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{{Short description|Automatic mechanical calculator}}
{{For|the novel by William Gibson and Bruce Sterling|The Difference Engine}}
[[File:Babbage Difference Engine.jpg|thumb|The London [[Science Museum (London)|Science Museum]]'s difference engine, the first one
A '''difference engine''' is an automatic [[mechanical calculator]] designed to tabulate [[polynomial]] functions. It was designed in the 1820s, and was
== History ==
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Charles Babbage began to construct a small difference engine in {{circa|1819}}<ref>{{Cite book |url=https://books.google.com/books?id=tXBVAgAAQBAJ&pg=PT22 |title=It Began with Babbage: The Genesis of Computer Science |last=Dasgupta |first=Subrata |date=2014 |publisher=Oxford University Press |isbn=978-0-19-930943-6|page=22}}</ref> and had completed it by 1822 (Difference Engine 0).<ref name=":0">{{Cite book |title=The Turing Guide |author-link1=Jack Copeland |last1=Copeland |first1=B. Jack |author-link2=Jonathan Bowen |last2=Bowen |first2=Jonathan P. |author-link3=Robin Wilson (mathematician) |last3=Wilson |first3=Robin |last4=Sprevak |first4=Mark |date=2017 |publisher=[[Oxford University Press]] |isbn=9780191065002 |page=251 |title-link=The Turing Guide }}</ref> He announced his invention on 14 June 1822, in a paper to the [[Royal Astronomical Society]], entitled "Note on the application of machinery to the computation of astronomical and mathematical tables".<ref>{{cite web |last1=O'Connor |first1=John J. |last2=Robertson |first2=Edmund F. |author-link2=Edmund F. Robertson |date=1998 |url=http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Babbage.html |title=Charles Babbage |work=MacTutor History of Mathematics archive |publisher=School of Mathematics and Statistics, University of St Andrews, Scotland |access-date=2006-06-14 |archive-url=https://web.archive.org/web/20060616002258/http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Babbage.html |archive-date=2006-06-16 }}</ref> This machine used the decimal number system and was powered by cranking a handle. The [[British government]] was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical.<ref name="Campbell-Kelly 2004">{{cite book |title=Computer: A History of the Information Machine 2nd ed. |last=Campbell-Kelly |first=Martin |publisher=Westview Press |date=2004 |isbn=978-0-8133-4264-1 |___location=Boulder, Colorado |author-link=Martin Campbell-Kelly |url-access=registration |url=https://archive.org/details/computerhistoryo02edcamp }}</ref>
In 1823, the British government gave Babbage £1700 to start work on the project. Although Babbage's design was feasible, the metalworking techniques of the era could not economically make parts in the precision and quantity required. Thus the implementation proved to be much more expensive and doubtful of success than the government's initial estimate. According to the 1830 design for Difference Engine No. 1, it would have about 25,000 parts, weigh 4 [[ton]]s,<ref>{{Cite web |title=The Engines {{!}} Babbage Engine |url=https://www.computerhistory.org/babbage/engines/ |publisher=Computer History Museum |access-date=2022-07-10 }}</ref> and operate on 20-digit numbers by sixth-order differences. In 1832, Babbage and [[Joseph Clement]] produced a small working model (one-seventh of the plan),<ref name=":0" /> which operated on 6-digit numbers by second-order differences.<ref name=":1">{{Cite book |url=https://books.google.com/books?id=QqrItgm351EC&pg=PA204 |title=A Brief History of Computing |last=O'Regan |first=Gerard |date=2012 |publisher=Springer Science & Business Media |isbn=978-1-4471-2359-0|page=204}}</ref><ref name=":2">{{Cite book |url=https://books.google.com/books?id=JckCvpOQDOoC&pg=PP1 |title=The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World |last=Snyder |first=Laura J. |date=2011 |publisher=Crown/Archetype|isbn=978-0-307-71617-0 |pages=192, 210, 217 }}</ref> [[Lady Byron]] described seeing the working prototype in 1833: "We both went to see the thinking machine (or so it seems) last Monday. It raised several Nos. to the 2nd and 3rd powers, and extracted the root of a Quadratic equation."<ref>{{Cite book |title=Ada, the Enchantress of Numbers |last1=Toole |first1=Betty Alexandra |last2=Lovelace |first2=Ada |date=1998 |publisher=Strawberry Press |isbn=978-0912647180 |___location=Mill Valley, California |oclc=40943907 |page=[https://archive.org/details/adaenchantressof00tool/page/38 38] |url=https://archive.org/details/adaenchantressof00tool/page/38 }}</ref> Lady Byron's daughter [[Ada Lovelace]] would later become fascinated with and work on creating the first computer program intended to solve Bernoulli's equation utilizing the difference engine. Work on the larger engine was suspended in 1833.
By the time the government abandoned the project in 1842,<ref name=":2" /><ref>{{Cite book |url=https://books.google.com/books?id=UmNJAAAAYAAJ&pg=PA387 |title=A History of the Royal Society: With Memoirs of the Presidents |last=Weld |first=Charles Richard |date=1848 |publisher=J. W. Parker |pages=387–390 }}</ref> Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine. The government valued only the machine's output (economically produced tables), not the development (at unpredictable cost) of the machine itself. Babbage refused to recognize that predicament.<ref name="Campbell-Kelly 2004" /> Meanwhile, Babbage's attention had moved on to developing an [[analytical engine]], further undermining the government's confidence in the eventual success of the difference engine. By improving the concept as an analytical engine, Babbage had made the difference engine concept obsolete, and the project to implement it an utter failure in the view of the government.<ref name="Campbell-Kelly 2004" />
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The incomplete Difference Engine No. 1 was put on display to the public at the [[1862 International Exhibition]] in [[South Kensington]], London.<ref>{{Cite book |url=https://books.google.com/books?id=aDJRAAAAYAAJ |title=Cyclopaedia of useful arts, mechanical and chemical, manufactures, mining and engineering: in three volumes, illustrated by 63 steel engravings and 3063 wood engravings |last=Tomlinson |first=Charles |date=1868 |publisher=Virtue & Co. |page=136 }}</ref><ref>{{Cite book |url=https://archive.org/details/bub_gb_z7MpAAAAYAAJ|title=Official catalogue of the industrial department |date=1862 |page=[https://archive.org/details/bub_gb_z7MpAAAAYAAJ/page/n70 49] }}</ref>
Babbage went on to design his much more general analytical engine, but later
=== Scheutzian calculation engine ===
[[File:Difference engine Scheutz.jpg|thumb|upright=1.8|Per Georg Scheutz's third difference engine, in the [[Science Museum, London|Science Museum]], London]]
Inspired by Babbage's difference engine in 1834, the Swedish inventor [[Per Georg Scheutz]] built several experimental models. In 1837 his son Edward proposed to construct a working model in metal, and in 1840 finished the calculating part, capable of calculating series with 5-digit numbers and first-order differences, which was later extended to third-order (1842). In 1843, after adding the printing part, the model was completed.
In 1851, funded by the government, construction of the larger and improved (15-digit numbers and fourth-order differences) machine began, and finished in 1853. The machine was demonstrated at the [[Exposition Universelle (1855)|World's Fair in Paris, 1855]] and then sold in 1856 to the [[Dudley Observatory]] in [[Albany, New York]]. Delivered in 1857, it was the first printing calculator sold.<ref name=":3">{{Cite book|url=https://archive.org/details/bub_gb_Ut1wgt6kSBEC|title=Specimens of Tables, Calculated, Stereomoulded, and Printed by Machinery|last1=Scheutz|first1=George|last2=Scheutz|first2=Edward|date=1857 |publisher=Whitnig |pages=VIII–XII, XIV–XV, 3}}</ref><ref name="SI">{{cite web |title=Scheutz Difference Engine |url=https://americanhistory.si.edu/collections/search/object/nmah_997042 |website=Smithsonian National Museum of American History |access-date=June 14, 2019}}</ref><ref name=":6" /> In 1857 the British government ordered the next [[Per Georg Scheutz|Scheutz's]] difference machine, which was built in 1859.<ref>{{Cite book |url=https://archive.org/details/differenceengine00doro|url-access=registration|title=The Difference Engine: Charles Babbage and the Quest to Build the First Computer|last=Swade|first=Doron|date=2002-10-29 |publisher=Penguin Books |isbn=9780142001448 |pages=[https://archive.org/details/differenceengine00doro/page/4 4], 207 }}</ref><ref>{{Cite book|url=https://books.google.com/books?id=jlmVKZ1psCkC&pg=PA37|title=The Universal Machine: From the Dawn of Computing to Digital Consciousness|last=Watson|first=Ian|date=2012|publisher=Springer Science & Business Media|isbn=978-3-642-28102-0|pages=37–38}}</ref> It had the same basic construction as the previous one, weighing about {{Convert|10|-Lcwt|lb kg|lk=on|abbr=on}}.<ref name=":6">{{Cite book |title=First Printing Calculator |last1=Merzbach |first1=Uta C. |author-link=Uta Merzbach |last2=Ripley |first2=S. Dillon |last3=Merzbach |first3=Uta C. |pages=8–9, 13, 25–26, 29–30 |citeseerx=10.1.1.639.3286 }}</ref>
=== Others ===
[[Martin Wiberg]] improved Scheutz's construction ({{circa|1859}}, his machine has the same capacity as Scheutz's:
Alfred Deacon of London in {{circa|1862}} produced a small difference engine (20-digit numbers and third-order differences).<ref name=":3" /><ref name=":4">{{Cite book|at=[https://books.google.com/books?id=O170gWPZ7M8C&pg=PA136 pp. 132–136]|title=The History of Mathematical Tables: From Sumer to Spreadsheets|last=Campbell-Kelly|first=Martin|date=2003|publisher=OUP Oxford|isbn=978-0-19-850841-0|title-link= The History of Mathematical Tables}}</ref>
American [[George B. Grant]] started working on his calculating machine in 1869, unaware of the works of Babbage and Scheutz (Schentz). One year later (1870) he learned about difference engines and proceeded to design one himself, describing his construction in 1871. In 1874 the Boston Thursday Club raised a subscription for the construction of a large-scale model, which was built in 1876. It could be expanded to enhance precision and weighed about {{convert|2000|lb|kg}}.<ref name=":4" /><ref>{{Cite web|archive-url=https://web.archive.org/web/20120225033434/http://history-computer.com/Babbage/NextDifferentialEngines/
[[Christel Hamann]] built one machine (16-digit numbers and second-order differences) in 1909 for the "Tables of [[Julius Bauschinger|Bauschinger]] and Peters" ("Logarithmic-Trigonometrical Tables with eight decimal places"), which was first published in Leipzig in 1910. It weighed about {{convert|40|kg|lb}}.<ref
[[Burroughs Corporation]] in about 1912 built a machine for the [[HM Nautical Almanac Office|Nautical Almanac Office]] which was used as a difference engine of second-order.<ref name=":5">{{Cite journal|last=Comrie|first=L. J.|date=1928-03-01|title=On the application of the BrunsvigaDupla calculating machine to double summation with finite differences|bibcode=1928MNRAS..88..447C|journal=Monthly Notices of the Royal Astronomical Society|volume=88|issue=5|pages=451, 453–454, 458–459|doi=10.1093/mnras/88.5.447|issn=0035-8711|via=[[Astrophysics Data System]]|doi-access=free}}</ref>{{Rp|451}}<ref>{{Cite book|url=https://archive.org/stream/moderninstrument00horsuoft#page/127/mode/1up/search/hudson|title=Modern instruments and methods of calculation : a handbook of the Napier Tercentenary Exhibition|last1=Horsburg|first1=E. M.|date=1914|___location=London|publisher=G. Bell|pages=127–131}}</ref> It was later replaced in 1929 by a Burroughs Class 11 (13-digit numbers and second-order differences, or 11-digit numbers and <nowiki>[at least up to]</nowiki> fifth-order differences).<ref>{{Cite journal|last=Comrie|first=L. J.|date=1932-04-01|title=The Nautical Almanac Office Burroughs machine|bibcode=1932MNRAS..92..523C|journal=Monthly Notices of the Royal Astronomical Society|volume=92|issue=6|pages=523–524, 537–538|doi=10.1093/mnras/92.6.523|issn=0035-8711|via=[[Astrophysics Data System]]|doi-access=free}}</ref>
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The printer's primary purpose is to produce [[Stereotype (printing)|stereotype]] plates for use in printing presses, which it does by pressing type into soft plaster to create a [[flong]]. Babbage intended that the Engine's results be conveyed directly to mass printing, having recognized that many errors in previous tables were not the result of human calculating mistakes but from slips in the manual [[typesetting]] process.<ref name="Campbell-Kelly 2004" /> The printer's paper output is mainly a means of checking the engine's performance.
In addition to funding the construction of the output mechanism for the Science Museum's difference engine, [[Nathan Myhrvold]] commissioned the construction of a second complete Difference Engine No. 2, which was on exhibit at the [[Computer History Museum]] in [[Mountain View, California]], from May 2008 to January 2016.<ref name="CHM Press Releases" /><ref>{{Cite web |url=http://www.computerhistory.org/exhibits/babbage/ |title=The Babbage Difference Engine No. 2 |publisher=Computer History Museum |access-date=2018-10-26 }}</ref><ref name="chm2">{{cite web |author-link=Daniel Terdiman |last=Terdiman |first=Daniel |date=April 10, 2008 |title=Charles Babbage's masterpiece difference engine comes to Silicon Valley |url=https://www.cnet.com/culture/charles-babbages-masterpiece-difference-engine-comes-to-silicon-valley/ |work=[[CNET News]]}}</ref><ref>{{Cite web |last=Noack |first=Mark |title=Computer Museum bids farewell to Babbage engine |url=https://www.mv-voice.com/news/2016/01/29/computer-museum-bids-farewell-to-babbage-engine |access-date=2022-07-10 |website=Mv-voice.com |date=29 January 2016 }}</ref> It has since been transferred to [[Intellectual Ventures]] in [[Seattle]] where it is on display just outside the main lobby.<ref>{{Cite web |last=Boyle |first=Alan |date=2016-09-11 |title=Inside the invention factory: Get a peek at Intellectual Ventures' lab |url=https://www.geekwire.com/2016/inside-intellectual-ventures-lab/ |access-date=2024-04-21}}</ref><ref>{{Cite web |title=Intellectual Ventures on LinkedIn: #ivlab #coolscience |url=https://www.linkedin.com/posts/intellectual-ventures_ivlab-coolscience-activity-6568159438295965696-tGHx |access-date=2024-04-21 |website=www.linkedin.com |language=en}}</ref><ref>{{Cite web |last=Ventures |first=Intellectual |date=September 1, 2016 |title=IV's Favorite Inventions: The Babbage Machine |url=https://www.intellectualventures.com/buzz/insights/ivs-favorite-inventions-the-babbage-machine#:~:text=Visit%20the%20Intellectual%20Ventures%20Lab,in%20the%20IV%20Lab%20foyer. |access-date=March 24, 2024 |website=Intellectual Ventures}}</ref>
== Operation ==
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* [[Allan G. Bromley]]
* [[Johann Helfrich von Müller]]
* [[Logical machine]]
* [[Martin Wiberg]]
* [[Pinwheel calculator]]
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== Further reading ==
{{Refbegin|}}
* {{cite book |title=The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World |last=Snyder |first=Laura J. |publisher=Broadway |date=2011 |isbn=978-0-7679-3048-2 |url-access=registration |url=https://archive.org/details/philosophicalbre0000snyd
* {{cite book |url=http://ed-thelen.org/bab/bab_tech.html |title=Charles Babbage's Difference Engine No. 2 – Technical Description |last=Swade |first=Doron |date=September 1996 |publisher=[[National Museum of Science and Industry]] |series=Science Museum Papers in the History of Technology No 5 |___location=London |access-date=2009-01-11}}
* {{cite book |title
* {{cite book |title=The Cogwheel Brain |last=Swade |first=Doron |publisher=Abacus |date=2001 |isbn=978-0-349-11239-8
* {{cite video |people=Doron Swade, [[Nathan Myhrvold]] |title=Myhrvold & Swade Discuss Babbage's Difference Engine |url=https://www.youtube.com/watch?v=p1sEowi1Txc |archive-url=https://ghostarchive.org/varchive/youtube/20211211/p1sEowi1Txc |archive-date=2021-12-11 |url-status=live |medium=lecture: [[Len Shustek]], intro; Doron Swade @7:35, Nathan Myhrvold @36:25; discussion @46:45 |publisher=Computer History Museum |date=June 10, 2008 |access-date=2009-11-06
* {{cite book |chapter-url=https://books.google.com/books?id=O170gWPZ7M8C |title=The History of Mathematical Tables: From Sumer to Spreadsheets |last1=Campbell-Kelly |first1=Martin |date=2003 |publisher=OUP Oxford |others=Michael R. Williams |isbn=9780198508410 |chapter=Difference engines: from Müller to Comrie
*Hollings, C., Martin, U., & Rice, A. C. (2018). Ada lovelace: The making of a computer scientist. Bodleian Library.{{Refend}}
== External links ==
{{Commons category|Difference engines}}
* [
* [
* [http://www.meccano.us/difference_engines/rde_2/index.html Meccano Difference Engine #2]
* [
* [http://sites.google.com/site/babbagedifferenceengine/analysisofexpenditureondifferenceenginen Analysis of Expenditure on Babbage's Difference Engine No. 1]
* [
* [https://web.archive.org/web/20100311120130/http://www.powerhousemuseum.com/collection/database/?irn=150269&img=146773 Difference Engine No1 specimen piece at the Powerhouse Museum, Sydney]
* [
* [https://www.youtube.com/watch?v=YtZCYnBlZpk Scheutz Difference Engine in action video. Purchased by the Dudley Observatory's first director, Benjamin Apthorp Gould, in 1856. Gould was an acquaintance of Babbage. The Difference Engine performed astronomical calculations for the Observatory for many years, and is now part of the national collection at the Smithsonian.]
* Links to videos about Babbage DE 2 and its construction: {{cite web |title=Computer Histories: To Learn More |url=http://www.computerhistories.org/ToLearnMore.html |website=www.computerhistories.org|at=Topic 5 - Computers in the Steam Era (Not Hackers But Clackers)}}
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[[Category:Articles containing video clips]]
[[Category:Charles Babbage]]
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[[Category:Computer-related introductions in the 19th century]]
[[Category:English inventions]]
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