Babbage’s Calculating Engines

3D front cover of Passages from the Life of a Philosopher by Charles BabbageCharles Babbage (1791–1871) is  one of the few authors (Joseph Priestley being another) reissued in the Cambridge Library Collection whose books have covers in all three colours – red for his work on the printing industry, On the Economy of Machinery and Manufactures; blue for The Ninth Bridgewater Treatise, and The Exposition of 1851, and green for Reflections on the Decline of Science in England, and on Some of its Causes, Babbage’s Calculating Engines (papers edited by his son [Major-General] Henry Prevost Babbage) and Passages from the Life of a Philosopher. This spread between science and technology, the social sciences and the humanities is typical of a remarkable polymath whose pioneering work on ‘calculating engines’ is now widely recognized as having laid the foundations of modern computing.

A biography of Babbage was written by one H.W. Buxton between 1872 and 1880, but not published until 1988. His own Passages from the Life of a Philosopher, published in 1864, ‘does not aspire to the name of autobiography’, though the chapters sketch out the contours of his life, beginning with his family and his childhood: beautifully told anecdotes include his getting lost in London and being ‘cried for’ by the town crier, and attempting to summon up the Devil. Born into a banking family with roots in Devon, Charles was a sickly child. As a result his education was patchy, and after a particularly ‘violent fever’ at the age of ten, he was sent into Devon and into the care of a clergyman-teacher who had instructions to attend to his health, ‘but not to press too much knowledge upon me: a mission which he faithfully accomplished’.

While enduring this enforced ‘great idleness’, Babbage made an important discovery: that ‘occupation of the mind is such a source of pleasure that it can relieve even the pain of a headache’. (Bored, and believing himself ill, he was distracted and ‘cured’ by finding a brass weight on the ground which he believed to be golden treasure.) He seems to have applied this maxim on many difficult occasions in his later personal and professional life. Destined for Cambridge, after his convalescence he was sent to school in Enfield, where Frederick Marryat was a fellow pupil and where he first discovered the delights of algebra, and to two more clergymen-coaches: studying the classics at Totnes, he read mathematical works, including Lagrange, as a leisure activity.

Arriving at Trinity College in April 1810 (he later ‘migrated’ to Peterhouse), he was disappointed at the state of the mathematics curriculum. Far from following the developments in algebra then taking place on the continent, Cambridge seemed to regard the new mathematics as both atheistic and immoral (coming from France, and all that…).  Early experience of tutors who clearly knew less than he did seems to have had the effect of turning him from formal studies: he pursued the works of Euler and Laplace through such mathematical journals as could get through the Continental Blockade, and spent a lot of time playing chess and whist, sailing in the Fens, and proposing new university societies. The Ghost Society did paranormal research: ‘some of this was both interesting and instructive’ – one of the problems with Passages is that it’s not always clear when Babbage is joking: however, the rules of The Extractors’ Society leave one in very little doubt. However, the Analytical Society, which began as a result of a parody by Babbage of the then current biblical criticism, applied to the works of Lacroix, became something more serious.

Formed by Babbage and his friend John Herschel (son of William) in 1812, it consisted of students disillusioned as Babbage was by the intellectual climate of Cambridge. Other members were George Peacock, William Whewell and Alexander D’Arblay, the son of Fanny Burney. Their subversive and laudable aim was to import continental mathematics into Britain, but like many university societies, this one did not last long. On the other hand, not many university societies were later characterized as having created ‘a crucial moment in the adoption of the differential calculus within English mathematics’. They did issue one volume of Memoirs, in 1813, but decided that Cambridge was beyond reforming and that London would be a better field for the new science. Babbage left Cambridge with only a pass degree: his viva seems to have been thought blasphemous (or French-inspired, or both), and he did not attend the final exams – it’s not clear whether he was excluded, or refused to take part.  In London, the ‘Analyticals’ were among the founding members of the (later Royal) Astronomical Society in 1820.

Babbage had become independently wealthy on the death of his father in 1827, but in the same year his wife and two of his children also died. He sought distraction by an extended European tour, visiting scientists, mathematicians, and manufactories: this seemed to have confirmed his view that Britain was falling badly behind the continent in all aspects of science and technology as well as in mathematics. In 1830, he published Reflections on the Decline of Science in England, and on Some of its Causes,which attacked both the government for its lack of support for science, and the learned societies, whose members he accused of dilettantism and snobbery. This made him enemies (and even John Herschel was annoyed), but it led in due course to the establishment of both the British Association for the Advancement of Science and the Statistical Society.

Babbage subsequently made himself unpopular with an attack on the Great ExhibitionThe Exposition of 1851 – again inveighing against the lack of governmental and popular support for the sciences. He makes it clear that he was driven by resentment that he himself had not been invited to take part in the planning of the Crystal Palace. He tells us in Passages that on the death of the Prince Consort (who he had met and admired), he turned with some anxiety to the 1851 work, ‘lest, in speaking of that event, I might have committed some injustice, whilst I was indignant at that under which I was myself suffering’. And in spite of his disappointing time as a student in Cambridge, he accepted the Lucasian chair of mathematics, ‘and still feel deeply grateful for the honour the university conferred upon me – the only honour I received in my own country’. (A chapter in Passages lists all the positions for which he was pre-eminently suited, and the reasons why he was appointed to none of them.)

Of course, what Babbage is remembered for is his calculating engines: and here I am completely out of my depth. He states that ‘To describe the successive improvements of the Analytical Engine would require many volumes’: however, those ‘acquainted with the principles of the Jacquard loom, and who are also familiar with analytical formulae’ have a chance of understanding his great work, and I fail on both counts. His original inspiration, as he describes it, came one night in Cambridge: he was sitting half asleep in front of a table of logarithms (and how that evokes maths lessons on Friday afternoons!), when a friend asked, ‘Well, Babbage, what are you dreaming about?’ to which he answered, ‘I am thinking that all these Tables… might be calculated by machinery.’ The rest was history – a history which was rounded off two hundred years after Babbage’s birth when the Science Museum in London unveiled a working version of the Difference Engine No. 2. (And apparently there are plans to raise funds for the construction of an Analytical Engine…)

So I am afraid I skipped many ‘difficult’ passages in Passages, but there is still much to enjoy: the versatility of the man is astonishing. He experimented with walking on water (and nearly drowned). He devised a revolutionary use of colour in theatre lighting (and devised a ballet, put on at Covent Garden, to demonstrate its use: the manager loved the effects but was concerned about the fire risk). He investigated earthquakes in Italy and London. He was lowered by ropes into the crater of Vesuvius, carrying an enormous barometer and several thermometers: his walking stick caught fire, and his boots were burnt through. He worked to create an ‘unbreakable’ cipher, then thought a bit more and realized that his, and indeed any, cipher could be broken. He invented a type of ‘cowcatcher’ for steam engines in the wake of William Huskisson’s death in the world’s first railway tragedy in 1830. He went down in a diving bell, and subsequently proposed a type of ‘open’ submarine. He nearly collided at full speed with Isambard Kingdom Brunel when both men were running trains in opposite directions on the same line. (Brunel, being asked what he would have done if collision seemed inevitable, said he would have piled on speed in the hope of driving the other engine off the track.) And there are lots of good stories: I particularly enjoyed the one about the archbishop of Dublin being mistaken for George Borrow, and congratulated on his ‘gipsy-like’ experiences.

It’s arguable that the most interesting of Babbage’s works in purely intellectual terms is the one which to some will seem antithetical to science: the Ninth Bridgewater Treatise of 1837. In 1829, the earl of Bridgewater’s will had provided for ‘one thousand copies of a work “On the Power, Wisdom, and Goodness of God, as manifested in the Creation”, illustrating such work by all reasonable arguments, as, for instance, the variety and formation of God’s creatures in the animal, vegetable, and mineral kingdoms; the effect of digestion, and thereby of conversion; the construction of the hand of man, and an infinite variety of other arguments: as also by discoveries, ancient and modern, in arts, sciences, and the whole extent of literature’.

But Babbage decided to add his own contribution to the debate between science and theology, attempting to bridge the growing gulf (‘there exists no such fatal collision between the words of Scripture and the facts of nature’), and adding to Paley’s famous argument about the watchmaker the analogy of the building of the Difference Engine: it works according to rules which its maker understands, while the Universe works according to rules understood (as yet) only by God, the divine programmer.




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