Charles Babbage

Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.

Babbage is considered by some to merit the title of "father of the computer". 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. As part of his computer work, he also designed the first computer printers. He had a broad range of interests in addition to his work on computers, covered in his 1832 book Economy of Manufactures and Machinery. 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 Saturday evening soirées. His varied work in other fields has led him to be described as "pre-eminent" among the many polymaths of his century.

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 Science Museum in London. In 1991, a functioning difference engine was constructed from the original plans. Built to tolerances achievable in the 19th century, the success of the finished engine indicated that Babbage's machine would have worked.

Early life

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. A blue plaque on the junction of Larcom Street and Walworth Road commemorates the event.

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 St. Mary's, Newington, London, shows that Babbage was baptised on 6 January 1792, supporting a birth year of 1791.

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. In 1808, the Babbage family moved into the old Rowdens house in East Teignmouth. Around the age of eight, Babbage was sent to a country school in Alphington near Exeter to recover from a life-threatening fever. For a short time, he attended King Edward VI Grammar School in Totnes, South Devon, but his health forced him back to private tutors for a time.

Babbage then joined the 30-student Holmwood Academy, in Baker Street, Enfield, Middlesex, under the Reverend Stephen Freeman. 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. He was brought home, to study at the Totnes school: this was at age 16 or 17. The second was an 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. He was already self-taught in some parts of contemporary mathematics; 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.

Babbage, John Herschel, George Peacock, and several other friends formed the Analytical Society in 1812; they were also close to Edward Ryan. 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.

In 1812, Babbage transferred to Peterhouse, Cambridge. 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.

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. 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 and John Playfair, but lost out to Henry Walter. In 1819, Babbage and Herschel visited Paris and the Society of Arcueil, meeting leading French mathematicians and physicists. 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.

With Herschel, Babbage worked on the electrodynamics of Arago's rotations, publishing in 1825. Their explanations were only transitional, being picked up and broadened by Michael Faraday. The phenomena are now part of the theory of eddy currents, and Babbage and Herschel missed some of the clues to unification of electromagnetic theory, staying close to Ampère's force law.

Babbage purchased the actuarial tables of 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. This interest followed a project to set up an insurance company, prompted by Francis Baily and mooted in 1824, but not carried out. Babbage did calculate actuarial tables for that scheme, using Equitable Society mortality data from 1762 onwards.

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. On his father's death in 1827, Babbage inherited a large estate (value around £100,000, equivalent to £9.14 million or $12.5 million today), making him independently wealthy. 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. 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).

Royal Astronomical Society

Babbage was instrumental in founding the Royal Astronomical Society in 1820, initially known as the Astronomical Society of London. Its original aims were to reduce astronomical calculations to a more standard form, and to circulate data. These directions were closely connected with Babbage's ideas on computation, and in 1824 he won its Gold Medal, cited "for his invention of an engine for calculating mathematical and astronomical tables".

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). 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. 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.

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 in 1839 and 1840. Colby was another of the founding group of the Society. 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.

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.

Reference to 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 equations (including the difference equations fundamental to the difference engine) and operator (D-module) methods for differential equations. 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 Cauchy concept of limit was kept at bay. Woodhouse had already founded this second "British Lagrangian School" with its treatment of Taylor series as formal.

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. In the period to 1820 Babbage worked intensively on functional equations in general, and resisted both conventional finite differences and Arbogast's approach (in which Δ and D were related by the simple additive case of the exponential map). But via Herschel he was influenced by Arbogast's ideas in the matter of iteration, i.e. composing a function with itself, possibly many times. Writing in a major paper on functional equations in the Philosophical Transactions (1815/6), Babbage said his starting point was work of Gaspard Monge.

Academic

From 1828 to 1839, Babbage was Lucasian Professor of Mathematics at Cambridge. Not a conventional resident 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. Babbage was out of sympathy with colleagues: George Biddell Airy, his predecessor as Lucasian Professor of Mathematics at Trinity College, Cambridge, 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 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 lasted for six years. He never did give a lecture.

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. He twice stood for Parliament as a candidate for the borough of 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. 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. In 1834 Babbage finished last among four. In 1832, Babbage, Herschel and Ivory were appointed Knights of the Royal Guelphic Order, however they were not subsequently made 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).

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