Charles Babbage 26 December 1791 – 18 October 1871
Charles Babbage 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 be "father of the computer".Babbage 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 Babbage's Analytical Engine. 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 Babbage's incomplete mechanisms are on display in the Science Museum
in London. In 1991, a functioning difference engine was constructed from
Babbage's 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 c. 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. 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 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 in Robert Woodhouse, Joseph Louis Lagrange, and Marie 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
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 founded a large family. On his father's death in
1827, Babbage inherited a large estate (value around £100,000, equivalent to
£8.72 million or $11.1 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 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.[45] 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.
"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. The term was introduced in 1974 by Harry Braverman.
Related formulations are the "principle of multiples" of Philip
Sargant Florence, and the "balance of processes".
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.[78] 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. His view of human capital was restricted to
minimising the time period for recovery of training costs.
Difference engine
The Science Museum's Difference Engine No. 2, built from
Babbage's design
Portion of Babbage's
difference engine.
Babbage began in 1822 with what he called the difference
engine, made to compute values of polynomial functions. 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.
For a prototype difference engine, Babbage brought in Joseph
Clement to implement the design, in 1823. Clement worked to high standards, but
his machine tools 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.
Some parts of the prototype survive in the Museum of the
History of Science, Oxford.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 fifteen tons (13,600 kg), and would have been 8 ft 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.
Nine years later, in 2000, the Science Museum completed
the printer Babbage had designed for the difference engine.
Religious views
Babbage was raised in the Protestant form of the
Christian faith, his family having inculcated in him an orthodox form of
worship. He explained:
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.
— Babbage, (1864)
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.
In his autobiography 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:
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. Advocating for natural
theology, he wrote:
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.
— Babbage, (1864)
Like Samuel Vince, Babbage also wrote a defence of the
belief in divine miracles. 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." 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."
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