Tons of Sums

Most people know that Charles Babbage was a pioneer of the computer. This absorbing, though hagiographical, new life makes very clear how many other things he was as well: pure mathematician, economist, inventor, reformer of scientific institutions, craftsman, even salon host. But Anthony Hyman does not seek to displace the computers from centre-stage in Babbage’s life, and this seems correct. They provide the most sustained theme in his variegated career, and may be seen as a point of convergence for most of the tendencies of his mind. To consider the computers is to consider Babbage. Indeed his story falls under a triple rubric that belongs to computers from Babbage onwards: software, hardware, and applications.

The young Babbage was a good mathematician by international standards, at a time (the 1810s) when English maths was generally backward. He conceived his first calculating-machine in 1821, when he was 30. Thereafter he did no interesting work in mathematics, not even in connection with the mathematics of computing. There is something shocking in the spectacle of this fertile mind (which could raise the strategy of noughts-and-crosses to a sophisticated level of mathematical description) making nothing of the theory of computation by machine: especially since modern computing has spawned so much abstractness about itself.

There is admittedly a danger of unhistorical judgment here. Babbage was working quite on his own, as far as the broad design of the machines was concerned, and he had to do what he could, with the technical means at his command. He designed two computers, which were themselves families of machines. The first, the Difference Engine, was entirely arithmetical, being intended to compute and print out long series of values for various arithmetical operations. Its workings depended on a solitary arithmetical principle, which Babbage brilliantly saw could be given a mechanical representation. It is a fact that many functions, applied to the series of natural numbers, will yield results that are separated by a constant amount. For multiplication by two, for example, this constant amount is two and separates the results themselves(2,4,6,8 ... ). But it may be that the ‘constant difference’ is a second-order one: separating, not the results proper, but the differences between the results. Squaring successive numbers, for example, gives results that are separated by a series of increasing amounts, and it is these which are separated by a constant interval of 2 (2²-1²=3, 3²-2²=5, 4²-3²=7, etc). There can be constant third-order differences, and so on.

The upshot is that many operations in arithmetic can be expressed as additions, and a machine that adds quantities, as a gas-meter does, can perform them. The vertical axles of the Difference Engine with their cogs (part of one that Babbage constructed may be seen in the Science Museum – Babbage’s own brain is preserved in the Royal College of Surgeons) are simply columns of differences. The end column retains whatever constant value you set it at; the others will successively add the preceding column’s value to their own, and hold the result. You transfer the constant value time and again into the machine, the other columns change by non-constant amounts, and, depending on their initial settings, the results of some arithmetical operation or other will emerge, in order of magnitude, at the other end.

Babbage’s second computer, the Analytical Engine, which he envisaged in 1834 and worked on intermittently until his death 37 years later, was radically different. It did not embody any one principle, but was flexibly conceived so that an assortment of methods of calculation could be used, many involving a degree of feedback. The abstract, algebraic character of the new machine was certainly well-recognised by Babbage, but he seems never to have attempted a theoretical account of its powers. This is partly explicable from the physical nature of the thing. It was, or would have been, a stupendous mass of interconnecting parts, which posed countless challenges simply for it to move efficiently. Machinery adapts itself to mathematical thought much more reluctantly than electrical circuitry: so this gifted mathematician was absorbed for years, and all his ingenuity called forth, by the search for mechanical solutions to mathematical puerilities. It is poignant, and almost ludicrous, that Babbage had to write of his grand conception, at the end of his life, that ‘the most important part of the Analytical Engine was undoubtedly the mechanical method of carrying the tens. On this I laboured incessantly.’

Lastly, the Analytical Engine was planned wholly numerically, as a device for manipulating quantities. It had no logical elements. Babbage failed to take account of the work of George Boole, whose formalisation of logic opened the way to a simple physical representation of logical processes, and became fundamental in modern computer design. We cannot know if this was because of the burden of trivial problems the Engine presented, or because of something deeper – a lack of insight. Mr Hyman is charitable about the failure to use Boole. Babbage’s note in his copy of Boole’s The Mathematical Analysis of Logic (1847), ‘This is the work of a real thinker,’ and the social links between the two men (Augustus De Morgan, for example) seem to be thought of as mitigations, but they can only be the opposite. Babbage did not even try to meet Boole before 1862.

A close involvement with the hardware of his machines was far from uncongenial to Babbage: a well-to-do gentleman, subsequently Lucasian Professor of Mathematics at Cambridge, who nevertheless owned a lathe which he would have used to machine the prototype of the Difference Engine if it had possessed the necessary facilities. His machines, especially the Difference Engine, are not just landmarks in computing: they were of the first importance in the history of modern engineering. They set new standards of accuracy, and prompted a major improvement in machine-tool design. But, given that the utmost regularity and uniformity in scores of components was essential for the Engines, need they have been such physically grandiose objects? The Analytical Engine, at one stage of its development, would have stood 15 feet tall. (It had the capacity to handle one thousand variables of fifty figures each, thus easily out-stripping the ambitions of the designers of the first working computer in 1937.) The Difference Engine, in its complete form, would have weighed about two tons. A much lighter machine, following the main lines of Babbage’s conception, was assembled by a Swedish firm in 1855, and marketed for 1/50th of the projected cost of Babbage’s version. When the British Government finally commissioned a Difference Engine they went for a copy of the Swedish machine, rather than the domestic product.

The Analytical Engine never came remotely near completion. Reading about its history is akin to reading certain kinds of literary fantasy – the inventions of Borges, for example. ‘A vague glimpse even of an Analytical Engine at length opened out,’ wrote Babbage in his autobiography, ‘and I pursued with enthusiasm the shadowy vision. The drawings and the experiments were of the most costly kind. Draftsmen of the highest order were necessary to economise the labour of my own head, whilst skilled workmen were required to execute the experimental machinery to which I was constantly obliged to have recourse.’ The sense this gives, however, of something phantasmal, of physical embodiment continuously dissolving into unspecified ‘drawings and experiments’, is partly misleading. The plans and tests were real enough. Babbage had set himself a colossal task of mechanical design, and the postponement of a physical incarnation of the Analytical Engine reflects this. But in 1855 Joseph Whitworth, a leading engineer, offered to build the machine, on terms generous to Babbage. The latter declined the offer, apparently because government help would also be required. This strange and surely instructive moment is not explained by Mr Hyman. Would Whitworth’s creation, a number-cruncher as high as a room, requiring minutes to do multiplication, have worked? No one knows. Babbage’s son Henry built part of an Analytical Engine after his father’s death; for what the information is worth, it always tended to jam.

Babbage did have some reason to be sensitive about government finance. The Difference Engine was funded to the tune of £17,000 under Wellington’s administration in 1829, but the money dried up under Peel in 1842. This was one important suggestion to Charles Dickens for his portrait of Daniel Doyce, inventor-victim of the Circumlocution Office in Little Dorrit. The other was Babbage’s readiness, in both senses, with his hands, which yielded the Doyce thumb: ‘a certain free use of the thumb that is never seen but in a hand accustomed to tools’. The information on Doyce’s origins came from Forster, and as Forster remarks, Dickens departs from the facts in not making Doyce well-born. This may suggest how very unusual, and even doomed to failure, was Babbage’s combination of the intellectual and the practical, the speculative and the banausic. The great geologist Lyell thought that Babbage ‘acquired influence for science’ by ‘the manner in which he has firmly and successfully asserted the rank in society due to science’. But Mr Hyman believes that the forces in Victorian Britain opposing Babbage’s great dream of science in the places of power – and, within science, of a reconciliation of the pure and the applied – were too strong. He urges what is plausible: that the thwarting and isolation of Babbage reflects a snobbery about science in Britain for which we are still paying the penalty.

Babbage actually stood for Parliament: for the constituency of Finsbury in the general election that followed the Reform Bill of 1832. He told a meeting of voters at the Crown Tavern, Clerkenwell Green that science had taught him ‘one important tendency’: ‘a habit of regarding facts solely as facts, and of reasoning on those facts solely with a view to the elucidation of the truth’. This may put us in mind of the famous opening of another Dickens novel:

‘Now what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts.’

Not that any versions of Babbage occur in Hard Times, but there are echoes of Coke-town in his life. He sent his sons to a Utilitarian school, Bruce Castle in Tottenham, whose headmaster’s methods were admired by Bentham himself. The tables printed by the Difference Engine were meant to be the mechanical equivalent of those which the French scientist, de Prony, had earlier generated with a force of several score human ‘computers’, and de Prony’s method – breaking down the calculations into elementary steps and distributing these among mathematically unskilled workers – was confessedly inspired by Adam Smith’s doctrine of the division of labour. Babbage’s own dissatisfaction with human calculators made him express the wish that ‘we could calculate by steam,’ and soon after he conceived the Difference Engine. He again implemented his belief that machinery affords a check ‘against the inattention, the idleness, or the dishonesty of human agents’ when he invented the factory clocking-on machine. The central calculating portion of the Analytical Engine was called ‘The Mill’, and there is an uncanny resemblance between the fragment of it now in the Science Museum and the model of a Mid-Victorian engineering shop that may be seen on the floor below. Power enters both on a great revolving shaft, and is distributed by belts or gears to ranks of specialised working units.

Dickens did almost certainly depict Babbage in one further place. His two ‘Reports’ of ‘The Mudfog Association for the Advancement of Everything’ were inspired by the meetings of the British Association for the Advancement of Science in 1837 and 1838. Babbage was the chairman of the statistical section of the British Association and ‘Mr Slug’ is variously the President and the chief speaker of the Statistics Section of Dickens’s Mudfog. He reports such ‘curious calculations’ as the degree of ignorance of mathematics and geography, and knowledge of romances, among London children (‘the preponderance of Valentine and Orsons over Goody Two Shoes was as three and an eighth of the former to half a one of the latter’), and the annual wastage of dogs’-meat skewers. Babbage was indeed a passionate believer in statistics, and some of his researches were as risible, or as indifferent to human nature, as Mr Slug’s. He published a ‘Table of the Relative Frequency of Occurrence of the Causes of Breaking Plate Glass Windows’; he timed the incidence of jolts on the new English railways; he did a survey of the hard-luck stories of London beggars. One of the main applications envisaged for the Difference Engine was to provide really accurate tables for a tabular-based society. In the event, the British copy of the Swedish imitation of Babbage’s machine printed the English Life Table No 3, of 1864. And that was that.

Robert Browning remarked to Elizabeth Barrett that certain revisions Tennyson had made to his poems in deference to the critics were ‘much as if Babbage were to take my opinion – undo his calculating machine by it’. Browning spoke truer than he knew, for Babbage had actually written to Tennyson with a statistical, Malthusian-minded quibble about the lines from ‘The Vision of Sin’:

Every minute dies a man,
Every minute one is born.

He proposed instead:

Every moment dies a man
And one and a sixteenth is born.

He added that ‘the exact figures are 1.167, but something must, of course, beconceded to the laws of scansion.’ But this is so ludicrous thatit is almost certainly a joke. Indeed, where geniality stops and grimness starts in Babbage is a question that has puzzled students of his personality. The last biography of him was called Irascible Genius, but Mr Hyman does not perceive irascibility. Dickens found another duality in him: Doyce and Mr Slug are startlingly different versions of one man.

Babbage partook, too, of a duality in Early Victorian culture: at this time a radical attitude to social and cultural affairs, which had sprung from the era of revolution and romanticism, was somehow transformed into Grad-grindery. Babbage was born in a decade, the 1790s, which saw several illustrious births, and he conforms to the curious rule that seems to apply to this generation: that its members should either flourish, as romantics, very young, or, as proto-Victorians, some years later, but not in both periods. It is, for example, as if Keats perished and John Clare went mad so that their contemporary, Carlyle, could emerge. Babbage was older than any of these men, but he did not conceive his Difference Engine until the year of Keats’s death. Strangely, the two were educated for a time at a pair of boarding-schools that must have been only a few hundred yards apart, in Enfield. They may have met around 1805, and even have discussed their favourite boyhood topics (already algebra in Babbage’s case, and literature in Keats’s). Such an encounter seems improbable, even weird, but only because subsequent cultural history has placed an illusory prohibition on it.