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Other early mechanical devices used to perform one or another type of calculations include the [[planisphere]] and other mechanical computing devices invented by [[Al-Biruni]] (c. AD 1000); the [[equatorium]] and universal latitude-independent astrolabe by [[Al-Zarqali]] (c. AD 1015); the astronomical analog computers of other medieval [[Islamic astronomy|Muslim astronomers]] and engineers; and the astronomical [[clock tower]] of [[Su Song]] (1094) during the [[Song dynasty]]. The [[castle clock]], a [[hydropower]]ed mechanical [[astronomical clock]] invented by [[Ismail al-Jazari]] in 1206, was the first [[Computer programming|programmable]] analog computer.{{Disputed inline|for=The cited source doesn't support the claim, and the claim is misleading.|date=June 2022}}<ref name="Ancient Discoveries">{{citation|title=Episode 11: Ancient Robots|work=[[Ancient Discoveries]]|publisher=[[History Channel]]|url=https://www.youtube.com/watch?v=rxjbaQl0ad8|url-status=dead |access-date=2008-09-06|archive-date=2014-03-01 |archive-url=https://web.archive.org/web/20140301151115/https://www.youtube.com/watch?v=rxjbaQl0ad8}}</ref><ref>{{Cite book |last=Turner |first=Howard R. |title=Science in Medieval Islam: An Illustrated Introduction |page=184 |date=1997 |publisher=University of Texas press |isbn=978-0-292-78149-8 |___location=Austin}}</ref><ref>{{cite magazine |author-link=Donald Routledge Hill |last=Hill |first=Donald Routledge |title=Mechanical Engineering in the Medieval Near East |magazine=Scientific American |date=May 1991 |pages=64–69}} ([[cf.]] {{cite web |last=Hill |first=Donald Routledge |title=IX. Mechanical Engineering |url= http://home.swipnet.se/islam/articles/HistoryofSciences.htm |work=History of Sciences in the Islamic World |archive-url=https://web.archive.org/web/20071225091836/http://home.swipnet.se/islam/articles/HistoryofSciences.htm |archive-date=2007-12-25 |url-status=dead}})</ref> [[Ramon Llull]] invented the Lullian Circle: a notional machine for calculating answers to philosophical questions (in this case, to do with Christianity) via logical combinatorics. This idea was taken up by [[Gottfried Leibniz|Leibniz]] centuries later, and is thus one of the founding elements in computing and [[information science]].
=== Renaissance calculating tools=== ▼=== '''Impact of the Industrial Revolution on Computing Hardware''' {{discuss|section=New section}}===
The Industrial Revolution (late 18th to early 19th century) played a pivotal role in advancing computing hardware, setting the stage for modern mechanised and automated computing systems. During this time, industries demanded precise and large-scale calculations for tasks in fields such as navigation, engineering, and finance, leading to innovations in both design and function.
One of the most significant advancements was the creation of '''Charles Babbage’s Difference Engine''' (1822), a mechanical device designed to automate the calculation of polynomial functions. Babbage’s vision of a fully mechanical computer included a system of gears and wheels, powered by steam, capable of solving complex calculations that previously required extensive manual work. Although never fully realised in his lifetime, Babbage's designs led to later developments in computational logic and paved the way for programmable computers.<ref>{{Cite journal |last=Hutton |first=D.M. |date=2002-08-01 |title=The Difference Engine: Charles Babbage and the Quest to Build the First Computer |url=http://dx.doi.org/10.1108/k.2002.06731fae.009 |journal=Kybernetes |volume=31 |issue=6 |doi=10.1108/k.2002.06731fae.009 |issn=0368-492X}}</ref><ref>{{Cite journal |last=Campbell-Kelly |first=Martin |date=1988-07 |title=Charles Babbage's Table of Logarithms (1827) |url=http://dx.doi.org/10.1109/mahc.1988.10023 |journal=IEEE Annals of the History of Computing |volume=10 |issue=3 |pages=159–169 |doi=10.1109/mahc.1988.10023 |issn=1058-6180}}</ref>
In addition to Babbage, '''Ada Lovelace''' is credited with conceptualising algorithms that could be executed by a machine, making her one of the first to recognise the potential for computers to perform more than arithmetic tasks. Lovelace’s notes on Babbage’s Analytical Engine in the 1840s are often considered the first examples of computer programming.<ref>{{Cite journal |last=Toole |first=Betty Alexandra |date=1991-03 |title=Ada, an analyst and a metaphysician |url=http://dx.doi.org/10.1145/122028.122031 |journal=ACM SIGAda Ada Letters |volume=XI |issue=2 |pages=60–71 |doi=10.1145/122028.122031 |issn=1094-3641}}</ref>
The Industrial Revolution also spurred advancements in '''punched card technology''', initially developed by Joseph Marie Jacquard in 1804 for automated looms.<ref>{{Cite journal |last=Ceruzzi |first=Paul E |date=2006-01 |title=Jacquard's Web: How a Hand-Loom Led to the Birth of the Information Age (review) |url=http://dx.doi.org/10.1353/tech.2006.0061 |journal=Technology and Culture |volume=47 |issue=1 |pages=197–198 |doi=10.1353/tech.2006.0061 |issn=1097-3729}}</ref> This concept of using punched cards to control a machine was later adapted by Herman Hollerith in the 1890s for data processing, particularly during the U.S. Census.<ref>{{Cite journal |last=Olley |first=Allan |date=2008-12 |title=David Alan Grier. <i>When Computers Were Human</i>. 424 pp., apps., bibl., index. Princeton, N.J.: Princeton University Press, 2005. $19.95 (paper). |url=http://dx.doi.org/10.1086/597732 |journal=Isis |volume=99 |issue=4 |pages=870–871 |doi=10.1086/597732 |issn=0021-1753}}</ref> Hollerith’s machines could sort and tabulate data far faster than manual methods, establishing a direct link between industrial machinery and data processing technologies.<ref>{{Cite journal |last=Cortada |first=James W. |date=2015-12-31 |title=Before the Computer: IBM, NCR, Burroughs, and Remington Rand and the Industry They Created, 1865-1956 |url=http://dx.doi.org/10.1515/9781400872763 |doi=10.1515/9781400872763}}</ref>
By the end of the Industrial Revolution, innovations in '''mechanical computing and automation''' had laid the foundation for 20th-century breakthroughs in electronics and computing hardware. These early mechanical systems demonstrated the potential for machines to carry out complex calculations, leading to more efficient designs in the early 1900s and the first fully electronic computers in the mid-20th century.<ref>{{Cite journal |last=L. |first=K. |date=1990-06-29 |title=Computing Before Computers. William Aspray, Ed. Iowa State University Press, Ames, 1990. x, 266 pp., illus. $27.95 |url=http://dx.doi.org/10.1126/science.248.4963.1670-a |journal=Science |volume=248 |issue=4963 |pages=1670–1670 |doi=10.1126/science.248.4963.1670-a |issn=0036-8075}}</ref><ref>{{Cite journal |last=USSELMAN |first=STEVEN W. |date=2004-06 |title=A History of Modern Computing. Second edition. By Paul E. Ceruzzi. Cambridge, MA: MIT Press, 1998, 2003. Pp. xi, 445. $22.95, paper |url=http://dx.doi.org/10.1017/s0022050704352915 |journal=The Journal of Economic History |volume=64 |issue=02 |doi=10.1017/s0022050704352915 |issn=0022-0507}}</ref>
▲===Renaissance calculating tools===
Scottish mathematician and physicist [[John Napier]] discovered that the multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the [[logarithm]]s of those numbers. While producing the first logarithmic tables, Napier needed to perform many tedious multiplications. It was at this point that he designed his '[[Napier's bones]]', an abacus-like device that greatly simplified calculations that involved multiplication and division.{{efn|A Spanish implementation of [[Napier's bones]] (1617), is documented in {{harvnb|Montaner|Simon|1887|pp=19–20}}.}}
==First proposed general-purpose computing device==
{{Main|Analytical Engine}}
[[File:Difference engine plate 1853.jpg|thumb|A portion of [[Charles Babbage|Babbage]]'s [[Difference Engine]] ]][[File:AnalyticalMachine Babbage London.jpg|thumb|left|Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum, London]]
The '''Industrial Revolution''' (late 18th to early 19th century) had a significant impact on the evolution of computing hardware, as the era's rapid advancements in machinery and manufacturing laid the groundwork for mechanized and automated computing. Industrial needs for precise, large-scale calculations—especially in fields such as navigation, engineering, and finance—prompted innovations in both design and function, setting the stage for devices like '''Charles Babbage's Difference Engine''' (1822).<ref>{{Cite book |last=Babbage |first=Charles |url=http://dx.doi.org/10.1017/cbo9781139103671 |title=Passages from the Life of a Philosopher |date=2011-10-12 |publisher=Cambridge University Press |isbn=978-1-108-03788-4}}</ref><ref>{{Cite book |last=Babbage |first=Charles |url=http://dx.doi.org/10.1017/cbo9780511696374 |title=On the Economy of Machinery and Manufactures |date=2010-03-04 |publisher=Cambridge University Press |isbn=978-1-108-00910-2}}</ref> This mechanical device was intended to automate the calculation of polynomial functions and represented one of the earliest applications of computational logic.<ref>{{Cite journal |last=Hutton |first=D.M. |date=2002-08-01 |title=The Difference Engine: Charles Babbage and the Quest to Build the First Computer |url=http://dx.doi.org/10.1108/k.2002.06731fae.009 |journal=Kybernetes |volume=31 |issue=6 |doi=10.1108/k.2002.06731fae.009 |issn=0368-492X}}</ref>
[[Charles Babbage]], an English mechanical engineer and [[polymath]], originated the concept of a programmable computer, though none of his designs were successfully implemented until 1991. Often regarded as the "[[computer pioneer|father of the computer]]",<ref>{{cite book | author=Halacy, Daniel Stephen | title = Charles Babbage, Father of the Computer | url=https://archive.org/details/charlesbabbagefa00hala | url-access=registration | year = 1970 | publisher=Crowell-Collier Press | isbn = 0-02-741370-5 }}</ref> he conceptualized and invented the first [[mechanical computer]] in the early 19th century. After working on his revolutionary [[difference engine]], designed to aid in navigational calculations, in 1833 he realized that a much more general design, an [[Analytical Engine]], was possible. The input of programs and data was to be provided to the machine via [[punched card]]s, a method being used at the time to direct mechanical [[loom]]s such as the [[Jacquard loom]]. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary [[base-10]] fixed-point arithmetic.
The Engine incorporated an [[arithmetic logic unit]], [[control flow]] in the form of [[conditional branching]] and [[program loop#Loops|loops]], and integrated [[computer memory|memory]], making it the first design for a general-purpose computer that could be described in modern terms as [[Turing-complete]].<ref name="babbageonline">{{cite web |title=Babbage |work=Online stuff |publisher=Science Museum |url=https://www.sciencemuseum.org.uk/onlinestuff/stories/babbage.aspx?page=5|date=2007-01-19|access-date=2012-08-01 |archive-date=2012-08-07 |archive-url=https://web.archive.org/web/20120807185334/http://www.sciencemuseum.org.uk/onlinestuff/stories/babbage.aspx?page=5 |url-status=dead}}</ref><ref>{{cite magazine |url=https://www.newscientist.com/article/mg20827915.500-lets-build-babbages-ultimate-mechanical-computer.html |title=Let's build Babbage's ultimate mechanical computer |department=opinion |magazine=New Scientist |issue=2791 |author=John Graham-Cumming |date=23 December 2010 |access-date=2012-08-01|archive-date=2012-08-05 |archive-url=https://web.archive.org/web/20120805050111/http://www.newscientist.com/article/mg20827915.500-lets-build-babbages-ultimate-mechanical-computer.html|url-status=live}}</ref>
Babbage, often regarded as the "father of the computer," envisioned a fully mechanical system of gears and wheels, powered by steam, capable of handling complex calculations that previously required intensive manual labor.<ref>{{Cite journal |last=Tropp |first=Henry S. |date=1975-12 |title=<i>The Origins of Digital Computers: Selected Papers</i>. Brian Randell |url=http://dx.doi.org/10.1086/351520 |journal=Isis |volume=66 |issue=4 |pages=572–573 |doi=10.1086/351520 |issn=0021-1753}}</ref> His Difference Engine, designed to aid navigational calculations, ultimately led him to conceive the '''Analytical Engine''' in 1833.<ref>{{Cite journal |last=W. |first=J. W. |last2=Hyman |first2=Anthony |date=1986-04 |title=Charles Babbage, Pioneer of the Computer. |url=http://dx.doi.org/10.2307/2008013 |journal=Mathematics of Computation |volume=46 |issue=174 |pages=759 |doi=10.2307/2008013 |issn=0025-5718}}</ref> This concept, far more advanced than his Difference Engine, included an '''arithmetic logic unit''', control flow through conditional branching and loops, and integrated memory.<ref>{{Cite journal |last=Campbell-Kelly |first=Martin |last2=Aspray |first2=William |last3=Ensmenger |first3=Nathan |last4=Yost |first4=Jeffrey R. |date=2018-04-20 |title=Computer |url=http://dx.doi.org/10.4324/9780429495373 |doi=10.4324/9780429495373}}</ref> Babbage’s plans made his Analytical Engine the first general-purpose design that could be described as '''Turing-complete''' in modern terms.<ref>{{Citation |last=Turing |first=Alan |title=Computing Machinery and Intelligence (1950) |date=2004-09-09 |work=The Essential Turing |pages=433–464 |url=http://dx.doi.org/10.1093/oso/9780198250791.003.0017 |access-date=2024-10-30 |publisher=Oxford University PressOxford |isbn=978-0-19-825079-1}}</ref><ref>{{Cite journal |last=Davis |first=Martin |date=2018-02-28 |title=the Universal Computer |url=http://dx.doi.org/10.1201/9781315144726 |doi=10.1201/9781315144726}}</ref>
There was to be a store (that is, a memory) capable of holding 1,000 numbers of 50 decimal digits each (ca. 16.6 [[kilobyte|kB]]). An [[arithmetic logic unit|arithmetic unit]] (the "mill") would be able to perform all four [[arithmetic operations]], plus comparisons and optionally [[square root]]s. 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. Later drawings (1858) depict a regularised grid layout.<ref>{{cite web |url=https://cse.stanford.edu/classes/sophomore-college/projects-98/babbage/ana-mech.htm |title=Babbage's Analytical Engine: The First True Digital Computer |access-date=2008-08-21 |url-status=dead |archive-url=https://web.archive.org/web/20080821191451/http://cse.stanford.edu/classes/sophomore-college/projects-98/babbage/ana-mech.htm |archive-date=2008-08-21 |website=The Analytical Engine}}</ref><ref>{{cite web|url=https://projects.exeter.ac.uk/babbage/engines.html |title=The Babbage Pages: Calculating Engines |publisher=Projects.exeter.ac.uk |date=8 January 1997 |access-date=23 April 2024 |archive-date=2008-03-12 |archive-url=https://web.archive.org/web/20080312060230/http://www.projects.ex.ac.uk/babbage/engines.html |url-status=live }}</ref> Like the [[central processing unit]] (CPU) in a modern computer, the mill would rely on its own internal procedures, roughly equivalent to [[microcode]] in modern CPUs, 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.<ref>{{cite web |first=Tim |last=Robinson |date=2007-05-28 |url=https://www.meccano.us/analytical_engine/index.html |title=Difference Engines |publisher=Meccano.us |access-date=2012-08-01 |archive-date=2020-10-05 |archive-url=https://web.archive.org/web/20201005153610/http://www.meccano.us/analytical_engine/index.html |url-status=live}}</ref>
The '''Analytical Engine''' was programmed using '''punched cards''', a method adapted from the Jacquard loom invented by Joseph Marie Jacquard in 1804, which controlled textile patterns with a sequence of punched cards.<ref>{{Cite journal |last=d'Ucel |first=Jeanne |last2=Dib |first2=Mohammed |date=1958 |title=Le métier à tisser |url=http://dx.doi.org/10.2307/40098349 |journal=Books Abroad |volume=32 |issue=3 |pages=278 |doi=10.2307/40098349 |issn=0006-7431}}</ref> These cards became foundational in later computing systems as well.<ref>{{Cite book |last=Heide |first=Lars |url=http://dx.doi.org/10.1353/book.3454 |title=Punched-Card Systems and the Early Information Explosion, 1880–1945 |date=2009 |publisher=Johns Hopkins University Press |isbn=978-0-8018-9143-4}}</ref> Babbage’s machine would have featured multiple output devices, including a printer, a curve plotter, and even a bell, demonstrating his ambition for versatile computational applications beyond simple arithmetic.<ref>{{Cite journal |last=Bromley |first=A.G. |date=1998 |title=Charles Babbage's Analytical Engine, 1838 |url=http://dx.doi.org/10.1109/85.728228 |journal=IEEE Annals of the History of Computing |volume=20 |issue=4 |pages=29–45 |doi=10.1109/85.728228 |issn=1058-6180}}</ref>
[[File:AnalyticalMachine Babbage London.jpg|thumb|left|Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum, London]]
The programming language to be employed by users was akin to modern day [[assembly language]]s. 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.
'''Ada Lovelace''' expanded on Babbage’s vision by conceptualizing algorithms that could be executed by his machine.<ref>{{Cite journal |last=Toole |first=Betty Alexandra |date=1991-03 |title=Ada, an analyst and a metaphysician |url=http://dx.doi.org/10.1145/122028.122031 |journal=ACM SIGAda Ada Letters |volume=XI |issue=2 |pages=60–71 |doi=10.1145/122028.122031 |issn=1094-3641}}</ref> Her notes on the Analytical Engine, written in the 1840s, are now recognized as the earliest examples of computer programming.<ref>{{Cite journal |last=Howard |first=Emily |last2=De Roure |first2=David |date=2015 |title=Turning numbers into notes |url=http://dx.doi.org/10.1145/2867731.2867746 |journal=Ada Lovelace Symposium 2015- Celebrating 200 Years of a Computer Visionary on - Ada Lovelace Symposium '15 |___location=New York, New York, USA |publisher=ACM Press |pages=13 |doi=10.1145/2867731.2867746}}</ref> Lovelace saw potential in computers to go beyond numerical calculations, predicting that they might one day generate complex musical compositions or perform tasks like language processing.<ref>{{Cite journal |last=Haugtvedt |first=Erica |last2=Abata |first2=Duane |title=Ada Lovelace: First Computer Programmer and Hacker? |url=http://dx.doi.org/10.18260/1-2--36646 |journal=2021 ASEE Virtual Annual Conference Content Access Proceedings |publisher=ASEE Conferences |doi=10.18260/1-2--36646}}</ref>
The project was slowed by various problems including disputes with the chief machinist building parts for it. All the parts for his machine had to be made by hand—this was a major problem for a machine with thousands of parts. Eventually, the project was dissolved with the decision of the British Government to cease funding. Babbage's failure to complete the analytical engine can be chiefly attributed to difficulties not only of politics and financing, but also to his desire to develop an increasingly sophisticated computer and to move ahead faster than anyone else could follow. [[Ada Lovelace]] translated and [[Ada Byron's notes on the analytical engine|added notes]] to the "''Sketch of the Analytical Engine''" by [[Luigi Federico Menabrea]]. This appears to be the first published description of programming, so Ada Lovelace is widely regarded as the first computer programmer.{{sfn|Menabrea|Lovelace|1843}}
Though Babbage’s designs were never fully realized due to technical and financial challenges, they influenced a range of subsequent developments in computing hardware. Notably, in the 1890s, '''Herman Hollerith''' adapted the idea of punched cards for automated data processing, which was utilized in the U.S. Census and sped up data tabulation significantly, bridging industrial machinery with data processing.<ref>{{Cite thesis |last=Blodgett |first=John H. |title=Herman Hollerith, data processing pioneer |publisher=Drexel University Libraries |url=http://dx.doi.org/10.17918/00004750}}</ref>
Following Babbage, although at first unaware of his earlier work, was [[Percy Ludgate]], a clerk to a corn merchant in Dublin, Ireland. He independently designed a programmable mechanical computer, which he described in a work that was published in 1909.<ref>{{Cite web |url=https://scss.tcd.ie/SCSSTreasuresCatalog/miscellany/TCD-SCSS-X.20121208.002/TCD-SCSS-X.20121208.002.pdf/ |title=The John Gabriel Byrne Computer Science Collection |access-date=2019-08-08 |archive-url=https://web.archive.org/web/20190416071721/https://www.scss.tcd.ie/SCSSTreasuresCatalog/miscellany/TCD-SCSS-X.20121208.002/TCD-SCSS-X.20121208.002.pdf |archive-date=2019-04-16 |url-status=dead }}</ref><ref>{{Cite web |url=https://ingeniousireland.ie/2012/10/1909-a-novel-irish-computer/|title=1907: was the first portable computer design Irish? | Ingenious Ireland|access-date=2022-12-02 |url-status=live |archive-date=2022-12-02 |archive-url=https://web.archive.org/web/20221202161626/https://ingeniousireland.ie/2012/10/1909-a-novel-irish-computer/}}</ref>
The Industrial Revolution’s advancements in mechanical systems demonstrated the potential for machines to conduct complex calculations, influencing engineers like '''Leonardo Torres Quevedo''' and '''Vannevar Bush''' in the early 20th century. Torres Quevedo designed an electromechanical machine with floating-point arithmetic<ref>{{Citation |last=Torres y Quevedo |first=Leonardo |title=Essays on Automatics |date=1982 |work=The Origins of Digital Computers |pages=89–107 |url=http://dx.doi.org/10.1007/978-3-642-61812-3_6 |access-date=2024-10-30 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-642-61814-7}}</ref>, while Bush’s later work explored electronic digital computing.<ref>{{Citation |title=6 Vannevar Bush, from “As We May Think” (1945) |date=2021 |work=Information |url=http://dx.doi.org/10.7312/hayo18620-032 |access-date=2024-10-30 |publisher=Columbia University Press |isbn=978-0-231-54654-6}}</ref> By the mid-20th century, these innovations paved the way for the first fully electronic computers.<ref>{{Cite book |last=Haigh |first=Thomas |url=http://dx.doi.org/10.7551/mitpress/11436.001.0001 |title=A New History of Modern Computing |last2=Ceruzzi |first2=Paul E. |date=2021-09-14 |publisher=The MIT Press |isbn=978-0-262-36648-9}}</ref>
Two other inventors, [[Leonardo Torres Quevedo]] and [[Vannevar Bush]], also did follow on research based on Babbage's work. In 1914, Torres published ''Essays on Automatics'', where he wrote about Babbage's efforts at constructing a mechanical Analytical Engine and designed an electromechanical analytical machine which was to be controlled by a read-only program. The paper also introduced the idea of [[floating-point arithmetic]].<ref name="LTQ1913es">L. Torres Quevedo. ''Ensayos sobre Automática – Su definicion. Extension teórica de sus aplicaciones,'' Revista de la Academia de Ciencias Exacta, Revista 12, pp. 391–418, 1914.</ref><ref>{{Cite journal |last=Torres Quevedo |first=Leonardo |date=1914-11-19 |title=Automática: Complemento de la Teoría de las Máquinas |url=https://quickclick.es/rop/pdf/publico/1914/1914_tomoI_2043_01.pdf |journal=Revista de Obras Públicas |pages=575–583}}</ref><ref name="LTQ1915fr">Torres Quevedo. L. (1915). [https://diccan.com/dicoport/Torres.htm "Essais sur l'Automatique - Sa définition. Etendue théorique de ses applications"], ''Revue Génerale des Sciences Pures et Appliquées'', vol. 2, pp. 601–611.</ref> In 1920, he presented in a Paris conference the [[Leonardo Torres y Quevedo#Analytical machines|Electromechanical Arithmometer]], an arithmetic unit on which commands could be typed and the results printed automatically.<ref name="Randell1982p109">B. Randell. ''Electromechanical Calculating Machine,'' [https://books.google.com/books?id=Dwj4RmcZ1AoC The Origins of Digital Computers], pp.109-120, 1982.</ref> Bush's paper ''Instrumental Analysis'' (1936) discussed using existing IBM punch card machines to implement Babbage's design. In the same year he started the Rapid Arithmetical Machine project to investigate the problems of constructing an electronic digital computer.<ref name=RANDELL>{{cite web|url=https://www.cs.ncl.ac.uk/publications/articles/papers/398.pdf |title=From Analytical Engine to Electronic Digital Computer: The Contributions of Ludgate, Torres, and Bush |last1=Randell |first1=Brian |author-link1=Brian Randell |access-date=9 September 2013 |url-status=dead |archive-date=21 September 2013 |archive-url=https://web.archive.org/web/20130921055055/http://www.cs.ncl.ac.uk/publications/articles/papers/398.pdf}}</ref>
==Analog computers==
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