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{{Short description|English mathematician, philosopher, and engineer (1791–1871)}}
{{Redirect|Babbage|other uses|Babbage (disambiguation)}}
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{{Use British English|date=November 2019}}
{{Use dmy dates|date=June 2022}}
{{Infobox scientist
| name              = Charles Babbage
| image             = Charles Babbage - 1860.jpg
| image_size        = 220
| caption           = Babbage in 1860
| birth_date        = {{birth date|df=y|1791|12|26}}
| birth_place       = London, England
| death_date        = {{death date and age|df=y|1871|10|18|1791|12|26}}
| death_place       = [[Marylebone]], London, England 
| field             = Mathematics, engineering, political economy, computer science
| work_institutions = [[Trinity College, Cambridge]], [[Peterhouse, Cambridge]]
| alma_mater        = [[Peterhouse, Cambridge]]
| known_for         = [[Analytical engine]]<br />[[Difference engine]]
| awards            = [[Gold Medal of the Royal Astronomical Society]] {{small|(1824)}}
| honorific_suffix  = {{post-nominals|country=GBR|size=100%|KH|FRS}}
| footnotes         =
| signature         = Charles Babbage Signature.svg
| spouse            = {{marriage|Georgiana Whitmore|1814|1827|end=d.}}
| children          = 8, including [[Benjamin Herschel Babbage]] and [[Henry Prevost Babbage]]
| relatives         = [[William Wolryche-Whitmore]] (brother-in-law) 
}}

'''Charles Babbage''' {{post-nominals|country=GBR|KH|FRS}} ({{IPAc-en|ˈ|b|æ|b|ɪ|dʒ}}; 26 December 1791&nbsp;– 18 October 1871) was an English [[polymath]].<ref name="Whalen1999">{{cite book |last=Whalen |first=Terence |url=https://archive.org/details/edgarallanpoemas0000whal |title=Edgar Allan Poe and the Masses: The Political Economy of Literature in Antebellum America |publisher=Princeton University Press |year=1999 |isbn=978-0-691-00199-9 |page=[https://archive.org/details/edgarallanpoemas0000whal/page/254 254] |access-date=18 April 2013 |url-access=registration}}</ref> A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.<ref name="babb">{{Cite encyclopedia|chapter-url=https://plato.stanford.edu/entries/computing-history/|title=The Modern History of Computing (Stanford Encyclopedia of Philosophy)| last= Copeland | first=B. Jack | authorlink=Jack Copeland | date=18 December 2000 | encyclopedia=[[Stanford Encyclopedia of Philosophy]]|access-date=1 March 2017|chapter=The Modern History of Computing |publisher=Metaphysics Research Lab, Stanford University}}</ref>

Babbage is considered by some to merit the title of "[[List of pioneers in computer science|father of the computer]]".<ref name= "babb"/><ref>{{cite book | last=Halacy| first= 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 = 978-0-02-741370-0 }}</ref><ref>{{cite web|url=http://www.cbi.umn.edu/about/babbage.html|title=Charles Babbage Institute: Who Was Charles Babbage?|website=cbi.umn.edu}}</ref><ref>{{cite book | author=Swade, Doron | title=The Difference Engine: Charles Babbage and the Quest to Build the First Computer. | url=https://archive.org/details/differenceengine00doro | url-access= registration | publisher=Penguin | year=2002 | isbn=9780142001448 }}</ref> He is credited with inventing the first [[mechanical computer]], the [[difference engine]], that eventually led to more complex electronic designs, though all the essential ideas of modern computers are to be found in his [[analytical engine]], programmed using a principle openly borrowed from the [[Jacquard loom]].<ref name="babb"/><ref>{{cite journal | author= Newman, M.H.A. | title=General Principles of the Design of All-Purpose Computing Machines | journal= Proceedings of the Royal Society of London, Series A  | volume=195 | issue= 1042 | year=1948 | pages=271–274 | bibcode=1948RSPSA.195..271N | doi= 10.1098/rspa.1948.0129 | s2cid= 64893534 | doi-access= }}</ref> As part of his computer work, he also designed the first [[Printer (computing)|computer printers]].<ref name=":2">{{Cite web |last=Eccles |first=Simon |date=2019-12-13 |title=How Charles Babbage invented computer printing |url=https://www.printweek.com/content/features/how-charles-babbage-invented-computer-printing/ |access-date=2025-04-26 |website=[[Printweek]] |language=en}}</ref> He had a broad range of interests in addition to his work on computers, covered in his 1832 book ''Economy of Manufactures and Machinery''.<ref>{{cite book |first= Herman H. |last= Goldstine |title=The Computer: from Pascal to von Neumann |publisher=Princeton University Press |year=1972 |isbn=0-691-02367-0}}</ref> He was an important figure in the social scene in London, and is credited with importing the "scientific soirée" from France with his well-attended [[Charles Babbage's Saturday night soirées|Saturday evening soirées]].<ref name=":0">{{Cite journal |last=Secord |first=James A. |date= 2007 |title=How Scientific Conversation Became Shop Talk |url=https://www.cambridge.org/core/product/identifier/S0080440107000564/type/journal_article |journal=Transactions of the Royal Historical Society |language=en |volume=17 |pages=129–156 |doi=10.1017/S0080440107000564 |s2cid=161438144 |issn=0080-4401|url-access=subscription }}</ref><ref name=":1">{{Cite book |last1=Collier |first1=Bruce |title=Charles Babbage and the engines of perfection |last2= MacLachlan |first2=James H. |date=1998 |publisher=Oxford Univ. Press |isbn= 978-0-19-508997-4 |series=Oxford portraits in science |location=New York}}</ref> His varied work in other fields has led him to be described as "pre-eminent" among the many polymaths of his century.<ref name="Whalen1999"/>

Babbage, who died before the complete successful engineering of many of his designs, including his Difference Engine and Analytical Engine, remained a prominent figure in the ideating of computing. Parts of his incomplete mechanisms are on display in the [[London Science Museum|Science Museum]] in London. In 1991, a functioning difference engine was constructed from the original plans. Built to [[engineering tolerance|tolerances]] achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked.

==Early life==
[[File:British (English) School - Charles Babbage (1792–1871) - 814168 - National Trust.jpg|thumb|right|Portrait of Charles Babbage ({{Circa|1820}})]]
Babbage's birthplace is disputed, but according to the ''[[Oxford Dictionary of National Biography]]'' he was most likely born at 44 Crosby Row, [[Walworth Road]], London, England.<ref name="ODNB">{{cite ODNB|id=962|title=Babbage, Charles|first=Doron|last=Swade}}</ref> A [[blue plaque]] on the junction of Larcom Street and Walworth Road commemorates the event.<ref>{{openplaque | 1140 }}</ref>

His date of birth was given in his obituary in ''[[The Times]]'' as 26 December 1792; but then a nephew wrote to say that Babbage was born one year earlier, in 1791. The parish register of [[Stoke Newington (parish)#Ecclesiastical parish|St. Mary's]], [[Newington, London|Newington]], London, shows that Babbage was [[Baptism|baptised]] on 6 January 1792, supporting a birth year of 1791.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA5 5]}}<ref>{{cite book | last = Moseley | first = Maboth | title = Irascible Genius, The Life of Charles Babbage | publisher=Henry Regnery | location = Chicago | year = 1964 | page = 29 |url=https://books.google.com/books?id=ELAMAQAAIAAJ }}</ref><ref>{{cite news | title = The Late Mr. Charles Babbage, F.R.S |work=The Times |location=UK |title-link=s:The Times/The Late Mr. Charles Babbage, F.R.S. }}</ref>
[[File:Charles Babbage by Antoine Claudet c1847-51-crop.jpg|thumb|Babbage {{Circa|1850}}]]

Babbage was one of four children of Benjamin Babbage and Betsy Plumleigh Teape. His father was a banking partner of [[William Praed]] in founding Praed's & Co. of [[Fleet Street]], London, in 1801.<ref>{{cite web|author=Members Constituencies Parliaments Surveys |url=http://www.historyofparliamentonline.org/volume/1790-1820/member/praed-william-1747-1833 |title=Praed, William (1747–1833), of Tyringham, Bucks. and Trevethoe, nr. St. Ives, Cornw. |publisher=Historyofparliamentonline.org |access-date=7 June 2014}}</ref> In 1808, the Babbage family moved into the old Rowdens house in [[Teignmouth|East Teignmouth]]. Around the age of eight, Babbage was sent to a country school in [[Alphington, Devon|Alphington]] near Exeter to recover from a life-threatening fever. For a short time, he attended [[King Edward VI Community College#Grammar school|King Edward VI Grammar School]] in [[Totnes]], South Devon, but his health forced him back to private tutors for a time.<ref>{{harvnb|Moseley|1964|p=39}}</ref>

Babbage then joined the 30-student Holmwood Academy, in Baker Street, [[Enfield, London|Enfield]], [[Middlesex]], under the Reverend Stephen Freeman.<ref>{{cite web| url=https://discovery.nationalarchives.gov.uk/details/r/db8b56cf-ea51-4c0b-ad46-320a2391d714 | title=Reverend Stephen Freeman's Schools Ponders End | work=74 – London Metropolitan Archives: City of London | publisher=[[The National Archives (United Kingdom)|The National Archives]] | location=UK | access-date=9 August 2021 }}</ref> The academy had a library that prompted Babbage's love of mathematics. He studied with two more private tutors after leaving the academy. The first was a clergyman near [[Cambridge]]; through him Babbage encountered [[Charles Simeon]] and his evangelical followers, but the tuition was not what he needed.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA17 17]}} He was brought home, to study at the Totnes school: this was at age 16 or 17.{{sfn|Collier|MacLachlan|2000|p=[https://books.google.com/books?id=-vzMEwf-bHEC&pg=PA11 11]}} The second was an [[University of Oxford|Oxford]] tutor, under whom Babbage reached a level in Classics sufficient to be accepted by the [[University of Cambridge]].

==At the University of Cambridge==
Babbage arrived at [[Trinity College, Cambridge]], in October 1810.<ref name="Venn">{{acad | id = BBG810C | name = Babbage, Charles }}</ref> He was already self-taught in some parts of contemporary mathematics;<ref>{{cite book| first=E. S. | last=Leedham-Green|title=A Concise History of the University of Cambridge|url=https://books.google.com/books?id=xvScOaG7mHYC&pg=PA142|year=1996|publisher=[[Cambridge University Press]] |isbn=978-0-521-43978-7|page=142}}</ref> he had read [[Robert Woodhouse]], [[Joseph Louis Lagrange]], and [[Maria Gaetana Agnesi]]. As a result, he was disappointed in the standard mathematical instruction available at the university.<ref name="ODNB"/>

Babbage, [[John Herschel]], [[George Peacock (mathematician)|George Peacock]], and several other friends formed the [[Analytical Society]] in 1812; they were also close to [[Edward Ryan (barrister)|Edward Ryan]].<ref name="wilkes">Wilkes (2002) ''p.''355</ref> As a student, Babbage was also a member of other societies such as [[The Ghost Club]], concerned with investigating supernatural phenomena, and the Extractors Club, dedicated to liberating its members from the madhouse, should any be committed to one.<ref name="GEB">{{cite book | last = Hofstadter | first = Douglas R. | author-link = Douglas Hofstadter | title = Gödel, Escher, Bach: an Eternal Golden Braid | publisher=[[Penguin Books]] | orig-year = 1979| year = 2000 | page = 726 | title-link = Gödel, Escher, Bach: an Eternal Golden Braid }}</ref><ref name="allsands">{{cite web | title = Charles Babbage'S Computer Engines | url = http://www.allsands.com/history/objects/history/objects/babbagecomputer_yy_gn.htm | access-date = 13 March 2012 | url-status = dead | archive-url = https://web.archive.org/web/20130430112345/http://www.allsands.com/history/objects/history/objects/babbagecomputer_yy_gn.htm | archive-date = 30 April 2013}}</ref>

In 1812, Babbage transferred to [[Peterhouse, Cambridge]].<ref name="Venn" /> He was the top mathematician there, but did not graduate with honours. He instead received a degree without examination in 1814. He had defended a thesis that was considered blasphemous in the preliminary public disputation, but it is not known whether this fact is related to his not sitting the examination.<ref name="ODNB"/>

==After Cambridge==
Considering his reputation, Babbage quickly made progress. He lectured to the [[Royal Institution]] on astronomy in 1815, and was elected a [[Fellow of the Royal Society]] in 1816.<ref name= "Essinger">{{cite book| first=James | last= Essinger |title=Jacquard's Web |year=2007 |publisher=Oxford University Press |isbn= 978-0-19-280578-2 |pages= 59, 98}}</ref> After graduation, on the other hand, he applied for positions unsuccessfully, and had little in the way of a career. In 1816 he was a candidate for a teaching job at [[Haileybury College]]; he had recommendations from [[James Ivory (mathematician)|James Ivory]] and [[John Playfair]], but lost out to [[Henry Walter (antiquary)|Henry Walter]].<ref>{{cite book| first1=Raymond | last1=Flood | authorlink1=Raymond Flood (mathematician) | first2=Adrian | last2= Rice| first3=Robin | last3=Wilson | authorlink3=Robin Wilson (mathematician) |title=Mathematics in Victorian Britain|url= https://books.google.com/books?id=QmzfJUShGYUC&pg=PA145|year= 2011| publisher=Oxford University Press|isbn=978-0-19-960139-4|page=145}}</ref> In 1819, Babbage and Herschel visited Paris and the [[Society of Arcueil]], meeting leading French mathematicians and physicists.<ref>{{cite book| title= George Green: Mathematician and Physicist, 1793–1841: The Background to His Life and Work|url=https://books.google.com/books?id=x2Y2eb9IzwwC&pg=PA255|year=2001|publisher=SIAM|isbn= 978-0-89871-463-0| page=255 note 19}}</ref> That year Babbage applied to be professor at the [[University of Edinburgh]], with the recommendation of [[Pierre Simon Laplace]]; the post went to [[William Wallace (mathematician)|William Wallace]].<ref>{{cite book| first=Roger |author1-link=Roger Hahn | last=Hahn|title=Pierre Simon Laplace: 1749–1827; a Determined Scientist|url=https://books.google.com/books?id=ROu0P-pYQekC&pg=PA295|access-date=8 May 2013|year=2005|publisher= Harvard University Press|isbn= 978-0-674-01892-1|pages=295 note 34}}</ref><ref>{{cite ODNB|id=28545|title= Wallace, William|first=Maria|last=Panteki}}</ref><ref>{{cite book|title=The Edinburgh magazine, and literary miscellany, a new series of The Scots magazine|url=https://books.google.com/books?id=4NsEAAAAQAAJ&pg=PA369|year= 1819| page=369}}</ref>

With Herschel, Babbage worked on the [[Electromagnetism|electrodynamics]] of [[Arago's rotations]], publishing in 1825. Their explanations were only transitional, being picked up and broadened by [[Michael Faraday]]. The [[Phenomenon|phenomena]] are now part of the theory of [[eddy current]]s, and Babbage and Herschel missed some of the clues to unification of [[electromagnetic theory]], staying close to [[Ampère's force law]].<ref>{{cite book | first=L. Pearce | last=Williams |title= Michael Faraday |year=1965 |publisher=Da Capo Press |isbn=978-0-306-80299-7 |pages=[https://archive.org/details/michaelfaradaybi0000will_g3v0/page/170 170–172] |url=https://archive.org/details/michaelfaradaybi0000will_g3v0/page/170 }}</ref>

Babbage purchased the actuarial tables of [[George Barrett (actuary)|George Barrett]], who died in 1821 leaving unpublished work, and surveyed the field in 1826 in ''Comparative View of the Various Institutions for the Assurance of Lives''.<ref>{{cite ODNB|id=1523|title= Barrett, George|first=Robert|last=Brown}}</ref> This interest followed a project to set up an insurance company, prompted by [[Francis Baily]] and mooted in 1824, but not carried out.{{sfn|Collier|MacLachlan|2000|p=[https://books.google.com/books?id=-vzMEwf-bHEC&pg=PA29 29–30]}} Babbage did calculate actuarial tables for that scheme, using [[Equitable Society]] mortality data from 1762 onwards.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA59 59]}}

During this whole period, Babbage depended awkwardly on his father's support, given his father's attitude to his early marriage, of 1814: he and Edward Ryan wedded the Whitmore sisters. He made a home in [[Marylebone]] in London and established a large family.<ref>{{cite book| author=James|title=Remarkable Engineers|url=https://books.google.com/books?id=0bwb5bevubwC&pg=PA45|access-date=26 April 2013|publisher= Cambridge University Press|isbn= 978-1-139-48625-5|page=45|date=25 February 2010}}</ref> On his father's death in 1827, Babbage inherited a large estate (value around £100,000, equivalent to £{{Format price|{{Inflation|UK|100000|1827}}}} or ${{Format price|{{To USD|{{Inflation|UK|100000|1827}}|GBR}}}} today), making him independently wealthy.<ref name="ODNB"/> After his wife's death in the same year he spent time travelling. In Italy he met [[Leopold II, Grand Duke of Tuscany]], foreshadowing a later visit to [[Piedmont]].<ref name="Essinger"/> In April 1828 he was in Rome, and relying on Herschel to manage the difference engine project, when he heard that he had become a professor at Cambridge, a position he had three times failed to obtain (in 1820, 1823 and 1826).{{sfn|Knox|2003|p=[https://books.google.com/books?id=QGX_rAeia4kC&pg=PA242 242; 258–72]}}

===Royal Astronomical Society===
Babbage was instrumental in founding the [[Royal Astronomical Society]] in 1820, initially known as the Astronomical Society of London.<ref>{{Cite web|url=http://www-history.mcs.st-and.ac.uk/Biographies/Babbage.html|title=Babbage biography|website=History.mcs.st-and.ac.uk|access-date=21 December 2017}}</ref> Its original aims were to reduce astronomical calculations to a more standard form, and to circulate data.<ref>{{cite book| first= Martin | last=Campbell-Kelly | authorlink= Martin Campbell-Kelly |title=The History of Mathematical Tables: From Sumer to Spreadsheets| at=[https://books.google.com/books?id=O170gWPZ7M8C&pg=PA8 p. 8]|year= 2003|publisher=Oxford University Press|isbn=978-0-19-850841-0|title-link= The History of Mathematical Tables}}</ref> These directions were closely connected with Babbage's ideas on computation, and in 1824 he won its [[Gold Medal of the Royal Astronomical Society|Gold Medal]], cited "for his invention of an engine for calculating [[Mathematical table|mathematical]] and [[Ephemeris|astronomical tables]]".<ref>{{Cite book|last1=Buxton|first1=Harry Wilmot|url= https://books.google.com/books?id=jrUmAAAAMAAJ|title=Memoir of the Life and Labours of the Late Charles Babbage Esq., F.R.S.|last2=Tomash|first2=Erwin|date=1988|publisher=MIT Press|isbn=978-0-262-02269-9|location= Cambridge|pages=77|language=en}}</ref>

Babbage's motivation to overcome errors in tables by mechanisation had been a commonplace since [[Dionysius Lardner]] wrote about it in 1834 in the ''[[Edinburgh Review]]'' (under Babbage's guidance).<ref>{{cite book|first1=Raymond | last1=Flood | authorlink1=Raymond Flood (mathematician) | first2=Adrian | last2= Rice| first3=Robin | last3=Wilson | authorlink3= Robin Wilson (mathematician) |title=Mathematics in Victorian Britain|url=https://books.google.com/books?id=YruifIx88AQC&pg=PA34|year=2011|publisher=Oxford University Press|isbn= 978-0-19-162794-1|page=34}}</ref><ref>{{cite book| first=Harro | last= Maas|title=William Stanley Jevons and the Making of Modern Economics|url=https://books.google.com/books?id=aGWvA6SiWfMC&pg=PA201|year= 2005|publisher=Cambridge University Press|isbn=978-0-521-82712-6|page= 201}}</ref> The context of these developments is still debated. Babbage's own account of the origin of the difference engine begins with the Astronomical Society's wish to improve ''[[The Nautical Almanac]]''. Babbage and Herschel were asked to oversee a trial project, to recalculate some part of those tables. With the results to hand, discrepancies were found. This was in 1821 or 1822, and was the occasion on which Babbage formulated his idea for mechanical computation.<ref>{{cite book| first=M. Norton | last= Wise|title=The values of precision|url=https://books.google.com/books?id=g8uvNtuPhgUC&pg=PA320|year=1997|publisher=Princeton University Press|isbn=978-0-691-01601-6|page= 320}}</ref> The issue of the ''Nautical Almanac'' is now described as a legacy of a polarisation in British science caused by attitudes to [[Sir Joseph Banks]], who had died in 1820.<ref>{{cite book|first1= Eleanor |last1= Robson| first2=Jacqueline |last2= Stedall|title=The Oxford Handbook of the History of Mathematics|url=https://books.google.com/books?id=HIMiWHVKLDkC&pg=RA1-PR34|access-date=25 April 2013|date=18 December 2008|publisher=Oxford University Press|isbn= 978-0-19-160744-8|page=xxxiv}}</ref>
[[File:Difference engine plate 1853.jpg|thumb|A portion of the [[difference engine]]]]
Babbage studied the requirements to establish a modern [[postal system]], with his friend [[Thomas Frederick Colby]], concluding there should be a uniform rate that was put into effect with the introduction of the [[Uniform Fourpenny Post]] supplanted by the [[Uniform Penny Post]]{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA115 115]}} in 1839 and 1840. Colby was another of the founding group of the Society.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA45 45]}} He was also in charge of the [[Survey of Ireland]]. Herschel and Babbage were present at a celebrated operation of that survey, the remeasuring of the [[Lough Foyle]] baseline.<ref>{{cite book|publisher=Royal Institution of Great Britain|title=Proceedings|url=https://books.google.com/books?id=LxNcKnmdDTIC&pg=PA518|year=1858|page=518}}</ref>

===British Lagrangian School===
The Analytical Society had initially been no more than an undergraduate provocation. During this period it had some more substantial achievements. In 1816, Babbage, Herschel and Peacock published a translation from French of the lectures of [[Sylvestre Lacroix]], which was then the state-of-the-art calculus textbook.<ref>{{cite book|title= Constructing a Bridge: An Exploration of Engineering Culture, Design, and Research in Nineteenth-century France and America|url=https://books.google.com/books?id=6P66Ofj6DiYC&pg=PA110|year=1997|publisher=MIT Press|isbn= 978-0-262-11217-8| page=110}}</ref>

Reference to [[Joseph-Louis Lagrange|Lagrange]] in calculus terms marks out the application of what are now called [[formal power series]]. British mathematicians had used them from about 1730 to 1760. As re-introduced, they were not simply applied as notations in [[differential calculus]]. They opened up the fields of [[functional equation]]s (including the [[difference equation]]s fundamental to the difference engine) and operator ([[D-module]]) methods for [[differential equation]]s.  The analogy of difference and differential equations was notationally changing Δ to D, as a "finite" difference becomes "infinitesimal". These symbolic directions became popular, as [[operational calculus]], and pushed to the point of diminishing returns. The [[(ε, δ)-definition of limit|Cauchy concept of limit]] was kept at bay.<ref name="Guicciardini2003">{{cite book|first=Niccolò | last= Guicciardini|title=The Development of Newtonian Calculus in Britain, 1700–1800|url=https://books.google.com/books?id=nIKVQCeI1FUC&pg=PA138|year=2003|publisher=Cambridge University Press|isbn=978-0-521-52484-1|page=138|author-link=Niccolò Guicciardini}}</ref> Woodhouse had already founded this second "British Lagrangian School" with its treatment of [[Taylor series]] as formal.<ref name="GabbayWoods2008">{{cite book|author1=Dov M. Gabbay|author2=John Woods|title=British Logic in the Nineteenth Century|url=https://books.google.com/books?id=UULl07dutBwC&pg=PA403|year=2008|publisher=Elsevier|isbn= 978-0-08-055701-4|pages=403–404}}</ref>

In this context [[function composition]] is complicated to express, because the [[chain rule]] is not simply applied to second and higher derivatives. This matter was known to Woodhouse by 1803, who took from [[Louis François Antoine Arbogast]] what is now called [[Faà di Bruno's formula]]. In essence it was known to [[Abraham De Moivre]] (1697). Herschel found the method impressive, Babbage knew of it, and it was later noted by [[Ada Lovelace]] as compatible with the analytical engine.<ref>Craik 2005, pp. 122–3.</ref> In the period to 1820 Babbage worked intensively on functional equations in general, and resisted both conventional [[finite difference]]s and Arbogast's approach (in which Δ and D were related by the simple additive case of the [[exponential function|exponential map]]). But via Herschel he was influenced by Arbogast's ideas in the matter of [[iterated function|iteration]], i.e. composing a function with itself, possibly many times.<ref name="GabbayWoods2008"/> Writing in a major paper on functional equations in the ''[[Philosophical Transactions]]'' (1815/6), Babbage said his starting point was work of [[Gaspard Monge]].<ref>{{cite book|first1=Jeremy J. | last1= Gray| first2=Karen | last2= Hunger Parshall|title=Episodes in the History of Modern Algebra (1800–1950)| url=https://books.google.com/books?id=HQijZjoTKnIC&pg=PA19|year=2011|publisher=American Mathematical Society |isbn= 978-0-8218-7257-4|page=19}}</ref>

==Academic==
From 1828 to 1839, Babbage was [[Lucasian Professor of Mathematics]] at Cambridge. Not a conventional resident [[university don|don]], and inattentive to his teaching responsibilities, he wrote three topical books during this period of his life. He was elected a Foreign Honorary Member of the [[American Academy of Arts and Sciences]] in 1832.<ref name="AAAS">{{cite web|title=Book of Members, 1780–2010: Chapter B|url=http://www.amacad.org/publications/BookofMembers/ChapterB.pdf |archive-url=https://web.archive.org/web/20060618085806/http://amacad.org/publications/BookofMembers/ChapterB.pdf |archive-date=2006-06-18 |url-status=live|publisher=American Academy of Arts and Sciences|access-date=28 April 2011}}</ref> Babbage was out of sympathy with colleagues: [[George Biddell Airy]], his predecessor as Lucasian Professor of Mathematics at Trinity College, Cambridge,<ref>[[George Biddell Airy#Biography]]</ref> thought an issue should be made of his lack of interest in lecturing. Babbage planned to lecture in 1831 on [[political economy]]. Babbage's reforming direction looked to see [[Higher education|university education]] more inclusive, universities doing more for research, a broader syllabus and more interest in applications; but [[William Whewell]] found the programme unacceptable. A controversy Babbage had with [[Richard Jones (economist)|Richard Jones]] lasted for six years.{{sfn|Knox|2003|p=[https://books.google.com/books?id=QGX_rAeia4kC&pg=PA284 284–285]}} He never did give a lecture.<ref name="Th35">{{ThoemmesBritish19C|Babbage, Charles|35}}</ref>

It was during this period that Babbage tried to enter politics. [[Simon Schaffer]] writes that his views of the 1830s included [[disestablishment]] of the [[Church of England]], a broader [[political franchise]], and inclusion of manufacturers as stakeholders.{{sfn|Knox|2003|p=[https://books.google.com/books?id=QGX_rAeia4kC&pg=PA243 243]}} He twice stood for Parliament as a candidate for the borough of [[Finsbury (UK Parliament constituency)|Finsbury]]. In 1832 he came in third among five candidates, missing out by some 500 votes in the two-member constituency when two other reformist candidates, [[Thomas Wakley]] and Christopher Temple, split the vote.<ref>{{cite web|author=Members Constituencies Parliaments Surveys |url=http://www.historyofparliamentonline.org/volume/1820-1832/constituencies/middlesex |title=historyofparliamentonline.org, ''Middlesex County 1820–1832'' |publisher=Historyofparliamentonline.org |access-date=7 June 2014}}</ref><ref>{{cite book|author=Sylvanus Urban|title=The Gentleman's Magazine|url=https://books.google.com/books?id=AbYUAAAAQAAJ&pg=PA659|year=1838|page=659}}</ref> In his memoirs Babbage related how this election brought him the friendship of [[Samuel Rogers]]: his brother Henry Rogers wished to support Babbage again, but died within days.<ref>{{cite book|author=Charles Babbage|title=Passages from the life of a philosopher|url=https://archive.org/details/bub_gb_2T0AAAAAQAAJ|access-date=1 May 2013|year=1864|publisher=Longman, Green, Longman, Roberts, & Green|pages=[https://archive.org/details/bub_gb_2T0AAAAAQAAJ/page/n199 190]–191}}</ref> In 1834 Babbage finished last among four.<ref>{{cite book | author = Crowther, J. G. | title = Scientific Types | year = 1968 | publisher = Barrie & Rockliff | location = London | page = [https://archive.org/details/scientifictypes00crow/page/266 266] | isbn = 978-0-248-99729-4 | url = https://archive.org/details/scientifictypes00crow/page/266 }}</ref>{{sfn|Hyman|1985|p=[https://archive.org/details/charlesbabbagepi0000hyma/page/82 82–87]}}<ref>{{harvnb|Moseley|1964|pp=120–121}}- Note some confusion as to the dates.</ref> In 1832, Babbage, Herschel and Ivory were appointed Knights of the [[Royal Guelphic Order]], however they were not subsequently made [[knight bachelor|knights bachelor]] to entitle them to the prefix ''Sir'', which often came with appointments to that foreign order (though Herschel was later created a [[baronet]]).<ref>{{Citation |last=Shaw |first=William Arthur |author-link=William Arthur Shaw |year=1906 |title=The Knights of England: A complete record from the earliest time to the present day of the knights of all the orders of chivalry in England, Scotland, and Ireland, and of knights bachelors, incorporating a complete list of knights bachelors dubbed in Ireland |volume=2 |location=London |publisher=Sherratt and Hughes|url=https://archive.org/details/knightsofengland02shawuoft}}</ref>

==="Declinarians", learned societies and the BAAS===
[[File:Babbage - Letter to sir Humphry Davy on the application of machinery to the purpose of calculating and printing mathematical tables, 1822 - 721620.tif|thumb|''Letter to Sir Humphry Davy'', 1822]]
Babbage now emerged as a [[polemicist]]. One of his biographers notes that all his books contain a "campaigning element". His ''Reflections on the Decline of Science and some of its Causes'' (1830) stands out, however, for its sharp attacks. It aimed to improve British science, and more particularly to oust [[Davies Gilbert]] as President of the Royal Society, which Babbage wished to reform.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA88 88]}} It was written out of pique, when Babbage hoped to become the junior secretary of the Royal Society, as Herschel was the senior, but failed because of his antagonism to [[Humphry Davy]].<ref>{{cite book|author=James|title=Remarkable Engineers|url=https://books.google.com/books?id=0bwb5bevubwC&pg=PA47|access-date=27 April 2013|publisher=Cambridge University Press|isbn=978-1-139-48625-5|page=47|date=25 February 2010}}</ref> Michael Faraday had a reply written, by [[Gerrit Moll]], as ''On the Alleged Decline of Science in England'' (1831).<ref name="Holmes">{{cite book |author=Richard Holmes|title=The Age of Wonder|year=2008 |publisher=Pantheon Books |isbn=978-0-375-42222-5 |pages=437–440|author-link=Richard Holmes (biographer)}}</ref> On the front of the Royal Society Babbage had no impact, with the bland election of the [[Prince Augustus Frederick, Duke of Sussex|Duke of Sussex]] to succeed Gilbert the same year. As a broad manifesto, on the other hand, his ''Decline'' led promptly to the formation in 1831 of the [[British Association for the Advancement of Science]] (BAAS).<ref name="Holmes"/>

The ''[[Mechanics' Magazine]]'' in 1831 identified as Declinarians the followers of Babbage. In an unsympathetic tone it pointed out [[David Brewster]] writing in the ''[[Quarterly Review]]'' as another leader; with the barb that both Babbage and Brewster had received public money.<ref>{{cite book|title=The Mechanics' Magazine, Museum, Register, Journal, and Gazette|url=https://books.google.com/books?id=7tQ3AAAAYAAJ&pg=PA373|year=1831|publisher=M. Salmon|pages=373–374}}</ref>

In the debate of the period on [[statistics]] (''qua'' data collection) and what is now [[statistical inference]], the BAAS in its Statistical Section (which owed something also to [[William Whewell|Whewell]]) opted for data collection. This Section was the sixth, established in 1833 with Babbage as chairman and [[John Elliot Drinkwater]] as secretary. The foundation of the [[Statistical Society]] followed.<ref>{{cite book|author=Mary Poovey|title=A History of the Modern Fact: Problems of Knowledge in the Sciences of Wealth and Society|url=https://books.google.com/books?id=AQ5ADoAjmd4C&pg=PA309|year=1998|publisher=University of Chicago Press|isbn=978-0-226-67526-8|page=309|author-link=Mary Poovey}}</ref><ref>{{cite book|author1=Dov M. Gabbay|author2=John Woods|title=British Logic in the Nineteenth Century|url=https://books.google.com/books?id=UULl07dutBwC&pg=PA164|year=2008|publisher=Elsevier|isbn=978-0-08-055701-4|page=164}}</ref><ref>{{cite book |author=Patricia Jones |title=Population Malthus |year=1979 |publisher=Routledge and Kegan Paul |isbn=978-0-7100-0266-2 |page=445}}</ref> Babbage was its public face, backed by Richard Jones and [[Robert Malthus]].<ref>{{cite book|author=James P. Henderson|title=Early Mathematical Economics: William Whewell and the British case|url=https://books.google.com/books?id=ye2p5tMnVAcC&pg=PA33|year=1996|publisher=Rowman & Littlefield|isbn=978-0-8476-8201-0|page=33}}</ref>

===''On the Economy of Machinery and Manufactures''===
[[File:Babbage - On the economy of machinery and manufactures, 1835 - 5864499.tif|thumb|''On the Economy of Machinery and Manufactures'', 1835]]
[[File:Babbage sign language.jpg|thumb|Babbage's notation for machine parts, explanation from ''On a method of expressing by signs the action of machinery'' (1827) of his "Mechanical Notation", invented for his own use in understanding the work on the difference engine, and an influence on the conception of the analytical engine<ref>{{cite book|author=Michael Lingren|title=Glory and Failure: The Difference Engines of Johann Müller, Charles Babbage and Georg and Edvard Scheutz|url=https://books.google.com/books?id=plgMl2yfVkwC&pg=PA54|year=1990|publisher=MIT Press|isbn=978-0-262-12146-0|page=54}}</ref>]]
Babbage published ''On the Economy of Machinery and Manufactures'' (1832), on the organisation of [[industrial production]]. It was an influential early work of [[operational research]].<ref>{{ThoemmesBritish19C|Babbage, Charles|39}}</ref> [[John Rennie the Younger]] in addressing the [[Institution of Civil Engineers]] on manufacturing in 1846 mentioned mostly surveys in encyclopaedias, and Babbage's book was first an article in the ''[[Encyclopædia Metropolitana]]'', the form in which Rennie noted it, in the company of related works by [[John Farey Jr.]], [[Peter Barlow (mathematician)|Peter Barlow]] and [[Andrew Ure]].<ref>{{cite book|author=Charles Manby|title=Minutes of the Proceedings of the Institution of Civil Engineers|url=https://books.google.com/books?id=zBMFAAAAQAAJ&pg=PA57|year=1846|page=57|author-link=Charles Manby}}</ref> From ''An essay on the general principles which regulate the application of machinery to manufactures and the mechanical arts'' (1827), which became the ''Encyclopædia Metropolitana'' article of 1829, Babbage developed the schematic classification of machines that, combined with discussion of factories, made up the first part of the book. The second part considered the "domestic and political economy" of manufactures.<ref>{{cite book|author1=M. Lucertini|author2=Ana Millán Gasca|author2-link=Ana Millán Gasca|author3=Fernando Nicolò|title=Technological Concepts and Mathematical Models in the Evolution of Modern Engineering Systems|url=https://books.google.com/books?id=YISIUycS4HgC&pg=PA30|year=2004|publisher=Springer|isbn=978-3-7643-6940-8|page=30}}</ref>

The book sold well, and quickly went to a fourth edition (1836).<ref>{{cite book|author=Mauro F. Guillén|author-link=Mauro F. Guillén|title=Models of Management: Work, Authority, and Organization in a Comparative Perspective|url=https://archive.org/details/modelsofmanageme0000guil|url-access=registration|access-date=18 April 2013|date=15 October 1994|publisher=University of Chicago Press|isbn=978-0-226-31036-7|page=[https://archive.org/details/modelsofmanageme0000guil/page/207 207]}}</ref> Babbage represented his work as largely a result of actual observations in factories, British and abroad. It was not, in its first edition, intended to address deeper questions of political economy; the second (late 1832) did, with three further chapters including one on [[piece rate]].<ref>{{cite book|author=Maxine Berg|title=The Machinery Question and the Making of Political Economy 1815–1848|url=https://books.google.com/books?id=azk7AAAAIAAJ&pg=PA181|year=1982|publisher=CUP Archive|isbn=978-0-521-28759-3|page=181}}</ref> The book also contained ideas on rational design in factories, and [[profit sharing]].<ref>{{cite book|author=Bruce E. Kaufman|title=The Global Evolution of Industrial Relations: Events, Ideas and the IIRA|url=https://books.google.com/books?id=Q4zzuwFRwCAC&pg=PA66|year=2004|publisher=Academic Foundation|isbn=978-81-7188-544-2|page=66}}</ref>

===="Babbage principle"====
In ''Economy of Machinery'' was described what is now called the "Babbage principle". It pointed out commercial advantages available with more careful [[division of labour]]. As Babbage himself noted, it had already appeared in the work of [[Melchiorre Gioia]] in 1815.<ref>{{cite book|author1=Julio Segura|author2=Carlos Rodríguez Braun|title=An Eponymous Dictionary of Economics: A Guide To Laws And Theorems Named After Economists|url=https://books.google.com/books?id=Z6Oy4L-6LSwC&pg=PA13|access-date=18 April 2013|year=2004|publisher=Edward Elgar Publishing|isbn=978-1-84542-360-5|page=13}}</ref> The term was introduced in 1974 by [[Harry Braverman]].<ref>{{cite book|title=Work|url=https://books.google.com/books?id=0332ru3Rx0sC&pg=PA39|year=2011|publisher=Polity|isbn=978-0-7456-4678-7|page=39}}</ref> Related formulations are the "principle of multiples" of [[Philip Sargant Florence]], and the "balance of processes".<ref>{{cite book|author=P. Sargant Florence|author-link=Philip Sargant Florence|title=The Logic of British and American Industry: A Realistic Analysis of Economic Structure and Government|url=https://books.google.com/books?id=QLgCocKRIkAC&pg=PA51|year=1953|publisher=Routledge|page=51}} {{isbn|978-0-415-31350-6}}</ref><ref>{{cite book|title=The Theory of the Growth of the Firm [Electronic book]|url=https://books.google.com/books?id=aigWHVhP5tsC&pg=PA68|year=1995|publisher=Oxford University Press|isbn=978-0-19-828977-7|page=68}}</ref>

What Babbage remarked is that skilled workers typically spend parts of their time performing tasks that are below their skill level. If the labour process can be divided among several workers, labour costs may be cut by assigning only high-skill tasks to high-cost workers, restricting other tasks to lower-paid workers.<ref>{{cite book|author1=Giddens, Anthony|author2=Held, David|title=Classes, Power and Conflict: Classical and Contemporary Debates|url=https://archive.org/details/classespowerconf00ials|url-access=registration|access-date=18 April 2013|year=1982|publisher=University of California Press|isbn=978-0-520-04627-6|page=[https://archive.org/details/classespowerconf00ials/page/155 155]}}</ref> He also pointed out that training or apprenticeship can be taken as fixed costs; but that [[returns to scale]] are available by his approach of standardisation of tasks, therefore again favouring the [[factory system]].<ref>{{cite book|author=Guang-Zhen Sun|title=Readings in the Economics of the Division of Labor: The classical tradition|url=https://books.google.com/books?id=Y16MEasCqicC&pg=PA10|year=2005|publisher=World Scientific|isbn=978-981-270-127-5|page=10}}</ref> His view of [[human capital]] was restricted to minimising the time period for recovery of training costs.<ref name="ArtiguesCalvet2007">{{cite book|author1=Pere Mir Artigues|author2=Josep Gonza ́lez Calvet|title=Funds, Flows and Time: An Alternative Approach to the Microeconomic Analysis of Productive Activities|url=https://books.google.com/books?id=s1n1LWVyTWoC&pg=PA72|year=2007|publisher=Springer|isbn=978-3-540-71291-6|page=72 note 15}}</ref>

====Publishing====
Another aspect of the work was its detailed breakdown of the cost structure of book publishing. Babbage took the unpopular line, from the publishers' perspective, of exposing the trade's profitability.<ref>{{cite book|author-link=James A. Secord|author=James A. Secord|title=Victorian Sensation: The Extraordinary Publication, Reception, and Secret Authorship of Vestiges of the Natural History of Creation|url=https://books.google.com/books?id=6LL9PGRhlXYC&pg=PA52|year=2000|publisher=University of Chicago Press|isbn=978-0-226-74410-0|page=52}}</ref> He went as far as to name the organisers of the trade's restrictive practices.<ref>{{cite book|author=Mary Poovey|title=Making a Social Body: British Cultural Formation, 1830–1864|url=https://books.google.com/books?id=NHwVKtTP8G8C&pg=PA193|year=1995|publisher=University of Chicago Press|isbn=978-0-226-67524-4|page=193 note 43}}</ref> Twenty years later he attended a meeting hosted by [[John Chapman (publisher)|John Chapman]] to campaign against the Booksellers Association, still a [[cartel]].<ref>{{cite book |author=Rosemary Ashton |title=G. H. Lewes: An Unconventional Victorian |year=2000 |publisher=Pimlico |isbn=978-0-7126-6689-3 |page=[https://archive.org/details/ghlewesunconvent0000asht/page/128 128] |url=https://archive.org/details/ghlewesunconvent0000asht/page/128 }}</ref>

====Influence====
It has been written that "what [[Arthur Young (writer)|Arthur Young]] was to agriculture, Charles Babbage was to the [[factory visit]] and machinery".<ref>{{Cite journal|last=Ashworth|first=William J.|year=1996|title=Memory, Efficiency, and Symbolic Analysis: Charles Babbage, John Herschel, and the Industrial Mind|journal=Isis|volume=87|issue=4|pages=629–653|jstor=235196|doi=10.1086/357650|s2cid=143404822}}</ref> Babbage's theories are said to have influenced the layout of the [[1851 Great Exhibition]],<ref>{{cite book|author=PeterH Hoffenberg|title=An Empire on Display: English, Indian, and Australian Exhibitions from the Crystal Palace to the Great War|url=https://books.google.com/books?id=ejEwvWvGwVUC&pg=PA178|year=2001|publisher=University of California Press|isbn=978-0-520-21891-8|page=178}}</ref> and his views had a strong effect on his contemporary [[George Julius Poulett Scrope]].<ref>{{cite book|author=Maxine Berg|title=The Machinery Question and the Making of Political Economy 1815–1848|url=https://books.google.com/books?id=azk7AAAAIAAJ&pg=PA127|year=1982|publisher=CUP Archive|isbn=978-0-521-28759-3|page=127}}</ref> [[Karl Marx]] argued that the source of the [[productivity]] of the factory system was exactly the combination of the division of labour with machinery, building on [[Adam Smith]], Babbage and Ure.<ref>{{cite book|author=Ákos Róna-Tas|title=The Great Surprise of the Small Transformation: The Demise of Communism and the Rise of the Private Sector of Hungary|url=https://books.google.com/books?id=npl_KOAojT4C&pg=PA20|year=1997|publisher=University of Michigan Press|isbn=978-0-472-10795-7|page=20}}</ref> Where Marx picked up on Babbage and disagreed with Smith was on the motivation for division of labour by the manufacturer: as Babbage did, he wrote that it was for the sake of [[Profit (accounting)|profitability]], rather than productivity, and identified an impact on the concept of a [[trade (occupation)|trade]].<ref>{{cite book|author1=Ben Fine|author2=Alfredo Saad-Filho|author3=Marco Boffo|title=The Elgar Companion to Marxist Economics|url=https://books.google.com/books?id=xe0VQArHt8sC&pg=PA190|year=2012|publisher=Edward Elgar Publishing|isbn=978-1-78100-122-6|page=190}}</ref>

[[John Ruskin]] went further, to oppose completely what manufacturing in Babbage's sense stood for.<ref>{{cite book|title=Sympathy of Things: Ruskin and the Ecology of Design|url=https://books.google.com/books?id=1LPEMLG98mgC&pg=PA52|year=2011|publisher=V2_ publishing|isbn=978-90-5662-827-7|pages=52–53}}</ref> Babbage also affected the economic thinking of [[John Stuart Mill]].<ref>{{cite book|author1=Patrice L. R. Higonnet|author2=David Saul Landes|author3=Rosovsky Henry|author-link3=Henry Rosovsky |title=Favorites Or Fortune: Technology, Growth, and Economic Development Since the Industrial Revolution|url=https://books.google.com/books?id=yizWdomTqesC&pg=PA401|year=1991|publisher=Harvard University Press|isbn=978-0-674-29520-9|page=401}}</ref> [[George Holyoake]] saw Babbage's detailed discussion of profit sharing as substantive, in the tradition of [[Robert Owen]] and [[Charles Fourier]], if requiring the attentions of a benevolent [[captain of industry]], and ignored at the time.<ref>[[George Jacob Holyoake]], ''The History of Co-operation in England: its literature and its advocates'', vol. 2 (1879) pp. 228–32; [https://archive.org/stream/historycooperat04holygoog#page/n241/mode/2up archive.org.]</ref>

[[Charles Babbage's Saturday night soirées]], held from 1828 into the 1840s, were important gathering places for prominent scientists, authors and aristocracy. Babbage is credited with importing the "scientific soirée" from France with his well-attended Saturday evening soirées.<ref name=":0" /><ref name=":1" />

Works by Babbage and Ure were published in French translation in 1830;<ref>{{cite book|author1=Thierry Pillon|author2=François Vatin|title=Traité de sociologie du travail|page=164|year=2003|publisher=Octarès}}</ref> ''On the Economy of Machinery'' was translated in 1833 into French by [[Édouard Biot]], and into German the same year by Gottfried Friedenberg.{{sfn|Hyman|1985|p=[https://books.google.com/books?id=YCddaWqWK2cC&pg=PA122 122]}} The French engineer and writer on industrial organisation [[Léon Lalanne]] was influenced by Babbage, but also by the economist [[Claude Lucien Bergery]], in reducing the issues to "technology".<ref>{{cite book|author=François Vatin|title=Morale industrielle et calcul économique dans le premier XIXème siècle: L'économie industrielle de Claude-Lucien Bergery (1787–1863)|url=https://books.google.com/books?id=pcJ2lTo97ywC&pg=PA123|date=May 2007|publisher=Editions L'Harmattan|isbn=978-2-296-17103-9|page=123|language=fr}}</ref> [[William Jevons]] connected Babbage's "economy of labour" with his own labour experiments of 1870.<ref>{{cite book|author=Philip Mirowski|title=Natural Images in Economic Thought: Markets Read in Tooth and Claw|url=https://books.google.com/books?id=GGmdRE3kpnMC&pg=PA206|year=1994|publisher=Cambridge University Press|isbn=978-0-521-47884-7|page=206}}</ref> The Babbage principle is an inherent assumption in [[Frederick Winslow Taylor]]'s [[scientific management]].<ref>{{cite book|author1=Yeheskel Hasenfeld|author2=Andrew Delano Abbott|title=Human Services as Complex Organizations|url=https://books.google.com/books?id=8O2juf0fZkMC&pg=PA211|year=1992|publisher=SAGE Publications|isbn=978-0-8039-4065-9|page=211}}</ref>

[[Mary Everest Boole]] claimed that there was profound influence – via her uncle [[George Everest]] – of Indian thought in general and [[Indian logic]], in particular, on Babbage and on her husband [[George Boole]], as well as on [[Augustus De Morgan]]:

<blockquote>Think what must have been the effect of the intense Hinduizing of three such men as Babbage, De Morgan, and George Boole on the mathematical atmosphere of 1830–65. What share had it in generating the ''[[Vector Analysis]]'' and the mathematics by which investigations in physical science are now conducted?<ref name="MaryBoole" /> </blockquote>

===Natural theology===
In 1837, responding to the series of eight ''[[Bridgewater Treatises]]'', Babbage published his ''[[Ninth Bridgewater Treatise]]'', under the title ''On the Power, Wisdom and Goodness of God, as manifested in the Creation''. In this work Babbage weighed in on the side of [[uniformitarianism]] in a current debate.<ref>{{cite book|title=Genesis and Geology: A Study in the Relations of Scientific Thought, Natural Theology, and Social Opinion in Great Britain, 1790–1850|url=https://books.google.com/books?id=PKERMZkA9A0C&pg=PA247|year=1996|publisher=Harvard University Press|isbn=978-0-674-34481-5|page=247}}</ref> He preferred the conception of creation in which a God-given [[natural law]] dominated, removing the need for continuous "contrivance".<ref>{{cite book|author=John G. Trapani|title=Truth matters: essays in honor of Jacques Maritain|url=https://books.google.com/books?id=I6S6dxBhMAIC&pg=PA109|year=2004|publisher=CUA Press|isbn=978-0-9669226-6-0|page=109}}</ref>

The book is a work of [[natural theology]], and incorporates extracts from related correspondence of Herschel with [[Charles Lyell]].<ref>Note I, in [http://darwin-online.org.uk/converted/Ancillary/1838_Bridgewater_A25/1838_Bridgewater_A25.html darwin-online.org.uk, ''Babbage, Charles. 1838. The Ninth Bridgewater Treatise. 2d edn. London: John Murray.'']</ref> Babbage put forward the thesis that God had the omnipotence and foresight to create as a divine legislator.  In this book, Babbage dealt with relating interpretations between science and religion; on the one hand, he insisted that "there exists no fatal collision between the words of [[The Bible|Scripture]] and the facts of nature;" on the other hand, he wrote that the [[Book of Genesis]] was not meant to be read literally in relation to scientific terms. Against those who said these were in conflict, he wrote "that the contradiction they have imagined can have no real existence, and that whilst the testimony of [[Moses]] remains unimpeached, we may also be permitted to confide in the testimony of our senses."<ref>Babbage, ''[http://www.victorianweb.org/science/science_texts/bridgewater/b4.htm Ninth Bridgewater Treatise]''. Chapter V. Further View of the same Subject. The Victorian Web.</ref>

The ''Ninth Bridgewater Treatise'' was quoted extensively in ''[[Vestiges of the Natural History of Creation]]''.<ref>{{cite book|author=James A. Secord|title=Victorian Sensation: The Extraordinary Publication, Reception, and Secret Authorship of Vestiges of the Natural History of Creation|url=https://books.google.com/books?id=6LL9PGRhlXYC&pg=PA107|year=2000|publisher=University of Chicago Press|isbn=978-0-226-74410-0|page=107}}</ref> The parallel with Babbage's computing machines is made explicit, as allowing plausibility to the theory that [[transmutation of species]] could be pre-programmed.<ref name="Chambers1994">{{cite book|author=Robert Chambers|title=Vestiges of the Natural History of Creation and Other Evolutionary Writings|url=https://books.google.com/books?id=nqyVl1ji7SAC&pg=PR16|access-date=19 April 2013|date=15 August 1994|publisher=University of Chicago Press|isbn=978-0-226-10073-9|pages=xvi–xvii}}</ref>

It was in The ''Ninth Bridgewater Treatise'' where Babbage proposed his 'library in the air' concept, where every breath, word and motion was imprinted at the atomic level in a record that could be accessed after the events occurred.
<blockquote>The air itself is one vast library on whose pages are for ever written all that man has ever said or woman whispered.<ref>{{Cite web|url=https://blog.scienceandindustrymuseum.org.uk/babbage-library-in-the-air/|title=Babbage's 'Library in the Air' {{pipe}} Science and Industry Museum|date=29 May 2019|website=Science and Industry Museum blog}}</ref><ref>{{Cite journal|url=https://trace.tennessee.edu/utk_graddiss/10446|title="The Air Itself is One Vast Library": Reading the Influence of Motive Expression in the Victorian Imagination|first=Allison Lyn|last=Clymer|date=1 August 2024|journal=Doctoral Dissertations}}</ref></blockquote>

[[File:Babbage curve singular points.png|thumb|Plate from the ''Ninth Bridgewater Treatise'', showing a parametric family of [[algebraic curve]]s acquiring isolated real points]]
Jonar Ganeri, author of ''Indian Logic'', believes Babbage may have been influenced by Indian thought; one possible route would be through [[Henry Thomas Colebrooke]].<ref name="Ganeri">{{cite book|author= Jonar Ganeri|title=Indian Logic: A Reader|url=https://books.google.com/books?id=t_nOiqFmxOIC&pg=PA7|year=2001|publisher=Routledge|isbn=978-0-7007-1329-5|page=7}}</ref> Mary Everest Boole argues that Babbage was introduced to Indian thought in the 1820s by her uncle George Everest:
<blockquote>Some time about 1825, [Everest] came to England for two or three years, and made a fast and lifelong friendship with Herschel and with Babbage, who was then quite young. I would ask any fair-minded mathematician to read Babbage's Ninth Bridgewater Treatise and compare it with the works of his contemporaries in England; and then ask himself whence came the peculiar conception of the nature of miracle which underlies Babbage's ideas of Singular Points on Curves (Chap, viii) – from European Theology or Hindu Metaphysic? Oh! how the English clergy of that day hated Babbage's book!<ref name="MaryBoole">{{cite book |author=Boole, Mary Everest |chapter=Indian Thought and Western Science in the Nineteenth Century |editor1=Cobham, E.M. |editor2=Dummer, E.S. |title=Boole, Mary Everest "Collected Works" |publisher=Daniel |location=London |year=1931 |pages=947–967 |chapter-url=https://books.google.com/books?id=-5wyxULAKpsC}}</ref></blockquote>

=== Religious views ===
Babbage was raised in the Protestant form of the Christian faith, his family having inculcated in him an orthodox form of worship.<ref>[[s:Passages from the Life of a Philosopher/Chapter II#8|''Passages from the Life of a Philosopher'']] (1864), p. 8.</ref> He explained:

{{blockquote|My excellent mother taught me the usual forms of my daily and nightly prayer; and neither in my father nor my mother was there any mixture of bigotry and intolerance on the one hand, nor on the other of that unbecoming and familiar mode of addressing the Almighty which afterwards so much disgusted me in my youthful years.<ref>{{harvnb|Babbage|1864}}</ref>}}

Rejecting the [[Athanasian Creed]] as a "direct contradiction in terms", in his youth he looked to [[Samuel Clarke]]'s works on religion, of which ''Being and Attributes of God'' (1704) exerted a particularly strong influence on him. Later in life, Babbage concluded that "the true value of the Christian religion rested, not on speculative [theology] ... but ... upon those doctrines of kindness and benevolence which that religion claims and enforces, not merely in favour of man himself but of every creature susceptible of pain or of happiness."<ref>[[s:Passages from the Life of a Philosopher/Chapter XXX#404|''Passages from the Life of a Philosopher'']] (1864), pp. 404–405</ref>

In his autobiography [[s:Passages from the Life of a Philosopher|''Passages from the Life of a Philosopher'']] (1864), Babbage wrote a whole chapter on the topic of religion, where he identified three sources of divine knowledge:<ref>[[s:Passages from the Life of a Philosopher/Chapter XXX#396|''Passages from the Life of a Philosopher'']] (1864), p. 396</ref>
# ''A priori'' or mystical experience
# From Revelation
# From the examination of the works of the Creator
He stated, on the basis of the [[design argument]], that studying the works of nature had been the more appealing evidence, and the one which led him to actively profess the [[existence of God]].<ref>Smithsonian Institution. (1846). [https://archive.org/stream/annualreportofbo1873smit#page/174/mode/2up Annual report of the Board of Regents of the Smithsonian Institution]. Washington Government Printing Office. Smithsonian Institution</ref><ref>[[s:Passages from the Life of a Philosopher/Chapter XXX#403|''Passages from the Life of a Philosopher'']] (1864), The Athanasian Creed, p. 403: "In the course of my inquiries, I met with the work upon the Trinity, by Dr. Samuel Clarke. This I carefully examined, and although very far from being satisfied, I ceased from further inquiry. This change arose probably from my having acquired the much more valuable work of the same author, on the Being and Attributes of God. This I studied, and felt that its doctrine was much more intelligible and satisfactory than that of the former work. I may now state, as the result of a long life spent in studying the works of the Creator, that I am satisfied they afford far more satisfactory and more convincing proofs of the existence of a supreme Being than any evidence transmitted through human testimony can possibly supply."</ref> Advocating for natural theology, he wrote:
{{blockquote|In the works of the Creator ever open to our examination, we possess a firm basis on which to raise the superstructure of an enlightened creed. The more man inquires into the laws which regulate the material universe, the more he is convinced that all its varied forms arise from the action of a few simple principles ...  The works of the Creator, ever present to our senses, give a living and perpetual testimony of his power and goodness far surpassing any evidence transmitted through human testimony. The testimony of man becomes fainter at every stage of transmission, whilst each new inquiry into the works of the Almighty gives to us more exalted views of his wisdom, his goodness, and his power.<ref>[[s:Passages from the Life of a Philosopher/Chapter XXX#396|''Passages from the Life of a Philosopher'']] (1864), pp. 396–402</ref>}}

Like [[Samuel Vince]], Babbage also wrote a defence of the belief in divine [[miracle]]s.<ref>Pickover, Clifford A. (2009). ''[https://books.google.com/books?id=JrslMKTgSZwC&q=Babbage The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics].'' Sterling Publishing Company, Inc. p. 218</ref> Against objections previously posed by [[David Hume]], Babbage advocated for the belief of divine agency, stating "we must not measure the credibility or incredibility of an event by the narrow sphere of our own experience, nor forget that there is a Divine energy which overrides what we familiarly call the laws of nature."<ref>Babbage, Charles. (1864) [[s:Passages from the Life of a Philosopher/Appendix#488|''Passages from the Life of a Philosopher'']], Appendix: "Miracles", p. 488</ref> He alluded to the limits of human experience, expressing: "all that we see in a miracle is an effect which is new to our observation, and whose cause is concealed. The cause may be beyond the sphere of our observation, and would be thus beyond the familiar sphere of nature; but this does not make the event a violation of any law of nature. The limits of man's observation lie within very narrow boundaries, and it would be arrogance to suppose that the reach of man's power is to form the limits of the natural world."<ref>Babbage, Charles. (1864) [[s:Passages from the Life of a Philosopher/Appendix#488|''Passages from the Life of a Philosopher'']], Appendix: "Miracles", pp. 487–488</ref>

==Later life==
[[File:Charles Babbage 1860.jpg|thumb|''The Illustrated London News'' (4 November 1871)<ref>{{cite book | last = Hook | first = Diana H. |author2=Jeremy M. Norman|author3=Michael R. Williams | title = Origins of cyberspace: a library on the history of computing, networking, and telecommunications | publisher=Norman Publishing | year = 2002 | pages = 161, 165 | url = https://books.google.com/books?id=fsICrp9shVIC&pg=PA165 | isbn = 978-0-930405-85-4 }}</ref>]]
The British Association was consciously modelled on the Deutsche Naturforscher-Versammlung, founded in 1822.<ref>{{cite book|author1=Andrew Ede|author2=Lesley B. Cormack|title=A History of Science in Society: From the Scientific Revolution to the Present|url=https://books.google.com/books?id=DMhg4sJsVFsC&pg=PA224|year=2012|publisher=University of Toronto Press|isbn=978-1-4426-0452-0|page=224}}</ref> It rejected [[romantic science]] as well as [[metaphysics]], and started to entrench the divisions of science from literature, and professionals from amateurs.<ref>{{cite book|author=Daniel Brown|title=The Poetry of Victorian Scientists: Style, Science and Nonsense|url=https://books.google.com/books?id=8cmgmOyglhsC&pg=PA6|year=2013|publisher=Cambridge University Press|isbn=978-1-107-02337-6|page=6}}</ref> Belonging as he did to the "Wattite" faction in the BAAS, represented in particular by [[James Watt the younger]], Babbage identified closely with industrialists. He wanted to go faster in the same directions, and had little time for the more gentlemanly component of its membership. Indeed, he subscribed to a version of [[conjectural history]] that placed [[industrial society]] as the culmination of human development (and shared this view with Herschel). A clash with [[Roderick Murchison]] led in 1838 to his withdrawal from further involvement.<ref>{{cite book|title=Discovering Water: James Watt, Henry Cavendish, and the Nineteenth Century 'Water Controversy'|url=https://books.google.com/books?id=orL4QRlvBfYC&pg=PA136|year=2004|publisher=Ashgate Publishing, Ltd.|isbn=978-0-7546-3177-4|pages=136–137}}</ref><ref>{{cite book|author=Iwan Rhys Morus|title=Bodies/Machines|url=https://books.google.com/books?id=HCSJaqeyrHIC&pg=PA44|year=2002|publisher=Berg|isbn=978-1-85973-695-1|page=44}}</ref> At the end of the same year he sent in his resignation as Lucasian professor, walking away also from the Cambridge struggle with Whewell. His interests became more focused, on computation and [[meteorology]], and on international contacts.{{sfn|Knox|2003|p=[https://books.google.com/books?id=QGX_rAeia4kC&pg=PA287 287]}}

===Metrology programme===
A project announced by Babbage was to tabulate all [[physical constant]]s (referred to as "constants of nature", a phrase in itself a neologism), and then to compile an encyclopaedic work of numerical information. He was a pioneer in the field of "absolute measurement".<ref>{{cite book|author=Mario Biagioli|title=The Science studies reader|url=https://books.google.com/books?id=i4iS5_AtZUkC&pg=PA459|year=1999|publisher=Routledge, Chapman & Hall, Incorporated|isbn=978-0-415-91868-8|pages=459–460}}</ref> His ideas followed on from those of [[Johann Christian Poggendorff]], and were mentioned to [[David Brewster|Brewster]] in 1832. There were to be 19 categories of constants, and [[Ian Hacking]] sees these as reflecting in part Babbage's "eccentric enthusiasms".<ref name="Hacking1990">{{cite book|author=Ian Hacking|title=The Taming of Chance|url=https://archive.org/details/isbn_9780521388849|url-access=registration|access-date=1 May 2013|date=31 August 1990|publisher=Cambridge University Press|isbn=978-0-521-38884-9|pages=[https://archive.org/details/isbn_9780521388849/page/55 55]–60}}</ref> Babbage's paper ''On Tables of the Constants of Nature and Art'' was reprinted by the [[Smithsonian Institution]] in 1856, with an added note that the physical tables of [[Arnold Henry Guyot]] "will form a part of the important work proposed in this article".<ref>{{cite book|title=Report of the Board of Regents|url=https://books.google.com/books?id=bc4rAQAAIAAJ&pg=PA289|year=1857|publisher=The Institution|pages=289–302}}</ref>

Exact measurement was also key to the development of machine tools. Here again Babbage is considered a pioneer, with [[Henry Maudslay]], [[William Sellers]], and [[Joseph Whitworth]].<ref>{{cite book|author=David F Noble|title=America by Design: Science, Technology, and the Rise of Corporate Capitalism David F. Noble|url=https://books.google.com/books?id=LBYlAV6VmpwC&pg=PA71|year=1979|publisher=Oxford University Press|isbn=978-0-19-502618-4|page=71}}</ref>

===Engineer and inventor===
Through the Royal Society Babbage acquired the friendship of the engineer [[Marc Brunel]]. It was through Brunel that Babbage knew of [[Joseph Clement]], and so came to encounter the artisans whom he observed in his work on manufactures.{{sfn|Collier|MacLachlan|2000|p=[https://books.google.com/books?id=-vzMEwf-bHEC&pg=PA28 28–29]}} Babbage provided an introduction for [[Isambard Kingdom Brunel]] in 1830, for a contact with the proposed [[Bristol & Birmingham Railway]].<ref>{{cite book |author=L. T. C. Rolt |title=Isambard Kingdom Brunel |year=1982 |publisher=Penguin Books |isbn=978-0-14-021195-5|page=74|author-link=L. T. C. Rolt }}</ref> He carried out studies, around 1838, to show the superiority of the [[broad gauge]] for railways, used by Brunel's [[Great Western Railway]].<ref name = "passages">{{harvnb|Babbage|1864|pp=317–318}}</ref><ref>{{Cite journal |pages=1149–1152 <!-- |at=p. 1151 -->|jstor = 2727614|title = Charles Babbage (1791 + 200 = 1991)|journal=Journal of Economic Literature|volume=29|issue=3|last1 = Stigler|first1 = George J.|year=1991}}</ref>

In 1838, Babbage invented the [[cowcatcher|pilot]] (also called a cow-catcher), the metal frame attached to the front of locomotives that clears the tracks of obstacles;<ref name="lee95">{{cite book|last=Lee|first=John A. N.|title=International biographical dictionary of computer pioneers|year=1995|publisher=Taylor & Francis US|page=60}}</ref> he also constructed a [[dynamometer car]].<ref name = "passages"/> His eldest son, [[Benjamin Herschel Babbage]], worked as an engineer for Brunel on the railways before emigrating to Australia in the 1850s.<ref name="BBH">{{cite web | url = http://www.asap.unimelb.edu.au/bsparcs/biogs/P000074b.htm | title = Babbage, Benjamin Herschel | work=Bright Sparcs Biographical entry | access-date =15 May 2008 }}</ref>

Babbage also invented an [[ophthalmoscope]], which he gave to [[Thomas Wharton Jones]] for testing. Jones, however, ignored it. The device only came into use after being independently invented by [[Hermann von Helmholtz]].<ref>{{cite ODNB|id=37617|title=Jones, Thomas Wharton|first=W. F.|last=Bynum}}</ref><ref>{{cite web | url = http://www.discoveriesinmedicine.com/Ni-Ra/Ophthalmoscope.html | title = Medical Discoveries, Ophthalmoscope | publisher=Discoveriesinmedicine.com | access-date =29 January 2009}}</ref>

===Cryptography===
Babbage achieved notable results in [[cryptography]], though this was still not known a century after his death. [[Letter frequency]] was category 18 of Babbage's tabulation project. [[Joseph Henry]] later defended interest in it, in the absence of the facts, as relevant to the management of [[movable type]].<ref name="Hacking1990"/>

As early as 1845, Babbage had solved a cipher that had been posed as a challenge by his nephew Henry Hollier, and in the process, he made a discovery about ciphers that were based on Vigenère tables.  Specifically, he realised that enciphering plain text with a keyword rendered the cipher text subject to [[modular arithmetic]].<ref name="Franksen, 1985" /> During the [[Crimean War]] of the 1850s, Babbage broke Vigenère's [[autokey cipher]] as well as the much weaker cipher that is called [[Vigenère cipher]] today. He intended to publish a book ''The Philosophy of Deciphering'', but never did.<ref>{{Cite journal |last=Franksen |first=Ole Immanuel |date=1993-10-01 |title=Babbage and cryptography. Or, the mystery of Admiral Beaufort's cipher |url=https://dx.doi.org/10.1016/0378-4754%2893%2990063-Z |journal=Mathematics and Computers in Simulation |volume=35 |issue=4 |pages=327–367 |doi=10.1016/0378-4754(93)90063-Z |issn=0378-4754|url-access=subscription }}</ref><ref>{{cite book|title=Introduction to Cryptography: With Mathematical Foundations in Computer Implementations|url=https://books.google.com/books?id=34cE8KzUwLgC&pg=PA187|year=2011|publisher=CRC Press|isbn=978-1-4398-1763-6|page=187}}</ref> His discovery was kept a military secret, and was not published. Credit for the result was instead given to [[Friedrich Kasiski]], a Prussian infantry officer, who made the same discovery some years later.<ref>{{cite book | author=Kahn, David L. | title = The Codebreakers: The Story of Secret Writing | year = 1996 | publisher=Scribner | location = New York | isbn = 978-0-684-83130-5 }}
</ref> However, in 1854, Babbage published the solution of a Vigenère cipher, which had been published previously in the ''Journal of the Society of Arts''.<ref name="Franksen, 1985" /><ref>See:
*  J. H. B. Thwaites (11 August 1854) [https://books.google.com/books?id=nxw9AQAAIAAJ&pg=PA663 "Secret, or cypher writing,"] ''Journal of the Society of Arts'', '''2''' (90) :  663–664.
*  "C." (Charles Babbage) (1 September 1854), [https://books.google.com/books?id=nxw9AQAAIAAJ&pg=PA707 "Mr. Thwaites's cypher,"] ''Journal of the Society of Arts'', '''2''' (93) :  707–708.
*  {{cite journal|last1=Thwaites|first1=John H. B.|title=Secret or cypher writing|journal=Journal of the Society of Arts|date=15 September 1854|volume=2|issue=95|pages=732–733|url=https://babel.hathitrust.org/cgi/pt?id=gri.ark:/13960/t4gn2h303;view=1up;seq=738}}
*  {{cite journal|last1="C" (Charles Babbage)|title=Mr. Thwaites's cypher|journal=Journal of the Society of Arts|date=6 October 1854|volume=2|issue=98|pages=776–777|url=https://babel.hathitrust.org/cgi/pt?id=gri.ark:/13960/t4gn2h303;view=1up;seq=782}}
*  Charles Babbage, ''Passages from the Life of a Philosopher'' (London, England:  Longman, 1864), [https://archive.org/details/bub_gb_2T0AAAAAQAAJ/page/n509 page 496.]</ref> In 1855, Babbage also published a short letter, "Cypher Writing", in the same journal.<ref>{{Cite journal |jstor = 41334443|title = Journal of the Society for Arts, Vol. 4, no. 159|journal = The Journal of the Society of Arts|volume = 4|issue = 159|pages = 29–44|last1 = Hooper|first1 = George N.|last2 = Babbage|first2 = Charles|last3 = Clarke|first3 = Hyde|last4 = Webster|first4 = Thomas|last5 = Bentham|first5 = M. S.|last6 = Good|first6 = S. A.|year = 1855}}</ref> Nevertheless, his priority was not established until 1985.<ref name="Franksen, 1985">{{Cite journal |jstor = 41374062|title = General Notes|journal = Journal of the Royal Society of Arts|volume = 133|issue = 5352|pages = 880–883|last1 = Franksen|first1 = OLE Immanuel|last2 = Rushton|first2 = RAY|date = November 1985}}</ref><ref>See also:  Ole Immanuel Franksen, ''Mr. Babbage's Secret.  The Tale of a Cypher – and APL'' (Birkerød, Denmark: Strandbergs Forlag, 1984; reprinted by:  Prentice-Hall, Englewood, New Jersey, US, 1985)</ref>

===Public nuisances===
Babbage involved himself in well-publicised but unpopular campaigns against public nuisances. He once counted all the broken panes of glass of a factory, publishing in 1857 a "Table of the Relative Frequency of the Causes of Breakage of Plate Glass Windows": Of 464 broken panes, 14 were caused by "drunken men, women or boys".<ref>{{cite journal | title = Table of the Relative Frequency of Occurrence of the Causes of Breaking of Plate Glass Windows | author=Babbage, Charles | journal=Mechanics Magazine | year = 1857 | volume = 66 | page = 82 }}</ref><ref>{{cite book | author=Babbage, Charles | title = The Works of Charles Babbage | volume = V | year = 1989 | publisher=William Pickering | location = London | page = 137 | editor = Martin Campbell-Kelly | isbn = 978-1-85196-005-7 }}</ref><ref>{{cite book|url=https://archive.org/details/insurancecyclop07walfgoog|page=[https://archive.org/details/insurancecyclop07walfgoog/page/n418 417]|title=The Insurance cyclopaedia |publisher=C. and E. Layton|access-date=22 February 2011|year=1878|last1=Walford |first1=Cornelius }}</ref>

Babbage's distaste for commoners (the Mob) included writing "Observations of Street Nuisances" in 1864, as well as tallying up 165 "nuisances" over a period of 80 days. He especially hated [[busking|street music]], and in particular the music of [[organ grinder]]s, against whom he railed in various venues. The following quotation is typical:

{{blockquote|It is difficult to estimate the misery inflicted upon thousands of persons, and the absolute pecuniary penalty imposed upon multitudes of intellectual workers by the loss of their time, destroyed by organ-grinders and other similar nuisances.<ref>{{cite book |author1=Campbell-Kelly, Martin |author2=Babbage, Charles | title = Passages from the Life of a Philosopher | publisher=Pickering & Chatto Publishers | year = 1994 | chapter = Ch 26 | page = 342 | isbn = 978-1-85196-040-8 }}</ref>}}

Babbage was not alone in his campaign. A convert to the cause was the MP [[Michael Thomas Bass]].<ref>{{cite book|author1=Karen Chase|author2=Michael Levenson|title=The Spectacle of Intimacy: A Public Life for the Victorian Family|url=https://books.google.com/books?id=GNitcKFsBBEC&pg=RA1-PA151|access-date=22 April 2013|date=15 August 2009|publisher=Princeton University Press|isbn=978-1-4008-3112-8|page=151}}</ref>

In the 1860s, Babbage also took up the anti-[[Hoop rolling#British Empire|hoop-rolling]] campaign. He blamed hoop-rolling boys for driving their iron hoops under horses' legs, with the result that the rider is thrown and very often the horse breaks a leg.<ref>{{harvnb|Babbage|1864|p=360}}</ref> Babbage achieved a certain notoriety in this matter, being denounced in debate in Commons in 1864 for "commencing a crusade against the popular game of [[tip-cat]] and the trundling of hoops."<ref>Hansard's parliamentary debates. Third Series Commencing With the Accession of William IV. 27° & 28° Victoria, 1864. Vol. CLXXVI. Comprising the Period From the Twenty-First Day of June 1864, To the Twenty-Ninth Day of July 1864. Parliament, Thomas Curson Hansard "Street Music (Metropolis) Bill "; V4, p471 [https://books.google.com/books?id=dugT3_K-1ZIC&q=trundling&pg=PA469]</ref>

==Computing pioneer==
[[File:BabbageDifferenceEngine.jpg|thumb|Part of Charles Babbage's [[Difference Engine]] (#1), assembled after his death by his son, Henry Prevost Babbage (1824–1918), using parts found in Charles' laboratory. [[Whipple Museum of the History of Science]], Cambridge, England.]]

Babbage's machines were among the first mechanical computers. That they were not actually completed was largely because of funding problems and clashes of personality, most notably with George Biddell Airy, the Astronomer Royal.<ref name="Swade">{{cite book |last=Swade |first=Doron |author-link=Doron Swade |title=The Cogwheel Brain |publisher=Little, Brown and Company |location=London |isbn=978-0-316-64847-9 |year=2000 |page=186 }}</ref>

Babbage directed the building of some steam-powered machines that achieved some modest success, suggesting that calculations could be mechanised. For more than ten years he received government funding for his project, which amounted to £17,000, but eventually the Treasury lost confidence in him.<ref name="Gleick">{{cite book |author=Gleick, J. |title=The Information: A History, a Theory, a Flood |publisher=Fourth Estate |location=London |year=2011 |page=104 |title-link=The Information: A History, a Theory, a Flood }}</ref>

While Babbage's machines were mechanical and unwieldy, their basic architecture was similar to that of a modern computer. The data and program memory were separated, operation was instruction-based, the control unit could make conditional jumps, and the machine had a separate [[Input/output|I/O]] unit.<ref name="Gleick" />

===Background on mathematical tables===
In Babbage's time, printed [[mathematical table]]s were calculated by [[human computer]]s; in other words, by hand. They were central to navigation, science and engineering, as well as mathematics. Mistakes were known to occur in transcription as well as calculation.<ref name="Th35"/>

At Cambridge, Babbage saw the fallibility of this process, and the opportunity of adding mechanisation into its management. His own account of his path towards mechanical computation references a particular occasion: {{blockquote|In 1812 he was sitting in his rooms in the Analytical Society looking at a table of logarithms, which he knew to be full of mistakes, when the idea occurred to him of computing all tabular functions by machinery. The French government had produced several tables by a new method. Three or four of their mathematicians decided how to compute the tables, half a dozen more broke down the operations into simple stages, and the work itself, which was restricted to addition and subtraction, was done by eighty computers who knew only these two arithmetical processes. Here, for the first time, mass production was applied to arithmetic, and Babbage was seized by the idea that the labours of the unskilled computers [people] could be taken over completely by machinery which would be quicker and more reliable.<ref>[[B. V. Bowden]], ''Faster than Thought'', Pitman (1953), p. 8.</ref>}}

There was another period, seven years later, when his interest was aroused by the issues around computation of mathematical tables. The French official initiative by [[Gaspard de Prony]], and its problems of implementation, were familiar to him. After the [[Napoleonic Wars]] came to a close, scientific contacts were renewed on the level of personal contact: in 1819 [[Charles Blagden]] was in Paris looking into the printing of the stalled de Prony project, and lobbying for the support of the Royal Society. In works of the 1820s and 1830s, Babbage referred in detail to de Prony's project.<ref>{{cite book|author=Martin Campbell-Kelly|title=The History of Mathematical Tables: From Sumer to Spreadsheets|url=https://books.google.com/books?id=O170gWPZ7M8C&pg=PA110|year=2003|publisher=Oxford University Press|isbn=978-0-19-850841-0|page=110}}</ref><ref>{{cite book|author=Charles Coulston Gillispie|title=Science and Polity in France: The End of the Old Regime|url=https://books.google.com/books?id=EPgIpRIvaSAC&pg=PA485|year=2009|publisher=Princeton University Press|isbn=978-1-4008-2461-8|page=485}}</ref>

===Difference engine===
{{main|Difference engine}}
[[File:Babbage Difference Engine.jpg|thumb|The Science Museum's Difference Engine No. 2, built from Babbage's design]]
[[File:Babbage difference engine drawing.gif|thumb|Portion of Babbage's difference engine]]

Babbage began in 1822 with what he called the difference engine, made to compute values of [[polynomial function]]s. It was created to calculate a series of values automatically. By using the method of finite differences, it was possible to avoid the need for multiplication and division.<ref>{{Cite web|url=https://www.britannica.com/technology/Difference-Engine|title=Difference Engine {{!}} calculating machine|website=Encyclopædia Britannica|access-date=13 May 2019}}</ref>

For a prototype difference engine, Babbage brought in [[Joseph Clement]] to implement the design, in 1823. Clement worked to high standards, but his [[machine tool]]s were particularly elaborate. Under the standard terms of business of the time, he could charge for their construction, and would also own them. He and Babbage fell out over costs around 1831.<ref>{{cite ODNB|id=37291|title=Clement, Joseph|first=Anita|last=McConnell}}</ref>

Some parts of the prototype survive in the [[Museum of the History of Science, Oxford]].<ref>{{Cite journal | first = Denis | last = Roegel | title = Prototype Fragments from Babbage's First Difference Engine | journal=IEEE Annals of the History of Computing | volume = 31 | pages = 70–75 | date = April–June 2009 | issue = 2 | doi = 10.1109/MAHC.2009.31 | bibcode = 2009IAHC...31b..70R | s2cid = 45564453 }}</ref> This prototype evolved into the "first difference engine". It remained unfinished and the finished portion is located at the Science Museum in London. This first difference engine would have been composed of around 25,000 parts, weighed {{Convert|15|short ton|kg|spell=in|lk=in|sigfig=3}}, and would have been {{Convert|8|ft|m|1|abbr=on}} tall. Although Babbage received ample funding for the project, it was never completed. He later (1847–1849) produced detailed drawings for an improved version,"Difference Engine No. 2", but did not receive funding from the British government. His design was finally constructed in 1989–1991, using his plans and 19th-century manufacturing tolerances. It performed its first calculation at the Science Museum, London, returning results to 31 digits.<ref>{{Cite web |title=Babbage's Difference Engine No 2, 2002. {{!}} Science Museum Group Collection |url=https://collection.sciencemuseumgroup.org.uk/objects/co62748/babbages-difference-engine-no-2-2002 |access-date=2025-03-25 |website=collection.sciencemuseumgroup.org.uk |language=en}}</ref>

Nine years later, in 2000, the Science Museum completed the [[Printer (computing)|printer]] Babbage had designed for the difference engine.<ref>{{cite news|url=https://news.bbc.co.uk/1/hi/sci/tech/710950.stm |title=SCI/TECH {{pipe}} Babbage printer finally runs |work=BBC News |date=13 April 2000 |access-date=27 April 2012}}</ref> His printers were the first computer printers invented.<ref name=":2" />

====Completed models====
The Science Museum has constructed two Difference Engines according to Babbage's plans for the Difference Engine No 2. One is owned by the museum. The other, owned by the technology multimillionaire [[Nathan Myhrvold]], went on exhibition at the [[Computer History Museum]]<ref>{{cite web | url = http://www.computerhistory.org/babbage/ | title = Overview&nbsp;– The Babbage Engine | publisher=Computer History Museum | access-date =29 January 2009 }}</ref> in [[Mountain View, California]] on 10 May 2008.<ref>{{cite news | last = Shiels | first = Maggie | title = Victorian 'supercomputer' is reborn | url = https://news.bbc.co.uk/2/hi/technology/7391593.stm | access-date =11 May 2008 |work=BBC News  | date = 10 May 2008 }}</ref> The two models that have been constructed are not replicas.

===Analytical Engine===
{{main|Analytical Engine}}
[[File:Babbages Analytical Engine, 1834-1871. (9660574685).jpg|thumb|Portion of the mill with a printing mechanism of the Analytical Engine, built by Charles Babbage, as displayed at the Science Museum (London)]]
After the attempt at making the first difference engine fell through, Babbage worked to design a more complex machine called the Analytical Engine. He hired C. G. Jarvis, who had previously worked for Clement as a draughtsman.{{sfn|Collier|MacLachlan|2000|p=[https://books.google.com/books?id=-vzMEwf-bHEC&pg=PA65 65]}} The Analytical Engine marks the transition from mechanised arithmetic to fully-fledged general purpose computation. It is largely on it that Babbage's standing as computer pioneer rests.<ref>{{cite web|title=The Baggage Engine|url=http://www.computerhistory.org/babbage/|publisher=Computer History Museum|access-date=6 March 2013}}</ref>

The major innovation was that the Analytical Engine was to be programmed using [[punched card]]s: the Engine was intended to use loops of [[Jacquard machine|Jacquard's]] punched cards to control a mechanical calculator, which could use as input the results of preceding computations.<ref name="Ceruzzi, Paul">{{cite book|last=Ceruzzi|first=Paul|title=Computing: A Concise History|year=2012|publisher=Smithsonian Institution|location=United States|isbn=978-0-262-51767-6|pages=7–8}}</ref><ref name="Gross">{{cite journal|last1=Gross|first1=Benjamin|title=The French connection|journal=Distillations Magazine|date=Fall 2015|volume=1|issue=3|pages=10–13|url=https://www.sciencehistory.org/distillations/magazine/the-french-connection|access-date=22 March 2018}}</ref> The machine was also intended to employ several features subsequently used in modern computers, including sequential control, branching and looping. It would have been the first mechanical device to be, in principle, [[Turing completeness|Turing-complete]]. Charles Babbage wrote a series of programs for the Analytical Engine from 1837 to 1840.<ref name="IEEE2021">{{Cite journal | last1 = Rojas | first1 = R. | title = The Computer Programs of Charles Babbage | journal = IEEE Annals of the History of Computing | volume = 43 | issue = 1 | pages = 6–18 | year = 2024 | doi = 10.1109/MAHC.2020.3045717}}</ref> The first program was finished in 1837.<ref name="IEEE2024">{{Cite journal | last1 = Rojas | first1 = R. | title = The First Computer Program | journal = Communications of the ACM | volume = 67 | issue = 6 | pages = 78–81 | year = 2024 | doi = 10.1145/3624731| doi-access = free }}</ref> The Engine was not a single physical machine, but rather a succession of designs that Babbage tinkered with until his death in 1871.<ref>{{Cite journal |last=Ashworth |first=William J. |date=March 2002 |title=Bruce Collier; James MacLachlan. ''Charles Babbage and the Engines of Perfection''. 123 pp., illus., figs., tables, apps., bibl., index. New York/Oxford: Oxford University Press, 2000. $11.95 (paper). |url=https://doi.org/10.1086/343300 |journal=Isis |volume=93 |issue=1 |pages=127–128 |doi=10.1086/343300 |issn=0021-1753|url-access=subscription }}</ref>
[[File:Opening George III museum.jpg|thumb|Part of the Analytical Engine on display, in 1843, left of centre in this engraving of the [[King George III Museum]] in [[King's College, London]]]]

===Ada Lovelace and Italian followers===
[[Ada Lovelace]], who corresponded with Babbage during his development of the Analytical Engine, is credited with developing an algorithm that would enable the Engine to calculate a sequence of [[Bernoulli number]]s.<ref name="Legacy">Robin Hammerman, Andrew L. Russell (2016). ''Ada's Legacy: Cultures of Computing from the Victorian to the Digital Age''. Association for Computing Machinery and Morgan & Claypool Publishers. {{ISBN|978-1-970001-51-8}}</ref> Despite documentary evidence in Lovelace's own handwriting,<ref name="Legacy" /> some scholars dispute to what extent the ideas were Lovelace's own.<ref>{{cite book |last=Bromley |first=Allan G. |author-link=Allan G. Bromley |contribution=Difference and Analytical Engines |title=Computing Before Computers |editor-first=William |editor-last=Aspray |publisher=Iowa State University Press |location=Ames |pages=59–98 |chapter-url=http://ed-thelen.org/comp-hist/CBC-Ch-02.pdf |archive-url=https://ghostarchive.org/archive/20221010/http://ed-thelen.org/comp-hist/CBC-Ch-02.pdf |archive-date=2022-10-10 |url-status=live |date=1990 |isbn=978-0-8138-0047-9}} p. 89.</ref><ref>{{cite journal |last=Stein |first=Dorothy K. |year=1984 |title=Lady Lovelace's Notes: Technical Text and Cultural Context |journal=Victorian Studies |pages=33–67 |volume=28 |issue=1}} p. 34.</ref><ref>{{cite thesis |last=Collier |first=Bruce |title=The Little Engines That Could've: The Calculating Machines of Charles Babbage |type=PhD |publisher=Harvard University |year=1970 |url=http://robroy.dyndns.info/collier |access-date=18 December 2015}} Chapter 3.</ref> For this achievement, she is often described as the first [[programmer|computer programmer]];<ref>{{cite journal |vauthors=Fuegi J, Francis J | title = Lovelace & Babbage and the creation of the 1843 'notes' | journal=Annals of the History of Computing | volume = 25 | issue = 4 | pages = 16–26 | date = October–December 2003 | doi = 10.1109/MAHC.2003.1253887 | bibcode = 2003IAHC...25d..16F }} See pages 19, 25</ref>{{Failed verification|date=March 2019|reason="computer programmer" or similar not found in article}} though no programming language had yet been invented.<ref name="Legacy" /><ref>{{Cite encyclopedia|url=https://www.britannica.com/biography/Charles-Babbage|title=Charles Babbage {{!}} Biography & Facts|encyclopedia=Encyclopædia Britannica|access-date=21 December 2017}}</ref>

Lovelace also translated and wrote literature supporting the project.  Describing the engine's programming by punch cards, she wrote: "We may say most aptly that the Analytical Engine weaves algebraical patterns just as the [[Jacquard loom]] weaves flowers and leaves."<ref name="Gross" />

Babbage visited [[Turin]] in 1840 at the invitation of [[Giovanni Plana]], who had developed in 1831 an analog computing machine that served as a [[Cappella dei Mercanti, Turin|perpetual calendar]]. Here in 1840 in Turin, Babbage gave the only public explanation and lectures about the Analytical Engine.<ref>{{Cite web|last=Wired|title=Charles Babbage Left a Computer Program in Turin in 1840. Here It Is.|url=https://cacm.acm.org/news/217292-charles-babbage-left-a-computer-program-in-turin-in-1840-here-it-is/fulltext|access-date=24 September 2021|website=cacm.acm.org|language=en}}</ref><ref>{{Cite magazine|last=Sterling|first=Bruce|title=Charles Babbage left a computer program in Turin in 1840. Here it is.|language=en-US|magazine=Wired|url=https://www.wired.com/beyond-the-beyond/2017/05/charles-babbage-left-computer-program-turin-1840/|access-date=24 September 2021|issn=1059-1028}}</ref> In 1842 [[Charles Wheatstone]] approached Lovelace to translate a paper of [[Luigi Menabrea]], who had taken notes of Babbage's Turin talks; and Babbage asked her to add something of her own. Fortunato Prandi who acted as interpreter in Turin was an Italian exile and follower of [[Giuseppe Mazzini]].<ref>{{cite book |author=Benjamin Woolley |title=The Bride of Science |year=1999 |publisher=Macmillan |isbn=978-0-333-72436-1 |pages=258–260, 338}}</ref>

===Swedish followers===
[[Per Georg Scheutz]] wrote about the difference engine in 1830, and experimented in automated computation. After 1834 and Lardner's ''Edinburgh Review'' article he set up a project of his own, doubting whether Babbage's initial plan could be carried out. This he pushed through with his son, Edvard Scheutz.<ref name="Lingren1990">{{cite book|author=Michael Lingren|title=Glory and Failure: The Difference Engines of Johann Müller, Charles Babbage and Georg and Edvard Scheutz|url=https://books.google.com/books?id=plgMl2yfVkwC&pg=PA98|year=1990|publisher=MIT Press|isbn=978-0-262-12146-0|pages=98–112}}</ref> Another Swedish engine was that of [[Martin Wiberg]] (1860).<ref>{{cite book|author=I. Grattan-Guinness|title=Companion encyclopedia of the history and philosophy of the mathematical sciences|url=https://books.google.com/books?id=2hDvzITtfdAC&pg=PA698|year=2003|publisher=JHU Press|isbn=978-0-8018-7396-6|page=698}}</ref>

===Legacy===
In 2011, researchers in Britain proposed a multimillion-pound project, "Plan 28",<ref>{{Cite web|url=http://blog.plan28.org/|title=Plan 28 Blog|website=Blog.plan28.org|access-date=10 June 2022}}</ref> to construct Babbage's Analytical Engine.  Since Babbage's plans were continually being refined and were never completed, they intended to engage the public in the project and [[crowdsourcing|crowd-source]] the analysis of what should be built.<ref>{{cite news | url = https://www.nytimes.com/2011/11/08/science/computer-experts-building-1830s-babbage-analytical-engine.html | title = It Started Digital Wheels Turning | newspaper=The New York Times | date = 7 November 2011 | access-date =10 November 2011 | last1 = Markoff | first1 = John }}</ref> It would have the equivalent of 675 bytes of memory, and run at a clock speed of about 7&nbsp;Hz.  They hoped to complete it by the 150th anniversary of Babbage's death, in 2021.<ref>{{cite news
 | url=https://www.bbc.co.uk/news/technology-15001514
 | title=Babbage Analytical Engine designs to be digitised
 | work=BBC News
 | date=21 September 2011
| access-date=19 March 2012 }}
</ref>

Advances in [[MEMS]] and [[nanotechnology]] have led to recent high-tech experiments in mechanical computation. The benefits suggested include operation in high radiation or high temperature environments.<ref>{{cite web|url=http://findarticles.com/p/articles/mi_m0WVI/is_1999_Oct_11/ai_56912203/print |archive-url=https://web.archive.org/web/20071013201309/http://findarticles.com/p/articles/mi_m0WVI/is_1999_Oct_11/ai_56912203/print |url-status=dead |archive-date=13 October 2007 |title=Electronics Times: Micro-machines are fit for space |via=Find Articles |date=11 October 1999 |access-date=29 January 2009 }}</ref> These modern versions of mechanical computation were highlighted in ''[[The Economist]]'' in its special "end of the millennium" black cover issue in an article entitled "Babbage's Last Laugh".<ref>{{cite news |title=Babbage's Last Laugh |newspaper=The Economist |date=9 September 1999 |url=https://www.economist.com/science-and-technology/1999/09/09/babbages-last-laugh}}</ref>

Due to his association with the town Babbage was chosen in 2007 to appear on the 5 [[Totnes pound]] note.<ref>{{cite web|url=http://www.westernmorningnews.co.uk/Meet-new-faces-local-currency/story-21152600-detail/story.html|title=Latest Devon News |website=Devon Live|access-date=5 December 2015|archive-url=https://web.archive.org/web/20140810153519/http://www.westernmorningnews.co.uk/Meet-new-faces-local-currency/story-21152600-detail/story.html|archive-date=10 August 2014|url-status=dead}}</ref> An image of Babbage features in the [[Culture of the United Kingdom|British cultural icons]] section of the newly designed [[British passport]] in 2015.<ref>{{cite news|title=Introducing the new UK passport design|url=https://www.gov.uk/government/uploads/system/.../HMPO_magazine.pdf|publisher=Government of the United Kingdom|date=7 November 2016}}</ref>

==Family==
[[File:Charles Babbage grave Kensal Green 2014.jpg|thumb|alt=A granite, horizontal, geometrically elaborate gravestone surrounded by other headstones|Babbage's grave at [[Kensal Green Cemetery]], London, photographed in 2014]]

On 25 July 1814, Babbage married Georgiana Whitmore, sister of British parliamentarian [[William Wolryche-Whitmore]], at St. Michael's Church in [[Teignmouth]], Devon.<ref name="wilkes" /> The couple lived at [[Dudmaston Hall]],<ref>{{cite web | url = http://www.visitbritain.co.uk/Attraction/Bridgnorth/Historic-House-or-Palace/157092/Dudmaston-Hall.htm | title = Attraction information for Dudmaston Hall | publisher=VisitBritain | access-date =29 January 2009 | date = 8 October 2015 }}</ref> Shropshire (where Babbage engineered the central heating system), before moving to 5 Devonshire Street, London in 1815.<ref name="Dubbey">{{cite book|last1=Dubbey|first1=John Michael|title=The Mathematical Work of Charles Babbage|date=12 February 2004|publisher=Cambridge University Press|isbn=978-0-521-52476-6|page=6}}</ref>

Charles and Georgiana had eight children,<ref>{{cite web|url=http://www.bavidge.co.uk/Babbage%20Family%20Tree%202005,%20InternetTree/wc03/wc03_074.htm |title=Babbage Family Tree 2005 |author=Valerie Bavidge-Richardson |access-date=9 February 2013 |archive-url=https://web.archive.org/web/20071013194355/http://bavidge.co.uk/Babbage%20Family%20Tree%202005%2C%20InternetTree/wc03/wc03_074.htm |archive-date=13 October 2007 |url-status=dead }} <br />Also see {{cite web|url=http://clanbarker.com/getperson.php?personID=I2894&tree=Br |title=Charles Babbage entry |publisher=ClanBarker |access-date=9 February 2013 }}</ref> but only four – [[Benjamin Herschel Babbage|Benjamin Herschel]], Georgiana Whitmore, [[Dugald Bromhead Babbage|Dugald Bromhead]] and Henry Prevost – survived childhood. Charles' wife Georgiana died in [[Worcester, England|Worcester]] on 1 September 1827, the same year as his father, their second son (also named Charles) and their newborn son Alexander.
* Benjamin Herschel Babbage (1815–1878)
* Charles Whitmore Babbage (1817–1827)
* Georgiana Whitmore Babbage (1818 – 26 September 1834)<ref>{{cite magazine |author= |title=Obituary |url=https://anno.onb.ac.at/cgi-content/anno-plus?aid=gen&datum=1834&page=1296 |magazine=The Gentleman's Magazine |location= |publisher= |date=1834 |access-date=19 October 2021}}</ref>
* Edward Stewart Babbage (1819–1821)
* Francis Moore Babbage (1821–????)
* Dugald Bromhead (Bromheald?) Babbage (1823–1901)
* (Maj-Gen) [[Henry Prevost Babbage]] (1824–1918)
* Alexander Forbes Babbage (1827–1827)

His youngest surviving son, Henry Prevost Babbage (1824–1918), went on to create six small demonstration pieces for Difference Engine No. 1 based on his father's designs,<ref>{{cite web | url = http://www.computerhistory.org/babbage/henrybabbage/ | title = Henry Prevost Babbage&nbsp;– The Babbage Engine | publisher=Computer History Museum | access-date =29 January 2009 }}</ref> one of which was sent to [[Harvard University]] where it was later discovered by [[Howard H. Aiken]], pioneer of the [[Harvard Mark I]]. Henry Prevost's 1910 Analytical Engine Mill, previously on display at Dudmaston Hall, is now on display at the Science Museum.<ref>{{cite web | url = http://collection.sciencemuseum.org.uk/objects/co62246 | title = Henry Babbage's Analytical Engine Mill, 1910 | publisher=Science Museum | date = 16 January 2007 | access-date =29 January 2009 }}</ref>

==Death==
[[File:Babbages Brain.jpg|thumb|Charles Babbage's brain is on display at [[The Science Museum (London)|The Science Museum]].]]
Babbage lived and worked for over 40 years at 1 Dorset Street, Marylebone, where he died, at the age of 79, on 18 October 1871; he was buried in London's [[Kensal Green Cemetery]]. According to Horsley, Babbage died "of renal inadequacy, secondary to [[cystitis]]."<ref>{{cite journal | author-link=Victor Horsley | last =Horsley | first= Victor | title = Description of the Brain of Mr. Charles Babbage, F.R.S | journal=[[Philosophical Transactions of the Royal Society B]] | year = 1909 | volume = 200 | pages = 117–132 | doi = 10.1098/rstb.1909.0003 | issue=262–273 | bibcode =1909RSPTB.200..117H | doi-access = free }} Subscription required.</ref> He had declined both a knighthood{{Failed verification|reason=Only baronetcy but no knighthood is mentioned in the source.|date=October 2021}} and baronetcy. He also argued against [[hereditary peer]]ages, favouring [[life peer]]ages instead.<ref>{{Cite book | url=https://books.google.com/books?id=0bwb5bevubwC&pg=PA50| title=Remarkable Engineers: From Riquet to Shannon | author=Ioan James | year=2010 | publisher=Cambridge University Press | page=50| isbn=978-1-139-48625-5 }}</ref>

=== Autopsy report ===
In 1983, the autopsy report for Charles Babbage was discovered and later published by his great-great-grandson.<ref>{{cite journal | author=Babbage, Neville | title = Autopsy Report on the Body of Charles Babbage ( "the father of the computer ") | journal=Medical Journal of Australia |date=June 1991 | volume = 154 | issue = 11 | pages = 758–759  | pmid = 2046574 | doi = 10.5694/j.1326-5377.1991.tb121318.x | s2cid = 37539400 }}</ref><ref>{{cite journal | author=Williams, Michael R. | title = The "Last Word " on Charles Babbage | doi = 10.1109/85.728225 | journal=IEEE Annals of the History of Computing | year = 1998 | volume = 20 | pages = 10–14 | issue=4}}{{subscription required}}</ref> A copy of the original is also available.<ref>{{cite web | url = http://www.scienceandsociety.co.uk/results.asp?X9=BABBAGE,%20CHARLES | title = Postmortem report by John Gregory Smith, F.R.C.S. (anatomist) | publisher=Science and society.co.UK | access-date =29 January 2009 }}</ref> Half of Babbage's brain is preserved at [[Hunterian Museum at the Royal College of Surgeons|the Hunterian Museum in the Royal College of Surgeons]] in London.<ref>{{cite web | url = http://www.danyey.co.uk/london.php | title = Babbage's brain | publisher=DanYEY.co.uk | access-date =29 January 2009 }}</ref> The other half of Babbage's brain is on display in the Science Museum, London.<ref>{{cite web|url=http://www.sciencemuseum.org.uk/visitmuseum/galleries/computing.aspx |title=Visit the museum, Galleries, Computing, Overview |publisher=Science Museum |access-date=25 October 2010 |url-status=dead |archive-url=https://web.archive.org/web/20100920225632/http://www.sciencemuseum.org.uk/visitmuseum/galleries/computing.aspx |archive-date=20 September 2010 }}</ref>

==Memorials==
[[File:Charles Babbage (5108336102).jpg|thumb|[[Green plaque]] in London]]

There is a black plaque commemorating the 40 years Babbage spent at 1 Dorset Street, London.<ref>{{openplaque|3061}}</ref> Locations, institutions and other things named after Babbage include:

* The [[Moon]] crater, [[Babbage (crater)|Babbage]]<ref>{{cite web|url=https://planetarynames.wr.usgs.gov/Feature/533 |website=Gazetteer of Planetary Nomenclature |title=Planetary Names: Babbage |date=18 October 2010 |access-date=7 July 2023}}</ref>
* The [[Charles Babbage Institute]], an information technology archive and research center at the [[University of Minnesota]]<ref>{{cite web|url=https://cse.umn.edu/cbi/about |website=cse.umn.edu |publisher=University of Minnesota, College of Science & Engineering |title=About CBI |access-date=7 July 2023}}</ref>
* Babbage River Falls, Yukon, Canada<ref>{{cite web|access-date=7 July 2023|title=Babbage River Falls, Yukon, Canada|url=https://www.worldwaterfalldatabase.com/waterfall/Babbage-River-Falls-19189|website=World Waterfall Database}}</ref>
* The [[Charles Babbage Premium]], an annual computing award<ref>{{cite web|url=http://www.ipdps.org/ipdps2019/babbage-flyer.pdf |title=IEEE-CS, Charles Babbage Award |website=[[IPDPS]] |access-date=7 July 2023}}</ref>
* [[British Rail]] named a [[British Rail Class 60|locomotive]] after Charles Babbage in the 1990s.<ref>{{cite web|url=https://www.modelraildatabase.com/locomotives/details/2373/ |title=Graham Farish 371-354 |website=modelraildatabase.com |access-date=7 July 2023}}</ref>
* Babbage Island, Western Australia<ref>{{cite web|url=https://www.city-facts.com/babbage-island/population |title=Babbage Island, WA 6701, Australia |website=city-facts.com |access-date=7 July 2023}}</ref>
* The Babbage Building at the [[University of Plymouth]], where the university's school of computing is based<ref>{{cite web|url=https://www.plymouth.ac.uk/facilities/babbage-building |title=Babbage Building: where engineering meets design |website=plymouth.ac.uk |access-date=7 July 2023}}</ref>
* The [[Babbage (programming language)|Babbage programming language]] for [[GEC 4000 series]] [[minicomputer]]s<ref>{{Cite book |title=Dictionary of computing |last=Illingworth |first=Valarie |publisher=Oxford University Press |year=1986 |isbn=978-0-19-853913-1 |edition=2nd |chapter=B.001 Babbage}}</ref>
* "Babbage", ''[[The Economist]]''{{'}}s Science and Technology blog<ref>{{cite news|url=https://www.economist.com/babbage |title=The Economist, Babbage blog |newspaper=The Economist |access-date=7 June 2014}}</ref>
* The former chain retail computer and video-games store "Babbage's" (now [[GameStop]]) was named after him.<ref>{{cite news|last1=Fisher|first1=Dan|title=No. 87 Babbage's Feels Growing Pains|work=Dallas Times Herald|date=6 May 1990}}</ref>

==In fiction and film==
Babbage frequently appears in [[steampunk]] works; he has been called an iconic figure of the genre.<ref>{{cite book |author1=Justin Edwards |author2=Agnieszka Soltysik Monnet |title=The Gothic in Contemporary Literature and Popular Culture: Pop Goth |url=https://books.google.com/books?id=lL0robqbiUMC&pg=PA157 |access-date=18 April 2013 |year=2012 |publisher=Routledge |isbn=978-0-415-80676-3 |page=157}}</ref> Other works in which Babbage appears include:

* The 2008 short film ''Babbage'',<ref>{{cite web| url=http://film-directory.britishcouncil.org/babbage | title=Film Detail – Babbage | work=British Films Directory | publisher=[[British Council]] | date=2010 | access-date=9 August 2021 }}</ref> screened at the [[2008 Cannes Film Festival]], a 2009 finalist with [[Haydenfilms]], and shown at the 2009 [[HollyShorts Film Festival]] and other international film festivals.<ref>{{cite web| url=https://www.youtube.com/watch?v=9QSkDzdQAms | archive-url=https://ghostarchive.org/varchive/youtube/20211124/9QSkDzdQAms| archive-date=24 November 2021 | url-status=live| title=Babbage | first=Trevor | last=Hughes | website=[[YouTube]] | date=10 December 2010 | access-date=9 August 2021}}{{cbignore}}</ref> The film shows Babbage at a [[Party#Dinner party|dinner party]], with guests discussing his life and work.<ref>{{cite web| url=https://www.complex.com/pop-culture/2013/09/tech-films/babbage | title=Babbage | work=Genius Decoded: 10 Films About the Tech World | first=Daniel | last=Horowitz | date=17 September 2008 | publisher=[[Complex Networks]] | access-date=9 August 2021}}</ref>
* [[Sydney Padua]] created ''[[The Thrilling Adventures of Lovelace and Babbage]]'', a cartoon alternate history in which Babbage and Lovelace succeed in building the Analytical Engine. It quotes heavily from the writings of Lovelace, Babbage and their contemporaries.<ref name="Redniss">{{cite news|last1=Redniss|first1=Lauren|title='The Thrilling Adventures of Lovelace and Babbage,' by Sydney Padua|url=https://www.nytimes.com/2015/06/07/books/review/the-thrilling-adventures-of-lovelace-and-babbage-by-sydney-padua.html |archive-url=https://ghostarchive.org/archive/20220101/https://www.nytimes.com/2015/06/07/books/review/the-thrilling-adventures-of-lovelace-and-babbage-by-sydney-padua.html |archive-date=1 January 2022 |url-access=limited|access-date=2 December 2015|work=The New York Times|date=5 June 2015}}{{cbignore}}</ref><ref name="Padua">{{cite book|last1=Padua|first1=Sydney|title=The Thrilling Adventures of Lovelace and Babbage|date=2015|publisher=Pantheon Graphic Novels|isbn=978-0-307-90827-8|url-access=registration|url=https://archive.org/details/thrillingadventu0000padu}}</ref>
* [[Kate Beaton]], cartoonist of webcomic ''[[Hark! A Vagrant]]'', devoted one of her comic strips to Charles and Georgiana Babbage.<ref>Beaton, Kate. [http://www.harkavagrant.com/index.php?id=5 "Charles and Georgiana Babbage"], ''Hark! A Vagrant''. Retrieved 3 December 2014.</ref>
* The ''[[Doctor Who]]'' episode "[[Spyfall, Part 2]]" (Season 12, episode 2) features Charles Babbage and Ada Gordon as characters who assist the Doctor when she's stuck in the year 1834.

==Publications==
[[File:Babbage, Charles – Account of the repetition of M. Arago's experiments on the magnetism manifested by various substances during the act of rotation, 1825 – BEIC 722599.jpg|thumb|upright|''Account of the repetition of M. Arago's experiments on the magnetism manifested by various substances during the act of rotation'', 1825]]

* {{Cite book|title=Account of the repetition of M. Arago's experiments on the magnetism manifested by various substances during the act of rotation|publisher=William Nicol|location=London|year=1825|language=en|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=722599}}
* {{cite book | last = Babbage | first = Charles | title = A Comparative View of the Various Institutions for the Assurance of Lives | publisher=J. Mawman | year = 1826 | location = London | url = https://archive.org/details/acomparativevie00babbgoog | quote = charles babbage. }}
* {{cite book | last = Babbage | first = Charles | title = Reflections on the Decline of Science in England, and on Some of Its Causes | publisher=B. Fellowes | year = 1830 | location = London | url = https://archive.org/details/reflectionsonde01babbgoog | quote = charles babbage. }}
* {{Cite book|title=Abstract of a paper entitled Observations on the Temple of Serapis at Pozzuoli|publisher=Richard Taylor|location=London|year=1834|language=en|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=683918}}
* {{cite book | last = Babbage | first = Charles | title = On the Economy of Machinery and Manufactures | publisher=Charles Knight | year = 1835 | edition = 4th | location = London | title-link = s:On the Economy of Machinery and Manufactures }}
* {{cite book | last = Babbage | first = Charles | title = The Ninth Bridgewater Treatise, a Fragment | publisher=John Murray | year = 1837 | location = London | url = https://archive.org/details/ninthbridgewate01babbgoog| quote = charles babbage. }} (Reissued by [[Cambridge University Press]] 2009, {{ISBN|978-1-108-00000-0}}.)
* {{cite book | last = Babbage | first = Charles | title = Table of the Logarithms of the Natural Numbers from 1 to 108000 | publisher=William Clowes and Sons | year = 1841 | location = London | url = https://archive.org/details/tablelogarithms01babbgoog | quote = charles babbage. }} (The LOCOMAT site contains a reconstruction of this table.)
* {{cite book | last = Babbage | first = Charles | title = The Exposition of 1851 | publisher=John Murray | year = 1851 | location = London | url = https://archive.org/details/expositionorvie00babbgoog | quote = charles babbage. }}
* {{Cite book|title=Laws of mechanical notation|year=1851|language=en|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=683935}}
* {{cite book | last = Babbage | first = Charles | title = Passages from the Life of a Philosopher | publisher=[[Longman]] | year = 1864 | location = London | title-link = s:Passages from the Life of a Philosopher }}
* {{cite book |first=Charles |last=Babbage |editor-first=Anthony |editor-last=Hyman |title=Science and Reform: Selected Works of Charles Babbage |url=https://books.google.com/books?id=0gZ7Bo2NnzAC |year=1989 |publisher=[[Cambridge University Press]] |isbn=978-0-521-34311-4}}
* {{cite web | last = Babbage | first = Charles | title = Charles Babbage's Lectures On Astronomy |orig-date = 1815 |year=1989 | location = London | url = https://babbageastronomy.blogspot.com/ }}<ref>C. J. D. Roberts, Compiler.  [https://books.google.com/books?id=DuEsnQEACAAJ Charles Babbage's Lectures On Astronomy]</ref>

== See also ==
{{Portal|Computer programming|Biography}}
* [[Wolstenholme's theorem|Babbage's congruence]]
* [[IEEE Computer Society Charles Babbage Award]]
* [[List of pioneers in computer science]]

==Notes==
{{Reflist|30em}}

==References==
* {{cite book| first1=Bruce | last1=Collier| first2=James | last2=MacLachlan | title=Charles Babbage: And the Engines of Perfection | url=https://books.google.com/books?id=-vzMEwf-bHEC | year=2000 |publisher=[[Oxford University Press]] |isbn=978-0-19-514287-7}}
* {{Cite journal |last=Craik |first=Alex D. D. |date=February 2005 |title=Prehistory of Faà di Bruno's Formula |journal=The American Mathematical Monthly |volume=112 |issue=2 |pages=119–130 |doi=10.2307/30037410 |jstor=30037410}}
* {{cite book|first=Anthony |last=Hyman |authorlink=R. Anthony Hyman |title=[[Charles Babbage: Pioneer of the Computer]]|date=1985|publisher=[[Princeton University Press]]|isbn=978-0-691-02377-9 }}
* {{cite book| first=Kevin C. | last=Knox |title=From Newton to Hawking: A History of Cambridge University's Lucasian Professors of Mathematics|url=https://books.google.com/books?id=QGX_rAeia4kC|access-date=26 April 2013|date=2003 |publisher=Cambridge University Press|isbn=978-0-521-66310-6}}

==External links==
{{Commons category}}
{{wikisource|works=or}}
{{Wikiquote}}
* {{StandardEbooks|Standard Ebooks URL=https://standardebooks.org/ebooks/charles-babbage}}
* {{Gutenberg author |id=556| name=Charles Babbage}}
* {{Internet Archive author |sname=Charles Babbage}}
* {{Librivox author |id=13530}}
* {{UK National Archives ID}}
* [http://collection.sciencemuseum.org.uk/documents/aa110000003/the-babbage-papers The Babbage Papers] The papers held by the Science Museum Library and Archives which relate mostly to Babbage's automatic calculating engines
* [http://www.computerhistory.org/babbage/ ''The Babbage Engine'']: Computer History Museum, Mountain View CA, US. Multi-page account of Babbage, his engines and his associates, including a video of the Museum's functioning replica of the Difference Engine No 2 in action
* [https://www.fourmilab.ch/babbage/ Analytical Engine Museum] [[John Walker (programmer)|John Walker]]'s (of [[AutoCAD]] fame) comprehensive catalogue of the complete technical works relating to Babbage's machine.
* [https://web.archive.org/web/20131030050438/http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Babbage.html Charles Babbage] A history at the School of Mathematics and Statistics, University of St Andrews Scotland.
* [https://books.google.com/books?id=0CMYAAAAMAAJ&dq=charles+babbage&pg=PA57 Mr. Charles Babbage]: obituary from ''The Times'' (1871)
* [http://www.projects.ex.ac.uk/babbage/ The Babbage Pages]
* [http://onlinebooks.library.upenn.edu/webbin/book/search?amode=start&author=Babbage%2C%20Charles%2C%201791-1871 Charles Babbage, The Online Books Page, University of Pennsylvania]
* [https://web.archive.org/web/20130820004041/http://satyam.com.ar/Babbage/en/index.html The Babbage Difference Engine]: an overview of how it works
*[https://ecommons.cornell.edu/handle/1813/57661 "On a Method of Expressing by Signs the Action of Machinery"], 1826. Original edition
* [http://www.cbi.umn.edu/about/babbage.html Charles Babbage Institute]: pages on "Who Was Charles Babbage?" including biographical note, description of Difference Engine No. 2, publications by Babbage, archival and published sources on Babbage, sources on Babbage and Ada Lovelace
* [https://web.archive.org/web/20080807172602/http://www.ballet.co.uk/old/history_js_babbages_ballet.htm ''Babbage's Ballet'' by Ivor Guest, Ballet Magazine, 1997]
* [http://lhldigital.lindahall.org/cdm/ref/collection/eng_tech/id/9 ''Babbage's Calculating Machine''] {{Webarchive|url=https://web.archive.org/web/20180620101230/http://lhldigital.lindahall.org/cdm/ref/collection/eng_tech/id/9 |date=20 June 2018 }} (1872) – full digital facsimile from [[Linda Hall Library]]
* [https://zbmath.org/authors/?q=ai:babbage.charles Author profile] in the database [[Zentralblatt MATH|zbMATH]]
* [https://www.computerhistory.org/babbage/georgedvardscheutz/ The 'difference engine' built by Georg & Edvard Scheutz in 1843]
* {{NPG name}}

{{Lucasian Professors of Mathematics}}
{{Timelines of computing}}
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