, Turing became the father of artificial intelligence, if not the father of general-purpose machines.

For those who may worry about the paucity of reprint requests they may receive on their latest paper, it should be pointed out that Turing received only two formal requests when his paper ’On Computable Numbers’ appeared.

After World War II, construction of automatic computers dominated Turing’s attention, at the National Physical Laboratory (ACE) and then at the University of Machenster with the late M. H. A. Newman. Recall that Newman had defined the logico-mathematical requirements for the Colossus computer used successfully to break the Enigma codes on a regular basis. In this period, Turing learned the real and frustrating difficulties of procuring novel equipment, selling management of the development of an ”ephemeral item” like good software to make the machines work and the petty politics of large bureaucracies. Through it all, he remained the solitary, eccentric, alienated, abused and misunderstood scientist breaking new theoretical and practical ground; a true Joycean hero.

All in all, this penetrating biography is highly recommended, especially for graduate students in computer science. I could find only two substantive errors: (1) On page 83, Hilbert posed 23 unsolved problems, not 17, in the year 1900; and (2) On page 135, the Riemann Hypothesis falls under Hilbert’s Problem 8, not under Problem 4.

The book under review is a thorough-going biography of Turing including his family background, interactions with many other scholars and his technical contributions. It goes far beyond the biography published by his mother in 1959. The discussions of Turing’s technical contributions on computable numbers, machinery and intelligence, ordinal logics and even the Riemann Hypothesis provide much technical detail worthy of use in undergraduate engineering and mathematics classes today. Indeed, the presentations on the important role of Hilbert’s Program on Turing’s development and on elementary Turing machine theory are clearer and closer to this reviewer’s approach than those in J. E. Hopcroft’s recent paper ”Turing machines” [Scientific American, May, 1984, 86-98], where, e.g., Hilbert’s 23rd problem is badly misidentified. There are numerous conversations with many of the pundits: Von Neumann, Wittgenstein, Ashby, Shannon, Church, Hardy, and Wiener. Some of Turing’s impressions are not laudatory! The story of Turing reads like a sympathetically composed Shakespearean tragedy with all the contradictions that coexist between the worlds of knowledge and power.

The book, with its punning title, is divided into two major parts: The Logical (5 chapters) and The Physical (4 chapters). For some enigmatic reason the chapter entitled ”Bridge Passage” i not numbered. The author is a historical journalist with formal training in mathematical physics and a deep knowledge of the British academic establishment and class structure. The book contains detailed technical workings of Enigma Machines.

Early in 1935, Turing moved rapidly and creatively toward the far frontiers of logic and its applications by tackling the last of three difficult problems posed by Hilbert in 1928: (1) Is mathematics complete?; (2) Is mathematics consistent?; and (3) Is mathematics decidable? The Late Gödel had settled (1) and (2), in 1931, with his two incompleteness theorems. Turing’s achievement was to settle (3), negatively and independently of Church, using the new idea of a ”mechanical process” in the form of a (Turing) machine, a sort of super typewriter. A useful and classroom adaptable discussion of Turing machines is given in the last 15 pages of chapter 2.

Only later did Turing worry about actually building a machine that could simulate any human computer. The capabilities of such a machine for breaking the super complex Enigma ciphers of the Nazi Armed Forces further supported the requirement for the construction of a suitable special-purpose machine at some later time. Indeed, by pushing to its limits the capabilities of his universal machine, Turing became the father of artificial intelligence, if not the father of general-purpose machines.

For those who may worry about the paucity of reprint requests they may receive on their latest paper, it should be pointed out that Turing received only two formal requests when his paper ’On Computable Numbers’ appeared.

After World War II, construction of automatic computers dominated Turing’s attention, at the National Physical Laboratory (ACE) and then at the University of Machenster with the late M. H. A. Newman. Recall that Newman had defined the logico-mathematical requirements for the Colossus computer used successfully to break the Enigma codes on a regular basis. In this period, Turing learned the real and frustrating difficulties of procuring novel equipment, selling management of the development of an ”ephemeral item” like good software to make the machines work and the petty politics of large bureaucracies. Through it all, he remained the solitary, eccentric, alienated, abused and misunderstood scientist breaking new theoretical and practical ground; a true Joycean hero.

All in all, this penetrating biography is highly recommended, especially for graduate students in computer science. I could find only two substantive errors: (1) On page 83, Hilbert posed 23 unsolved problems, not 17, in the year 1900; and (2) On page 135, the Riemann Hypothesis falls under Hilbert’s Problem 8, not under Problem 4.

Reviewer: Albert A. Mullin (Madison)

### MSC:

68-03 | History of computer science |

03-03 | History of mathematical logic and foundations |

01A70 | Biographies, obituaries, personalia, bibliographies |

68Q05 | Models of computation (Turing machines, etc.) (MSC2010) |

03D10 | Turing machines and related notions |