Turing a M (27 results)

21x14. Encuadernación rústica (tapa blanda). 64 pgs. 706101.

Encuadernación de tapa blanda. Condition: Bien. Sin Sobrecubierta. Titulo original: Perpectives on the Computer Revolution. Cubierta deslucida. Interior en muy buen estado. Los gastos de envío son calculados para un peso inferior a 1kg, superándose este peso le informaremos de los gastos de envío adicionales. ISBN: 8420621199.

RUSTICA. Condition: Libro nuevo. *En este trabajo, A. M. Turing defiende la posibilidad de que las máquinas lleguen a pensar y polemiza con quienes objetan, desde diferentes perspectivas, tal posibilidad. Su lectura nos plantea indirectamente la cuestión del significado de "ser consciente". 50p.

17x12. 94p. Rústica ed. Con solapas. Buen estado. LIBRO EN ESPAÑOL.

Encuadernación de tapa blanda. Condition: Muy bien. 1ª Edición. Título Original: "Perspectives on the Computer Revolution" Traducción de Luis García Llorente. Colección: "Alianza Universidad" Núm. 119. MUY BUEN ejemplar. 700pp + 2h.

1975 695pp Fotografías b/n Colecc. Alianza Universidad nº119 Selección y comentarios de Zenon W. Pylyshyn 8ºM(20x13) Rústica Buen estado levemente deslucido .

24,5 x 17 cm. Condition: Gut. 1. Auflage. XXII, 285 Seiten Innen sauberer, guter Zustand. Hardcover,Kunstledereinband, mit den üblichen Bibliotheks-Markierungen, Stempeln und Einträgen, innen wie außen, siehe Bilder. Kleiner Lederabrieb an der unteren Vorderdeckelkante. Rückendeckel mit zwei kleinen Blessuren oben. - Collected Works of A. M. Turing. B15-02-03D|A97 Sprache: Englisch Gewicht in Gramm: 780.

Broschiert. Condition: Befriedigend. 297 S. Mit leichtem Nikotingeruch. Einband lichtrandig, leicht bestoßen und berieben. Papier altersgemäß leicht gebräunt. Kopfschnitt leicht fleckig. Sprache: Italienisch Gewicht in Gramm: 308.

Hardcover. Condition: Very Good. (Alan M. Turing) COHEN, A. M. and M. J. E. Mayhew. In Proceedings of the London Mathematical Society, Third Series, Volume XVIII, 1968, pp. 691-713. Oxford: Oxford University Press, 1968. Offered is the entire hardback Very Good++ Ex-library vol XVIII with library bookplate front paste-down, library stamp title page and last page, no other library markings. Mild soil edges. 8vo. 768 pp. Hardcover. Very Good++. The authors begin the paper: "This paper is based on ideas of A. M. Turing as recorded in an unpublished, and in places inaccurate, manuscript. We reproduce part of Turing's introduction and, in substance, his first few lemmas, but diverge from his work in Lemma 6". This paper is included in the Collected Works of Alan Turing since it is completion of work he began (See Hodges 'Alan Turing Bibliography').

Oxford 1968 Offered is the entire hardback Very Good++ Ex-library vol XVIII with library bookplate front paste-down, library stamp title page and last page, no other library markings. Mild soil edges. 8vo. 768 pp. Very Good++ Hardcover The authors begin the paper: "This paper is based on ideas of A. M. Turing as recorded in an unpublished, and in places inaccurate, manuscript. We reproduce part of Turing's introduction and, in substance, his first few lemmas, but diverge from his work in Lemma 6". This paper is included in the Collected Works of Alan Turing since it is completion of work he began (See Hodges 'Alan Turing Bibliography'). Mathematics. Book.

Paperback. Condition: Collectible; Very Good.

Soft cover. Condition: Very Good. No Jacket. Entire volume offered. 137 pp; illus. Original printed wrappers. Very Good+. 'His last publication was in Penguin Science News, written like a modern Scientific American article, and entitled Solvable and unsolvable problems. Written vividly but from the perspective of a pure mathematician, its final words concerned the interpretation of unsolvable problems, such as the halting problem for Turing machines' (Andrew Hodges, 'Alan Turing: one of The Great Philosophers'; on Alan Turing Home Page).

HARDCOVER. 1st Edition. 8vo bound in plain full green cloth, gilt lettering to spine, 576pp. Complete year in one volume. Contains the first publication of 'Computing Machinery and Intelligence' (pp 433 - 460), Turing's landmark paper, and probably the single most influential paper on artificial intelligence ever published. This copy is protectively housed in a custom made cloth covered clam-shell case. CONDITION: An extremely well preserved FINE very clean and tight unmarked copy (slight tanning to end-papers and page-block edges) ] __NOTE. Depending on destination, this item may require an extra payment for shipping insurance. If so, orders made by card will be completed only after you have approved the extra cost._ ._We Ship in PROTECTIVE CARD PARCELS.

Torino, Paolo Boringhieri, 1965. A cura di Vittorio Somenzi. Volume N. 3 appartenente alla Collana: Universale scientifica Boringhieri. Dall'indice: Introduzione di Vittorio Somenzi; Le basi fisiche del pensiero; Calcolatori e automi; Macchine calcolatrici e intelligenza; Il calcolatore e il cervello; La logica degli automi e la loro autoriproduzione; Scienza e società; Appendici: Il libro delle macchine; Charles Babbage e le sue macchine; Tre giuochi. In 16mo (cm. 19,6); brossura editoriale illustrata con titoli al piatto e al dorso; pp. 295, (5). Buono stato di conservazione. PAx.

Hardcover. Condition: Near Fine. No Jacket. 1st Edition. Entire Volume 7 of The Journal of Symbolic Logic, bound in contemporary cloth. Copy of Alan Ross Anderson, (1925-1973), who taught at Yale from 1955-65 then was Professor of Philosophy at the University of Pittsburgh from 1965-73 and Chairman of the Department from 1967-70. Anderson twice served as editor of the Journal of Symbolic Logic.

Soft cover. Condition: Very Good. . In :The Journal of the London Mathematical Society. Vol. 10. Part 1. January, 1935. No. 37. pp. 284-285. London: C. F. Hodgson, 1935. Offered is the entire hardback Very Good++ Ex-library volumes 9-10, 1934-1935 (bound in one book) with mild soil edges. Library bookplate front paste down. Library stamps title page, last page. No other library markings. 8vo. 320 pp. + 320 pp. Hardcover. Very Good++.This is Turing's earliest published paper. it is preceded only by his thesis, 'On the Gaussian Error Function' (1935) which was never published. Only the preface of the thesis is reproduced in the 'Collected Works' (See Hodges-Alan Turing Bibliography). //// DW ////Ask for pictures.

Hardcover. Condition: Very Good. . In Proceedings of the London Mathematical Society. Third Series, Volume III (1953), pp. 99-117. Oxford: Clarendon Press, 1953. Offered is the Very Good++ complete volume III in blue buckram binding with scuffed leather spine label, gilt lettering. Deaccessioned from the John Cass College library with library bookplate front paste down, "withdrawn" stamp title page, last page. No other library markings. 8vo. 512 pp. Hardcover. Very Good++.After the publication of his paper "On computable numbers," Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers. (In 1900 Hilbert listed proving or disproving this hypothesis as one of the most important unsolved problems confronting mathematics; when this bibliography was written, the hypothesis remained unproven.) Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I. (Mind, Chapter 5, p. 468). This paper describes the first use of a digital computer to calculate the zeros of the Reimann Zeta Function. The Zeta Function is of great significance in number theory because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics (Hook & Norman Origins of Cyberspace #938). . //// DW ////Ask for pictures. //// DW ////Ask for pictures.

(No place), The Association for Symbolic Logic, 1942. Large 8vo. Bound in blue half cloth with silver lettering to spine. In "Journal of Symbolic Logic", Volume 7. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 28-33" 146-156 (Entire copy: (4), 180 pp.). First appearance of these two paper's by Turing.Turing's paper "A Formal Theorem in Church's Theory of Types" is a significant contribution to the fields of computer science and mathematical logic. By providing a formal proof within Church's theory, Turing expanded our understanding of computation and its relationship to logic. His work on computability and the theory of types laid the foundation for the development of theoretical computer science, proof theory, and automated reasoning. Turing's paper continues to be a landmark in the study of computation, inspiring further research and practical applications in diverse areas of science and technology. In "The Use of Dots as Brackets in Church's System", introducing the dot parentheses notation, Turing simplified the representation and manipulation of lambda calculus expressions, making them more intuitive and manageable. His work highlighted the relationship between syntax and semantics, laying the foundation for further research in formal semantics and the development of programming languages. Turing's paper continues to be influential, shaping the way complex expressions are represented and reasoned about in the fields of computation, formal systems, and logic.

(No place), The Association for Symbolic Logic, 1942, 1943 &1948. Lev8vo. Bound in two uniform red half cloth with gilt lettering to spine. In "Journal of Symbolic Logic", Volume 7, 8 [Bound together] & 13. Barcode label pasted on to back board. Small library stamp to lower part of 6 pages. Minor scratches to extremities of volume 13. A fine set. Pp. 28-33" Pp. 80-94. [Entire volumes: IV, 164 pp." IV, 236 pp.). First printing of the two important - but often overlooked - papers by Turing which provide "information about Turing's thoughts on the logical foundations of mathematics which is not to be found elsewhere in his writings". (Copeland, The Essential Turing, P. 206).

Condition: Very Good. First Edition. First edition. The first printing of Alan Turing's PhD dissertation and seminal work published in Proceedings of the London Mathematical Society, Second Series, Vol. 45., with Turing paper pp. 161-228. Pp. 475. Entire issue, bound without wraps in recent full green cloth with spine lettered in gilt. Circular eagle stamps to roughly 5% of pages, with three stamps on Turing paper but none on title page. Pages toned, lightly handled. "Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (19121954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the worldincluding Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleenewere at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science.".

London, Hodgson & Son, 1939. Royal8vo. In a recent nice red full cloth binding with gilt lettering to spine. Entire volume 45 of "Proceedings of the London Mathematical Society. Second Series". Small white square paper label pasted on to lower part of spine, covering year of publication stating: "A Gift / From /Anna Wheeler". A very nice and clean copy without any institutional stamps. Pp. 161-240. [Entire volume: (4), 475 pp.]. The rare first printing of Turing's Ph.D.-thesis, which "opened new fields of investigation in mathematical logic". This seminal work constitutes the first systematic attempt to deal with the Gödelian incompleteness theorem as well as the introduction to the notion of relative computing. After having studied at King's College at Cambridge from 1931 to 1934 and having been elected a fellow here in 1935, Turing, in 1936 wrote a work that was to change the future of mathematics, namely his seminal "On Computable Numbers", in which he answered the famous "Entscheidungsproblem", came up with his "Universal Machine" and inaugurated mechanical and electronic methods in computing. This most famous theoretical paper in the history of computing caught the attention of Church, who was teaching at Princeton, and in fact he gave to the famous "Turing Machine" its name. It was during Church's work with Turing's paper that the "Church-Turing Thesis" was born. After this breakthrough work, Newman, under whom Turing had studied at Cambridge, urged him to spend a year studying with Church, and in September 1936 he went to Princeton. It is here at Princeton, under the guidance of Church, that Turing in 1938 finishes his thesis [the present paper] and later the same year is granted the Ph.D. on the basis of it. The thesis was published in "Proceedings of the London Mathematical Society" in 1939, and after the publication of it, Turing did no more on the topic, leaving the actual breakthroughs to other generations. In his extraordinary Ph.D.-thesis Turing provides an ingenious method of proof, in which a union of systems prove their own consistency, disproving, albeit shifting the problem to even more complicated matters, Gödel's incompleteness theorem. It would be many years before the ingenious arguments and striking partial completeness result that Turing obtained in the present paper would be thoroughly investigated and his line of research continued. The present thesis also presents other highly important proofs and hypotheses that came to influence several branches of mathematics. Most noteworthy of these is the idea that was later to change the face of the general theory of computation, namely the attempt to produce an arithmetical problem that is not number-theoretical (in his sense). Turing's result is his seminal "o-machines"" he here introduces the notion of relative computing and augments the "Turing Machines" with so-called oracles ("o"), which allowed for the study of problems that could not be solved by the Turing machine. Turing, however, made no further use of his seminal o-machine, but it is that which Emil Post used as the basis for his theory of "Degrees of Unsolvability", crediting Turing with the result that for any set of natural numbers there is another of higher degree of unsolvability. This transformed the notion of computability from an absolute notion into a relative one, which led to entirely new developments and in turn to vastly generalized forms of recursion theory. "In 1939 Turing published "Systems of Logic Based on Ordinals,". This paper had a far-reaching influence" in 1942 E.L. Post drew upon it for one of his theories for classifying unsolvable problems, while in 1958 G. Kreisel suggested the use of ordinal logics in characterizing informal methods of proof. In the latter year S. Feferman also adapted Turing's ideas to use ordinal logics in predicative mathematics." (D.S.B. XIII:498). A part from these groundbreaking points, which Turing never returned to himself, he here also considers intuition versus technical ingenuity in mathematical reasoning, does so in an interesting and provocative manner and comes to present himself as one of the most important thinkers of modern mathematical as well as philosophical logic."Turing turned to the exploration of the uncomputable for his Princeton Ph.D. thesis (1938), which then appeared as "Systems of Logic based on Ordinals" (Turing 1939). It is generally the view, as expressed by Feferman (1988), that this work was a diversion from the main thrust of his work. But from another angle, as expressed in (Hodges 1997), one can see Turing's development as turning naturally from considering the mind when following a rule, to the action of the mind when not following a rule. In particular this 1938 work considered the mind when seeing the truth of one of Gödel's true but formally unprovable propositions, and hence going beyond rules based on the axioms of the system. As Turing expressed it (Turing 1939, p. 198), there are 'formulae, seen intuitively to be correct, but which the Gödel theorem shows are unprovable in the original system.' Turing's theory of 'ordinal logics' was an attempt to 'avoid as far as possible the effects of Gödel's theorem' by studying the effect of adding Gödel sentences as new axioms to create stronger and stronger logics. It did not reach a definitive conclusion.In his investigation, Turing introduced the idea of an 'oracle' capable of performing, as if by magic, an uncomputable operation. Turing's oracle cannot be considered as some 'black box' component of a new class of machines, to be put on a par with the primitive operations of reading single symbols, as has been suggested by (Copeland 1998). An oracle is infinitely more powerful than anything a modern computer can do, and nothing like an elementary component of a computer. Turing defined 'oracle-machines' as Turing machines with an additional configuration in which they 'call the oracle' so as to take an uncomputable step. But th.

London, Hodgson & Son, 1945. Royal8vo. In a recent nice green full cloth binding with gilt lettering to spine. Entire volumes 48 of "Proceedings of the London Mathematical Society. Second Series". A very nice and clean copy without any institutional stamps. Pp. 180-197. [Entire volume: (4),477 pp.] First printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous "Zeta-function Machine", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. "Turing had ideas for the design of an "analogue" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides." (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking "A Method for the Calculation of the Zeta-Function", which constitutes his first printed contribution to the subject."After the publication of his paper "On computable Numbers," Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers. Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]." (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).

Oxford, Clarendon Press, 1948. 8vo. Bound in contemporary full calf with gilt lettering to spine. In "The Quarterly Journal of Mechanics and Applied Mathematics", Vol. 1, 1948. Previous owner's name written to front free-endpaper. Ver fine and clean. Pp. 287-380. [Entire volume: (4), 474 pp.]. First printing of this important paper in which Turing for the very first time introduced the concept of LU factorization or LU decomposition. "Turing's paper was one of the earliest attempts to examine the error analysis of the various methods of solving linear equations and inverting matrices. His analysis was basically sound. The main importance of the paper was that it was published at the dawn of the modern computing era, and it gave indications of which methods were 'safe' when solving such problems on a computer". (Burgoyne, Collected Works of A M Turing)."In 1945, [Turing] declined an offer of a Fellowship at King's [College, Cambridge] in favour of joining the newly formed Mathematical Division at the National Physical Laboratory (NPL). His early work on computability, combined with his wartime experience in electronics, had fired him with an enthusiasm for working on the design of an electronic computer. \ethe machine he designed, which was called the Automatic Computing Engine (ACE) in recognition of Babbage's pioneering work, was characteristically original?"While in the Mathematics Division of NPL, Turing became keenly interested in numerical analysis. His paper, "Rounding-off Errors in Matrix Processes", showed that the acute anxiety about the effect of rounding errors in Gaussian elimination was largely unjustified. This paper has been overshadowed to some extent by the von Neumann and Goldstine paper on matrix inversion, but it is a brilliant piece of work and would have repaid closer study at the time". ("Turing, Alan M." by James H. Wilkinson, p. 1803, in Encyclopedia of Computer Science, A. Ralston et al (eds.), 4th edition, Nature Publishing Group, 2000).In linear algebra, LU decomposition factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. Not in Origins of Cyberspace nor The Erwin Tomash Library.

London, Hodgson & Son, 1945. Royal 8vo. Entire volume 48 of "Proceedings of the London Mathematical Society. Second Series" bound WITH ALL THE SIX ORIGINAL FRONT-WRAPPERS for all six parts of the volume (bound in at rear) in a very nice contemporary blue full cloth binding with gilt lettering and gilt ex-libris ("Belford College. Univ. London") to spine. Very minor bumping to extremities. Overall in excellent, very nice, clean, and fresh condition in- as well as ex-ternally. Small circle-stamp to pasted-down front free end-paper and to title-page ("Bedford College for Women"). Book-plate stating that the book was presented to the Library of Bedford College by "Professor H. Simpson./ 1945" + discreet library-markings to upper margin of pasted-down front free end-paper. Pp. 180-197. [Entire volume: (4),477, (1) pp + 1 plate (balance sheet)]. The very rare first printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous "Zeta-function Machine", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. "Turing had ideas for the design of an "analogue" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides." (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking "A Method for the Calculation of the Zeta-Function", which constitutes his first printed contribution to the subject."After the publication of his paper "On computable Numbers," Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers. Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]." (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).

1937. 8vo. Bound in recent marbled boards. Title-page for volume 2 of Journal of Symbolic Logic withbound. First edition of Turing's important paper, in which he links Kleene's recursive functions, Church's lambda-definable functions and his own computable functions and proves them to be identical. In the appendix of his milestone-paper "On Computable Numbers" from 1936, Turing gave a short outline of a method for proving that his notion of computability is equivalent with Alonzo Church's notion of lambda-definabilty. It was not until the present article, however, that it was proved that Steven Kleene's general recursive functions, Church's lambda-definable functions and Turing's computable functions were all identical. Kleene had already proved that every general recursive function is lambda-definable, so by showing that computability follows from lambda-definability and that general recursiveness follows from computability, Turing had ended the circle, which was a primary reason for its acceptance as a notion of "effective calculable" demanded by Hilbert's Entscheidungsproblem."The purpose of the present paper is to show that the computable functions introduced by the author (in "On computable numbers") are identical with the lambda-definable functions of Church and the general recursive functions due to Herbrand and Gödel and developed by Kleene." Turing wrote this paper while at Princeton studying with Church."(Hook and Norman No. 395).

London, Hodgson & Son, 1945. Royal 8vo. Entire volume 48 of "Proceedings of the London Mathematical Society. Second Series" bound in a nice contemporary blue full cloth binding with gilt ex-libris ("Sir John Cass College") to front board and gilt title-label and year to spine. Very minor wear to extremities. Nicely re-enforced at inner hinges. A very nice, clean, and tight copy. Large library-book-plate to inside of front board (stating that the volume was presented by "Dr. A.E.R. Church"), with "withdrawn"-stamp. Also "withdrawn"-stamp to title-page and to final page, and a library-stamp to p. (1). Otherwise a nice and clean copy with no markings, etc. Pp. 180-197. [Entire volume: (4),477, (1) pp. The very rare first printing of Turing's first published paper devoted to the Riemann-zeta function, the basis for his famous "Zeta-function Machine", a foundation for the digital computer.While working on his Ph.D.-thesis, Turing was concerned with a few other subjects as well, one of them seemingly having nothing to do with logic, namely that of analytic number theory. The problem that Turing here took up was that of the famous Riemann Hypothesis, more precisely the aspect of it that concerns the distribution of prime numbers. This is the problem that Hilbert in 1900 listed as one of the most important unsolved problems of mathematics. Turing began investigating the zeros of the Rieman zeta-function and certain of its consequences. The initial work on this was never published, though, but nevertheless he continued his work. "Turing had ideas for the design of an "analogue" machine for calculating the zeros of the Riemann zeta-function, similar to the one used in Liverpool for calculating the tides." (Herken, The Universal Turing Machine: A Half-Century Survey, p. 110). Having worked on the zeta-function since his Ph.D.-thesis but never having published anything directly on the topic, Turing began working as chief cryptanalyst during the Second World War and thus postponed this important work till after the war. Thus, it was not until 1945 that he was actually able to publish his first work on this most important subject, namely the work that he had presented already in 1939, the groundbreaking "A Method for the Calculation of the Zeta-Function", which constitutes his first printed contribution to the subject."After the publication of his paper "On computable Numbers," Turing had begun investigating the Riemann zeta-function calculation, an aspect of the Riemann hypothesis concerning the distribution of prime numbers. Turing's work on this problem was interrupted by World War II, but in 1950 he resumed his investigations with the aid of the Manchester University Mark I [one of the earliest general purpose digital computers]." (Origins of Cyberspace p. 468).Not in Origins of Cyberspace (on this subject only having his 1953-paper - No. 938).