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Analytical Engine

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   Proposed mechanical general-purpose computer

   Portion of the calculating machine with a printing mechanism of the
   Analytical Engine, built by Charles Babbage, as displayed at the
   Science Museum (London)^[1]
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   The Analytical Engine was a proposed mechanical general-purpose
   computer designed by English mathematician and computer pioneer Charles
   Babbage.^[2]^[3] It was first described in 1837 as the successor to
   Babbage's difference engine, which was a design for a simpler
   mechanical calculator.^[4]

   The Analytical Engine incorporated an arithmetic logic unit, control
   flow in the form of conditional branching and loops, and integrated
   memory, making it the first design for a general-purpose computer that
   could be described in modern terms as Turing-complete.^[5]^[6] In other
   words, the structure of the Analytical Engine was essentially the same
   as that which has dominated computer design in the electronic era.^[3]
   The Analytical Engine is one of the most successful achievements of
   Charles Babbage.

   Babbage was never able to complete construction of any of his machines
   due to conflicts with his chief engineer and inadequate
   funding.^[7]^[8] It was not until 1941 that Konrad Zuse built the first
   general-purpose computer, Z3, more than a century after Babbage had
   proposed the pioneering Analytical Engine in 1837.^[3]
   [ ]


     * 1 Design
     * 2 Construction
     * 3 Instruction set
     * 4 Influence
          + 4.1 Predicted influence
          + 4.2 Computer science
     * 5 Comparison to other early computers
     * 6 In popular culture
     * 7 References
     * 8 Bibliography
     * 9 External links


   Two types of punched cards used to program the machine. Foreground:
   'operational cards', for inputting instructions; background: 'variable
   cards', for inputting data

   Babbage's first attempt at a mechanical computing device, the
   Difference Engine, was a special-purpose machine designed to tabulate
   logarithms and trigonometric functions by evaluating finite differences
   to create approximating polynomials. Construction of this machine was
   never completed; Babbage had conflicts with his chief engineer, Joseph
   Clement, and ultimately the British government withdrew its funding for
   the project.^[9]^[10]^[11]

   During this project, Babbage realised that a much more general design,
   the Analytical Engine, was possible.^[9] The work on the design of the
   Analytical Engine started around 1833.^[12]^[4]

   The input, consisting of programs ("formulae") and data,^[13]^[9] was
   to be provided to the machine via punched cards, a method being used at
   the time to direct mechanical looms such as the Jacquard loom.^[14] For
   output, the machine would have a printer, a curve plotter, and a
   bell.^[9] The machine would also be able to punch numbers onto cards to
   be read in later. It employed ordinary base-10 fixed-point

   There was to be a store (that is, a memory) capable of holding 1,000
   numbers of 40 decimal digits^[15] each (ca. 16.6 kB). An arithmetic
   unit (the "mill") would be able to perform all four arithmetic
   operations, plus comparisons and optionally square roots.^[16]
   Initially (1838) it was conceived as a difference engine curved back
   upon itself, in a generally circular layout, with the long store
   exiting off to one side.^[17] Later drawings (1858) depict a
   regularised grid layout.^[18] Like the central processing unit (CPU) in
   a modern computer, the mill would rely upon its own internal
   procedures, to be stored in the form of pegs inserted into rotating
   drums called "barrels", to carry out some of the more complex
   instructions the user's program might specify.^[7]

   The programming language to be employed by users was akin to modern day
   assembly languages. Loops and conditional branching were possible, and
   so the language as conceived would have been Turing-complete as later
   defined by Alan Turing. Three different types of punch cards were used:
   one for arithmetical operations, one for numerical constants, and one
   for load and store operations, transferring numbers from the store to
   the arithmetical unit or back. There were three separate readers for
   the three types of cards. Babbage developed some two dozen programs for
   the Analytical Engine between 1837 and 1840, and one program
   later.^[14]^[19] These programs treat polynomials, iterative formulas,
   Gaussian elimination, and Bernoulli numbers.^[14]^[20]

   In 1842, the Italian mathematician Luigi Federico Menabrea published a
   description of the engine in French,^[21] based on lectures Babbage
   gave when he visited Turin in 1840.^[22] In 1843, the description was
   translated into English and extensively annotated by Ada Lovelace, who
   had become interested in the engine eight years earlier.^[13] In
   recognition of her additions to Menabrea's paper, which included a way
   to calculate Bernoulli numbers using the machine (widely considered to
   be the first complete computer program), she has been described as the
   first computer programmer.


   Henry Babbage's Analytical Engine Mill, built in 1910,^[23] in the
   Science Museum (London)

   Late in his life, Babbage sought ways to build a simplified version of
   the machine, and assembled a small part of it before his death in

   In 1878, a committee of the British Association for the Advancement of
   Science described the Analytical Engine as "a marvel of mechanical
   ingenuity", but recommended against constructing it. The committee
   acknowledged the usefulness and value of the machine, but could not
   estimate the cost of building it, and were unsure whether the machine
   would function correctly after being built.^[25]^[26]

   Intermittently from 1880 to 1910,^[27] Babbage's son Henry Prevost
   Babbage was constructing a part of the mill and the printing apparatus.
   In 1910, it was able to calculate a (faulty) list of multiples of
   pi.^[28] This constituted only a small part of the whole engine; it was
   not programmable and had no storage. (Popular images of this section
   have sometimes been mislabelled, implying that it was the entire mill
   or even the entire engine.) Henry Babbage's "Analytical Engine Mill" is
   on display at the Science Museum in London.^[23] Henry also proposed
   building a demonstration version of the full engine, with a smaller
   storage capacity: "perhaps for a first machine ten (columns) would do,
   with fifteen wheels in each".^[29] Such a version could manipulate
   20 numbers of 25 digits each, and what it could be told to do with
   those numbers could still be impressive. "It is only a question of
   cards and time", wrote Henry Babbage in 1888, "... and there is no
   reason why (twenty thousand) cards should not be used if necessary, in
   an Analytical Engine for the purposes of the mathematician".^[29]

   In 1991, the London Science Museum built a complete and working
   specimen of Babbage's Difference Engine No. 2, a design that
   incorporated refinements Babbage discovered during the development of
   the Analytical Engine.^[5] This machine was built using materials and
   engineering tolerances that would have been available to Babbage,
   quelling the suggestion that Babbage's designs could not have been
   produced using the manufacturing technology of his time.^[30]

   In October 2010, John Graham-Cumming started a "Plan 28" campaign to
   raise funds by "public subscription" to enable serious historical and
   academic study of Babbage's plans, with a view to then build and test a
   fully working virtual design which will then in turn enable
   construction of the physical Analytical Engine.^[31]^[32]^[33] As of
   May 2016, actual construction had not been attempted, since no
   consistent understanding could yet be obtained from Babbage's original
   design drawings. In particular it was unclear whether it could handle
   the indexed variables which were required for Lovelace's Bernoulli
   program.^[34] By 2017, the "Plan 28" effort reported that a searchable
   database of all catalogued material was available, and an initial
   review of Babbage's voluminous Scribbling Books had been

   Many of Babbage's original drawings have been digitised and are
   publicly available online.^[36]

Instruction set[edit]

   Plan diagram of the Analytical Engine from 1840

   Babbage is not known to have written down an explicit set of
   instructions for the engine in the manner of a modern processor manual.
   Instead he showed his programs as lists of states during their
   execution, showing what operator was run at each step with little
   indication of how the control flow would be guided.

   Allan G. Bromley has assumed that the card deck could be read in
   forwards and backwards directions as a function of conditional
   branching after testing for conditions, which would make the engine

     ...the cards could be ordered to move forward and reverse (and hence
     to loop)...^[14]

     The introduction for the first time, in 1845, of user operations for
     a variety of service functions including, most importantly, an
     effective system for user control of looping in user programs. There
     is no indication how the direction of turning of the operation and
     variable cards is specified. In the absence of other evidence I have
     had to adopt the minimal default assumption that both the operation
     and variable cards can only be turned backward as is necessary to
     implement the loops used in Babbage's sample programs. There would
     be no mechanical or microprogramming difficulty in placing the
     direction of motion under the control of the user.^[37]

   In their emulator of the engine, Fourmilab say:

     The Engine's Card Reader is not constrained to simply process the
     cards in a chain one after another from start to finish. It can, in
     addition, directed by the very cards it reads and advised by whether
     the Mill's run-up lever is activated, either advance the card chain
     forward, skipping the intervening cards, or backward, causing
     previously-read cards to be processed once again.

   This emulator does provide a written symbolic instruction set, though
   this has been constructed by its authors rather than based on Babbage's
   original works. For example, a factorial program would be written as:
N0 6
N1 1
N2 1

   where the CB is the conditional branch instruction or "combination
   card" used to make the control flow jump, in this case backward by 11


Predicted influence[edit]

   Babbage understood that the existence of an automatic computer would
   kindle interest in the field now known as algorithmic efficiency,
   writing in his Passages from the Life of a Philosopher, "As soon as an
   Analytical Engine exists, it will necessarily guide the future course
   of the science. Whenever any result is sought by its aid, the question
   will then arise--By what course of calculation can these results be
   arrived at by the machine in the shortest time?"^[38]

Computer science[edit]

   From 1872 Henry continued diligently with his father's work and then
   intermittently in retirement in 1875.^[39]

   Percy Ludgate wrote about the engine in 1914^[40] and published his own
   design for an Analytical Engine in 1909.^[41]^[42] It was drawn up in
   detail, but never built, and the drawings have never been found.
   Ludgate's engine would be much smaller (about 8 cubic feet (230 L),
   which corresponds to cube of side length 2 feet (61 cm)) than
   Babbage's, and hypothetically would be capable of multiplying two
   20-decimal-digit numbers in about six seconds.^[43]

   In his Essays on Automatics (1913) Leonardo Torres y Quevedo, inspired
   by Babbage, designed a theoretical electromechanical calculating
   machine which was to be controlled by a read-only program. The paper
   also contains the idea of floating-point arithmetic.^[44]

   Vannevar Bush's paper Instrumental Analysis (1936) included several
   references to Babbage's work. In the same year he started the Rapid
   Arithmetical Machine project to investigate the problems of
   constructing an electronic digital computer.^[43]

   Despite this groundwork, Babbage's work fell into historical obscurity,
   and the Analytical Engine was unknown to builders of electromechanical
   and electronic computing machines in the 1930s and 1940s when they
   began their work, resulting in the need to re-invent many of the
   architectural innovations Babbage had proposed. Howard Aiken, who built
   the quickly-obsoleted electromechanical calculator, the Harvard Mark I,
   between 1937 and 1945, praised Babbage's work likely as a way of
   enhancing his own stature, but knew nothing of the Analytical Engine's
   architecture during the construction of the Mark I, and considered his
   visit to the constructed portion of the Analytical Engine "the greatest
   disappointment of my life".^[45] The Mark I showed no influence from
   the Analytical Engine and lacked the Analytical Engine's most prescient
   architectural feature, conditional branching.^[45] J. Presper Eckert
   and John W. Mauchly similarly were not aware of the details of
   Babbage's Analytical Engine work prior to the completion of their
   design for the first electronic general-purpose computer, the

Comparison to other early computers[edit]

   If the Analytical Engine had been built, it would have been digital,
   programmable and Turing-complete. It would, however, have been very
   slow. Luigi Federico Menabrea reported in Sketch of the Analytical
   Engine: "Mr. Babbage believes he can, by his engine, form the product
   of two numbers, each containing twenty figures, in three minutes".^[48]
   By comparison the Harvard Mark I could perform the same task in just
   six seconds. A modern PC can do the same thing in well under a
   billionth of a second.
   Further information: History of computing hardware S: Early digital
   computer characteristics
   Name First operational Numeral system Computing mechanism Programming
   Turing complete Memory
   Difference Engine Not built until the 1990s (design 1820s) Decimal
   Mechanical Not programmable; initial numerical constants of polynomial
   differences set physically No Physical state of wheels in axes
   Analytical Engine Not built (design 1830s) Decimal Mechanical
   Program-controlled by punched cards Yes Physical state of wheels in
   Ludgate's Analytical Engine Not built (design 1909) Decimal Mechanical
   Program-controlled by punched cards Yes Physical state of rods
   Torres y Quevedo's Analytical machine 1920 Decimal Electromechanical
   Not programmable; input and output settings specified by patch cables
   No Mechanical relays
   Zuse Z1 (Germany) 1939 Binary floating point Mechanical Not
   programmable; cipher input settings specified by patch cables No
   Physical state of rods
   Bombe (Poland, UK, US) 1939 (Polish), March 1940 (British), May 1943
   (US) Character computations Electro-mechanical Not programmable; cipher
   input settings specified by patch cables No Physical state of rotors
   Zuse Z2 (Germany) 1940 Binary floating point Electro-mechanical
   (Mechanical memory) Program-controlled by punched 35 mm film stock No
   Physical state of rods
   Zuse Z3 (Germany) May 1941 Binary floating point Electro-mechanical
   Program-controlled by punched 35 mm film stock In principle Mechanical
   Atanasoff-Berry Computer (US) 1942 Binary Electronic Not programmable;
   linear system coefficients input using punched cards No Regenerative
   capacitor memory
   Colossus Mark 1 (UK) December 1943 Binary Electronic Program-controlled
   by patch cables and switches No Thermionic valves (vacuum tubes) and
   Harvard Mark I - IBM ASCC (US) May 1944 Decimal Electro-mechanical
   Program-controlled by 24-channel punched paper tape (but no conditional
   branch) No Mechanical relays^[49]
   Zuse Z4 (Germany) March 1945 (or 1948)^[50] Binary floating point
   Electro-mechanical Program-controlled by punched 35 mm film stock In
   1950 Mechanical relays
   ENIAC (US) July 1946 Decimal Electronic Program-controlled by patch
   cables and switches Yes Vacuum tube triode flip-flops
   Manchester Baby (UK) 1948 Binary Electronic Binary program entered into
   memory by keyboard^[51] (first electronic stored-program digital
   computer) Yes Williams cathode ray tube
   EDSAC (UK) 1949 Binary Electronic Five-bit opcode and variable-length
   operand (first stored-program computer offering computing services to a
   wide community). Yes Mercury delay lines

In popular culture[edit]

     * The cyberpunk novelists William Gibson and Bruce Sterling
       co-authored a steampunk novel of alternative history titled The
       Difference Engine in which Babbage's difference and Analytical
       Engines became available to Victorian society. The novel explores
       the consequences and implications of the early introduction of
       computational technology.
     * Moriarty by Modem, a short story by Jack Nimersheim, describes an
       alternative history where Babbage's Analytical Engine was indeed
       completed and had been deemed highly classified by the British
       government. The characters of Sherlock Holmes and Moriarty had in
       reality been a set of prototype programs written for the Analytical
       Engine. This short story follows Holmes as his program is
       implemented on modern computers and he is forced to compete against
       his nemesis yet again in the modern counterparts of Babbage's
       Analytical Engine.^[52]
     * A similar setting is used by Sydney Padua in the webcomic The
       Thrilling Adventures of Lovelace and Babbage.^[53]^[54] It features
       an alternative history where Ada Lovelace and Babbage have built
       the Analytical Engine and use it to fight crime at Queen Victoria's
       request.^[55] The comic is based on thorough research on the
       biographies of and correspondence between Babbage and Lovelace,
       which is then twisted for humorous effect.
     * The Orion's Arm online project features the Machina Babbagenseii,
       fully sentient Babbage-inspired mechanical computers. Each is the
       size of a large asteroid, only capable of surviving in microgravity
       conditions, and processes data at 0.5% the speed of a human


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External links[edit]

     * icon Computer programming portal

   Wikimedia Commons has media related to Analytical Engine.

     * The Babbage Papers, Science Museum archive
     * The Analytical Engine at Fourmilab, includes historical documents
       and online simulations

   "Image of the "General Plan of Babbage's great calculating engine"
   (1840), plus a modern description of operational & programming
   features". Archived from the original on 21 August 2008.

     Image of a later Plan of Analytical Engine with grid layout (1858)

     First working Babbage "barrel" actually assembled, circa 2005

     Special issue, IEEE Annals of the History of Computing, Volume 22,
   Number 4, October-December 2000 (subscription required)

     Babbage, Science Museum, London (archived)

     "The Marvellous Analytical Engine- How It Works". 2D Goggles. 31 May
   2015. Archived from the original on 26 November 2021. Retrieved 23
   August 2017.

     Plan 28: Building Charles Babbage's Analytical Engine

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