Automatic Card Counting Machine
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Historically, computers were human clerks who calculated in accordancewith effective methods. These human computers did the sorts ofcalculation nowadays carried out by electronic computers, and manythousands of them were employed in commerce, government, and researchestablishments. The term computing machine, used increasinglyfrom the 1920s, refers to any machine that does the work of a humancomputer, i.e., any machine that calculates in accordance witheffective methods. During the late 1940s and early 1950s, with theadvent of electronic computing machines, the phrase ‘computingmachine’ gradually gave way simply to ‘computer’,initially usually with the prefix ‘electronic’ or‘digital’. This entry surveys the history of thesemachines.
Babbage
Charles Babbage was Lucasian Professor of Mathematics at CambridgeUniversity from 1828 to 1839 (a post formerly held by Isaac Newton).Babbage's proposed Difference Engine was a special-purpose digitalcomputing machine for the automatic production of mathematical tables(such as logarithm tables, tide tables, and astronomical tables). TheDifference Engine consisted entirely of mechanical components —brass gear wheels, rods, ratchets, pinions, etc. Numbers wererepresented in the decimal system by the positions of 10-toothed metalwheels mounted in columns. Babbage exhibited a small working model in1822. He never completed the full-scale machine that he had designedbut did complete several fragments. The largest — one ninth ofthe complete calculator — is on display in the London ScienceMuseum. Babbage used it to perform serious computational work,calculating various mathematical tables. In 1990, Babbage's DifferenceEngine No. 2 was finally built from Babbage's designs and is also ondisplay at the London Science Museum.
The Swedes Georg and Edvard Scheutz (father and son) constructed amodified version of Babbage's Difference Engine. Three were made, aprototype and two commercial models, one of these being sold to anobservatory in Albany, New York, and the other to theRegistrar-General's office in London, where it calculated and printedactuarial tables.
Babbage's proposed Analytical Engine, considerably more ambitiousthan the Difference Engine, was to have been a general-purposemechanical digital computer. The Analytical Engine was to have had amemory store and a central processing unit (or ‘mill’) andwould have been able to select from among alternative actionsconsequent upon the outcome of its previous actions (a facilitynowadays known as conditional branching). The behaviour of theAnalytical Engine would have been controlled by a program ofinstructions contained on punched cards connected together with ribbons(an idea that Babbage had adopted from the Jacquard weaving loom).Babbage emphasised the generality of the Analytical Engine, saying‘the conditions which enable a finite machine to makecalculations of unlimited extent are fulfilled in the AnalyticalEngine’ (Babbage [1994], p. 97).
Babbage worked closely with Ada Lovelace, daughter of the poetByron, after whom the modern programming language ADA is named.Lovelace foresaw the possibility of using the Analytical Engine fornon-numeric computation, suggesting that the Engine might even becapable of composing elaborate pieces of music.
A large model of the Analytical Engine was under construction at thetime of Babbage's death in 1871 but a full-scale version was neverbuilt. Babbage's idea of a general-purpose calculating engine was neverforgotten, especially at Cambridge, and was on occasion a lively topicof mealtime discussion at the war-time headquarters of the GovernmentCode and Cypher School, Bletchley Park, Buckinghamshire, birthplace ofthe electronic digital computer.
Automated Counting Machine
Analog computers
The earliest computing machines in wide use were not digital butanalog. In analog representation, properties of the representationalmedium ape (or reflect or model) properties of the representedstate-of-affairs. (In obvious contrast, the strings of binary digitsemployed in digital representation do not represent by meansof possessing some physical property — such as length —whose magnitude varies in proportion to the magnitude of the propertythat is being represented.) Analog representations form a diverseclass. Some examples: the longer a line on a road map, the longer theroad that the line represents; the greater the number of clear plasticsquares in an architect's model, the greater the number of windows inthe building represented; the higher the pitch of an acoustic depthmeter, the shallower the water. In analog computers, numericalquantities are represented by, for example, the angle of rotation of ashaft or a difference in electrical potential. Thus the output voltageof the machine at a time might represent the momentary speed of theobject being modelled.
As the case of the architect's model makes plain, analogrepresentation may be discrete in nature (there is no suchthing as a fractional number of windows). Among computer scientists,the term ‘analog’ is sometimes used narrowly, to indicaterepresentation of one continuously-valued quantity by another(e.g., speed by voltage). As Brian Cantwell Smith has remarked:
‘Analog’ should … be a predicate on arepresentation whose structure corresponds to that of which itrepresents … That continuous representations should historicallyhave come to be called analog presumably betrays the recognition that,at the levels at which it matters to us, the world is morefoundationally continuous than it is discrete. (Smith [1991], p.271)
James Thomson, brother of Lord Kelvin, invented the mechanicalwheel-and-disc integrator that became the foundation of analogcomputation (Thomson [1876]). The two brothers constructed a device forcomputing the integral of the product of two given functions, andKelvin described (although did not construct) general-purpose analogmachines for integrating linear differential equations of any order andfor solving simultaneous linear equations. Kelvin's most successfulanalog computer was his tide predicting machine, which remained in useat the port of Liverpool until the 1960s. Mechanical analog devicesbased on the wheel-and-disc integrator were in use during World War Ifor gunnery calculations. Following the war, the design of theintegrator was considerably improved by Hannibal Ford (Ford [1919]).
Stanley Fifer reports that the first semi-automatic mechanicalanalog computer was built in England by the Manchester firm ofMetropolitan Vickers prior to 1930 (Fifer [1961], p. 29); however, Ihave so far been unable to verify this claim. In 1931, Vannevar Bush,working at MIT, built the differential analyser, the first large-scaleautomatic general-purpose mechanical analog computer. Bush's design wasbased on the wheel and disc integrator. Soon copies of his machine werein use around the world (including, at Cambridge and ManchesterUniversities in England, differential analysers built out of kit-setMeccano, the once popular engineering toy).
It required a skilled mechanic equipped with a lead hammer to set upBush's mechanical differential analyser for each new job. Subsequently,Bush and his colleagues replaced the wheel-and-disc integrators andother mechanical components by electromechanical, and finally byelectronic, devices.
A differential analyser may be conceptualised as a collection of‘black boxes’ connected together in such a way as to allowconsiderable feedback. Each box performs a fundamental process, forexample addition, multiplication of a variable by a constant, andintegration. In setting up the machine for a given task, boxes areconnected together so that the desired set of fundamental processes isexecuted. In the case of electrical machines, this was done typicallyby plugging wires into sockets on a patch panel (computing machineswhose function is determined in this way are referred to as‘program-controlled’).
Since all the boxes work in parallel, an electronic differentialanalyser solves sets of equations very quickly. Against this has to beset the cost of massaging the problem to be solved into the formdemanded by the analog machine, and of setting up the hardware toperform the desired computation. A major drawback of analog computationis the higher cost, relative to digital machines, of an increase inprecision. During the 1960s and 1970s, there was considerable interestin ‘hybrid’ machines, where an analog section is controlledby and programmed via a digital section. However, such machines are nowa rarity.
The Universal Turing Machine
In 1936, at Cambridge University, Turing invented the principle of themodern computer. He described an abstract digital computing machineconsisting of a limitless memory and a scanner that moves back andforth through the memory, symbol by symbol, reading what it finds andwriting further symbols (Turing [1936]). The actions of the scanner aredictated by a program of instructions that is stored in the memory inthe form of symbols. This is Turing's stored-program concept, andimplicit in it is the possibility of the machine operating on andmodifying its own program. (In London in 1947, in the course of whatwas, so far as is known, the earliest public lecture to mentioncomputer intelligence, Turing said, ‘What we want is a machinethat can learn from experience’, adding that the‘possibility of letting the machine alter its own instructionsprovides the mechanism for this’ (Turing [1947] p. 393). Turing'scomputing machine of 1936 is now known simply as the universal Turingmachine. Cambridge mathematician Max Newman remarked that right fromthe start Turing was interested in the possibility of actually buildinga computing machine of the sort that he had described (Newman ininterview with Christopher Evans in Evans [197?].
From the start of the Second World War Turing was a leadingcryptanalyst at the Government Code and Cypher School, Bletchley Park.Here he became familiar with Thomas Flowers' work involving large-scalehigh-speed electronic switching (described below). However, Turingcould not turn to the project of building an electronic stored-programcomputing machine until the cessation of hostilities in Europe in1945.
During the wartime years Turing did give considerable thought to thequestion of machine intelligence. Colleagues at Bletchley Park recallnumerous off-duty discussions with him on the topic, and at one pointTuring circulated a typewritten report (now lost) setting out some ofhis ideas. One of these colleagues, Donald Michie (who later foundedthe Department of Machine Intelligence and Perception at the Universityof Edinburgh), remembers Turing talking often about the possibility ofcomputing machines (1) learning from experience and (2) solvingproblems by means of searching through the space of possible solutions,guided by rule-of-thumb principles (Michie in interview with Copeland,1995). The modern term for the latter idea is ‘heuristicsearch’, a heuristic being any rule-of-thumb principle that cutsdown the amount of searching required in order to find a solution to aproblem. At Bletchley Park Turing illustrated his ideas on machineintelligence by reference to chess. Michie recalls Turing experimentingwith heuristics that later became common in chess programming (inparticular minimax and best-first).
Further information about Turing and the computer, including hiswartime work on codebreaking and his thinking about artificialintelligence and artificial life, can be found in Copeland 2004.
Electromechanical versus Electronic Computation
With some exceptions — including Babbage's purely mechanicalengines, and the finger-powered National Accounting Machine - earlydigital computing machines were electromechanical. That is to say,their basic components were small, electrically-driven, mechanicalswitches called ‘relays’. These operate relatively slowly,whereas the basic components of an electronic computer —originally vacuum tubes (valves) — have no moving parts saveelectrons and so operate extremely fast. Electromechanical digitalcomputing machines were built before and during the second world war by(among others) Howard Aiken at Harvard University, George Stibitz atBell Telephone Laboratories, Turing at Princeton University andBletchley Park, and Konrad Zuse in Berlin. To Zuse belongs the honourof having built the first working general-purpose program-controlleddigital computer. This machine, later called the Z3, was functioning in1941. (A program-controlled computer, as opposed to a stored-programcomputer, is set up for a new task by re-routing wires, by means ofplugs etc.)
Relays were too slow and unreliable a medium for large-scalegeneral-purpose digital computation (although Aiken made a valianteffort). It was the development of high-speed digital techniques usingvacuum tubes that made the modern computer possible.
The earliest extensive use of vacuum tubes for digitaldata-processing appears to have been by the engineer Thomas Flowers,working in London at the British Post Office Research Station at DollisHill. Electronic equipment designed by Flowers in 1934, for controllingthe connections between telephone exchanges, went into operation in1939, and involved between three and four thousand vacuum tubes runningcontinuously. In 1938–1939 Flowers worked on an experimentalelectronic digital in the machine.… Certain of these numbers, or 'words' are read, one afteranother, as orders. In one possible type of machine an order consistsof four numbers, for example 11, 13, 27, 4. The number 4 signifies'add', and when control shifts to this word the 'houses' H11 and H13will be connected to the adder as inputs, and H27 as output. Thenumbers stored in H11 and H13 pass through the adder, are added, andthe sum is passed on to H27. The control then shifts to the next order.In most real machines the process just described would be done by threeseparate orders, the first bringing [H11] (=content of H11) to acentral accumulator, the second adding [H13] into the accumulator, andthe third sending the result to H27; thus only one address would berequired in each order. … A machine with storage, with thisautomatic-telephone-exchange arrangement and with the necessary adders,subtractors and so on, is, in a sense, already a universal machine.(Newman [1948], pp. 271–272)
Following this explanation of Turing's three-address concept (source1, source 2, destination, function) Newman went on to describe programstorage (‘the orders shall be in a series of houses X1, X2,…’) and conditional branching. He then summed up:
From this highly simplified account it emerges that theessential internal parts of the machine are, first, a storage fornumbers (which may also be orders). … Secondly, adders,multipliers, etc. Thirdly, an 'automatic telephone exchange' forselecting 'houses', connecting them to the arithmetic organ, andwriting the answers in other prescribed houses. Finally, means ofmoving control at any stage to any chosen order, if a certain conditionis satisfied, otherwise passing to the next order in the normalsequence. Besides these there must be ways of setting up the machine atthe outset, and extracting the final answer in useable form. (Newman[1948], pp. 273–4)
In a letter written in 1972 Williams described in some detail whathe and Kilburn were told by Newman:
About the middle of the year [1946] the possibility of anappointment at Manchester University arose and I had a talk withProfessor Newman who was already interested in the possibility ofdeveloping computers and had acquired a grant from the Royal Society of£30,000 for this purpose. Since he understood computers and Iunderstood electronics the possibilities of fruitful collaboration wereobvious. I remember Newman giving us a few lectures in which heoutlined the organisation of a computer in terms of numbers beingidentified by the address of the house in which they were placed and interms of numbers being transferred from this address, one at a time, toan accumulator where each entering number was added to what was alreadythere. At any time the number in the accumulator could be transferredback to an assigned address in the store and the accumulator clearedfor further use. The transfers were to be effected by a stored programin which a list of instructions was obeyed sequentially. Orderedprogress through the list could be interrupted by a test instructionwhich examined the sign of the number in the accumulator. Thereafteroperation started from a new point in the list of instructions. Thiswas the first information I received about the organisation ofcomputers. … Our first computer was the simplest embodiment ofthese principles, with the sole difference that it used a subtractingrather than an adding accumulator. (Letter from Williams to Randell,1972; in Randell [1972], p. 9)
Turing's early input to the developments at Manchester, hinted at byWilliams in his above-quoted reference to Turing, may have been via thelectures on computer design that Turing and Wilkinson gave in Londonduring the period December 1946 to February 1947 (Turing and Wilkinson[1946–7]). The lectures were attended by representatives ofvarious organisations planning to use or build an electronic computer.Kilburn was in the audience (Bowker and Giordano [1993]). (Kilburnusually said, when asked from where he obtained his basic knowledge ofthe computer, that he could not remember (letter from Brian Napper toCopeland, 2002); for example, in a 1992 interview he said:‘Between early 1945 and early 1947, in that period, somehow orother I knew what a digital computer was … Where I got thisknowledge from I've no idea’ (Bowker and Giordano [1993], p.19).)
Whatever role Turing's lectures may have played in informingKilburn, there is little doubt that credit for the Manchester computer— called the ‘Newman-Williams machine’ in acontemporary document (Huskey 1947) — belongs not only toWilliams and Kilburn but also to Newman, and that the influence onNewman of Turing's 1936 paper was crucial, as was the influence ofFlowers' Colossus.
The first working AI program, a draughts (checkers) player writtenby Christopher Strachey, ran on the Ferranti Mark I in the ManchesterComputing Machine Laboratory. Strachey (at the time a teacher at HarrowSchool and an amateur programmer) wrote the program with Turing'sencouragement and utilising the latter's recently completedProgrammers' Handbook for the Ferranti. (Strachey later became Directorof the Programming Research Group at Oxford University.) By the summerof 1952, the program could, Strachey reported, ‘play a completegame of draughts at a reasonable speed’. (Strachey's program formed thebasis for Arthur Samuel's well-known checkers program.) The firstchess-playing program, also, was written for the Manchester Ferranti,by Dietrich Prinz; the program first ran in November 1951. Designed forsolving simple problems of the mate-in-two variety, the program wouldexamine every possible move until a solution was found. Turing startedto program his ‘Turochamp’ chess-player on the FerrantiMark I, but never completed the task. Unlike Prinz's program, theTurochamp could play a complete game (when hand-simulated) and operatednot by exhaustive search but under the guidance of heuristics.
ENIAC and EDVAC
The first fully functioning electronic digital computer to be built inthe U.S. was ENIAC, constructed at the Moore School of ElectricalEngineering, University of Pennsylvania, for the Army OrdnanceDepartment, by J. Presper Eckert and John Mauchly. Completed in 1945,ENIAC was somewhat similar to the earlier Colossus, but considerablylarger and more flexible (although far from general-purpose). Theprimary function for which ENIAC was designed was the calculation oftables used in aiming artillery. ENIAC was not a stored-programcomputer, and setting it up for a new job involved reconfiguring themachine by means of plugs and switches. For many years, ENIAC wasbelieved to have been the first functioning electronic digitalcomputer, Colossus being unknown to all but a few.
In 1944, John von Neumann joined the ENIAC group. He had become‘intrigued’ (Goldstine's word, [1972], p. 275) withTuring's universal machine while Turing was at Princeton Universityduring 1936–1938. At the Moore School, von Neumann emphasised theimportance of the stored-program concept for electronic computing,including the possibility of allowing the machine to modify its ownprogram in useful ways while running (for example, in order to controlloops and branching). Turing's paper of 1936 (‘On ComputableNumbers, with an Application to the Entscheidungsproblem’) wasrequired reading for members of von Neumann's post-war computer projectat the Institute for Advanced Study, Princeton University (letter fromJulian Bigelow to Copeland, 2002; see also Copeland [2004], p. 23).Eckert appears to have realised independently, and prior to vonNeumann's joining the ENIAC group, that the way to take full advantageof the speed at which data is processed by electronic circuits is toplace suitably encoded instructions for controlling the processing inthe same high-speed storage devices that hold the data itself(documented in Copeland [2004], pp. 26–7). In 1945, while ENIACwas still under construction, von Neumann produced a draft report,mentioned previously, setting out the ENIAC group's ideas for anelectronic stored-program general-purpose digital computer, the EDVAC(von Neuman [1945]). The EDVAC was completed six years later, but notby its originators, who left the Moore School to build computerselsewhere. Lectures held at the Moore School in 1946 on the proposedEDVAC were widely attended and contributed greatly to the disseminationof the new ideas.
Von Neumann was a prestigious figure and he made the concept of ahigh-speed stored-program digital computer widely known through hiswritings and public addresses. As a result of his high profile in thefield, it became customary, although historically inappropriate, torefer to electronic stored-program digital computers as ‘vonNeumann machines’.
The Los Alamos physicist Stanley Frankel, responsible with vonNeumann and others for mechanising the large-scale calculationsinvolved in the design of the atomic bomb, has described von Neumann'sview of the importance of Turing's 1936 paper, in a letter:
I know that in or about 1943 or ‘44 von Neumann waswell aware of the fundamental importance of Turing's paper of 1936… Von Neumann introduced me to that paper and at his urging Istudied it with care. Many people have acclaimed von Neumann as the'father of the computer' (in a modern sense of the term) but I am surethat he would never have made that mistake himself. He might well becalled the midwife, perhaps, but he firmly emphasized to me, and toothers I am sure, that the fundamental conception is owing to Turing,in so far as not anticipated by Babbage … Both Turing and vonNeumann, of course, also made substantial contributions to the'reduction to practice' of these concepts but I would not regard theseas comparable in importance with the introduction and explication ofthe concept of a computer able to store in its memory its program ofactivities and of modifying that program in the course of theseactivities. (Quoted in Randell [1972], p. 10)
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Other Notable Early Computers
Other notable early stored-program electronic digital computers were:
- EDSAC, 1949, built at Cambridge University by Maurice Wilkes
- BINAC, 1949, built by Eckert's and Mauchly's Electronic ControlCo., Philadelphia (opinions differ over whether BINAC ever actuallyworked)
- Whirlwind I, 1949, Digital Computer Laboratory, MassachusettsInstitute of Technology, Jay Forrester
- SEAC, 1950, US Bureau of Standards Eastern Division, WashingtonD.C., Samuel Alexander, Ralph Slutz
- SWAC, 1950, US Bureau of Standards Western Division, Institute forNumerical Analysis, University of California at Los Angeles, HarryHuskey
- UNIVAC, 1951, Eckert-Mauchly Computer Corporation, Philadelphia(the first computer to be available commercially in the U.S.)
- the IAS computer, 1952, Institute for Advanced Study, PrincetonUniversity, Julian Bigelow, Arthur Burks, Herman Goldstine, vonNeumann, and others (thanks to von Neumann's publishing thespecifications of the IAS machine, it became the model for a group ofcomputers known as the Princeton Class machines; the IAS computer wasalso a strong influence on the IBM 701)
- IBM 701, 1952, International Business Machine's first mass-producedelectronic stored-program computer.
High-Speed Memory
The EDVAC and ACE proposals both advocated the use of mercury-filledtubes, called ‘delay lines’, for high-speed internalmemory. This form of memory is known as acoustic memory. Delay lineshad initially been developed for echo cancellation in radar; the ideaof using them as memory devices originated with Eckert at the MooreSchool. Here is Turing's description:
It is proposed to build 'delay line' units consisting ofmercury … tubes about 5′ long and 1″ in diameter incontact with a quartz crystal at each end. The velocity of sound in… mercury … is such that the delay will be 1.024 ms. Theinformation to be stored may be considered to be a sequence of 1024‘digits’ (0 or 1) … These digits will be representedby a corresponding sequence of pulses. The digit 0 … will berepresented by the absence of a pulse at the appropriate time, thedigit 1 … by its presence. This series of pulses is impressed onthe end of the line by one piezo-crystal, it is transmitted down theline in the form of supersonic waves, and is reconverted into a varyingvoltage by the crystal at the far end. This voltage is amplifiedsufficiently to give an output of the order of 10 volts peak to peakand is used to gate a standard pulse generated by the clock. This pulsemay be again fed into the line by means of the transmitting crystal, orwe may feed in some altogether different signal. We also have thepossibility of leading the gated pulse to some other part of thecalculator, if we have need of that information at the time. Making useof the information does not of course preclude keeping it also. (Turing[1945], p. 375)
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Mercury delay line memory was used in EDSAC, BINAC, SEAC, PilotModel ACE, EDVAC, DEUCE, and full-scale ACE (1958). The chief advantageof the delay line as a memory medium was, as Turing put it, that delaylines were 'already a going concern' (Turing [1947], p. 380). Thefundamental disadvantages of the delay line were that random access isimpossible and, moreover, the time taken for an instruction, or number,to emerge from a delay line depends on where in the line it happens tobe.
In order to minimize waiting-time, Turing arranged for instructionsto be stored not in consecutive positions in the delay line, but inrelative positions selected by the programmer in such a way that eachinstruction would emerge at exactly the time it was required, in so faras this was possible. Each instruction contained a specification of thelocation of the next. This system subsequently became known as‘optimum coding’. It was an integral feature of everyversion of the ACE design. Optimum coding made for difficult and untidyprogramming, but the advantage in terms of speed was considerable.Thanks to optimum coding, the Pilot Model ACE was able to do a floatingpoint multiplication in 3 milliseconds (Wilkes's EDSAC required 4.5milliseconds to perform a single fixed point multiplication).
In the Williams tube or electrostatic memory, previously mentioned,a two-dimensional rectangular array of binary digits was stored on theface of a commercially-available cathode ray tube. Access to data wasimmediate. Williams tube memories were employed in the Manchesterseries of machines, SWAC, the IAS computer, and the IBM 701, and amodified form of Williams tube in Whirlwind I (until replacement bymagnetic core in 1953).
Drum memories, in which data was stored magnetically on the surfaceof a metal cylinder, were developed on both sides of the Atlantic. Theinitial idea appears to have been Eckert's. The drum providedreasonably large quantities of medium-speed memory and was used tosupplement a high-speed acoustic or electrostatic memory. In 1949, theManchester computer was successfully equipped with a drum memory; thiswas constructed by the Manchester engineers on the model of a drumdeveloped by Andrew Booth at Birkbeck College, London.
The final major event in the early history of electronic computationwas the development of magnetic core memory. Jay Forrester realisedthat the hysteresis properties of magnetic core (normally used intransformers) lent themselves to the implementation of athree-dimensional solid array of randomly accessible storage points. In1949, at Massachusetts Institute of Technology, he began to investigatethis idea empirically. Forrester's early experiments with metallic coresoon led him to develop the superior ferrite core memory. DigitalEquipment Corporation undertook to build a computer similar to theWhirlwind I as a test vehicle for a ferrite core memory. The MemoryTest Computer was completed in 1953. (This computer was used in 1954for the first simulations of neural networks, by Belmont Farley andWesley Clark of MIT's Lincoln Laboratory (see Copeland and Proudfoot[1996]).
Once the absolute reliability, relative cheapness, high capacity andpermanent life of ferrite core memory became apparent, core soonreplaced other forms of high-speed memory. The IBM 704 and 705computers (announced in May and October 1954, respectively) broughtcore memory into wide use.
Bibliography
Works Cited
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- Bennett, S., 1976, ‘F.C. Williams: his contribution to thedevelopment of automatic control’, National Archive for theHistory of Computing, University of Manchester, England. (This is atypescript based on interviews with Williams in 1976.)
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- Copeland, B.J. (ed.), 2004, The Essential Turing OxfordUniversity Press
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- Thomson, J., 1876, ‘On an Integrating Machine Having a NewKinematic Principle’ Proceedings of the Royal Society ofLondon, 24: 262–5
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- Turing, A.M., and Wilkinson, J.H., 1946–7, ‘TheTuring-Wilkinson Lecture Series (1946-7)’, in Alan Turing'sAutomatic Computing Engine (Copeland [2005])
- von Neumann, J., 1945, ‘First Draft of a Report on theEDVAC’, in Stern, N. From ENIAC to UNIVAC: An Appraisal ofthe Eckert-Mauchly Computers Bedford, Mass.: Digital Press (1981),pp. 181–246
- Williams, F.C., 1975, ‘Early Computers at ManchesterUniversity’ The Radio and Electronic Engineer,45 (1975): 237–331
- Wynn-Williams, C.E., 1932, ‘A Thyratron 'Scale of Two'Automatic Counter’ Proceedings of the Royal Society ofLondon, series A, 136: 312–324
Further Reading
- Copeland, B.J., 2004, ‘Colossus — Its Origins andOriginators’ Annals of the History of Computing,26: 38–45
- Metropolis, N., Howlett, J., Rota, G.C. (eds), 1980, A Historyof Computing in the Twentieth Century New York: AcademicPress
- Randell, B. (ed.), 1982, The Origins of Digital Computers:Selected Papers Berlin: Springer-Verlag
- Williams, M.R., 1997, A History of Computing TechnologyLos Alamitos: IEEE Computer Society Press
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computability and complexity recursive functions Turing, Alan Turing machines
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B. Jack Copeland<jack.copeland@canterbury.ac.nz>