"Innumerable are the illusions of Custom, but of all these, perhaps the cleverest is her knack of persuading us that the Miraculous, by simple repetition, ceases to be Miraculous....Am I to view the Stupendous with stupid indifference, because I have seen it twice, or two hundred, or two million times? There is no reason in Nature or in Art why I should: unless, indeed, I am a mere Work-Machine, for whom the divine gift of Thought were no other than the terrestrial gift of Steam is to the Steam-Engine, a power whereby Cotton might be spun, and money and money's worth realised" Thomas Carlyle, 1831. 
It was, perhaps, inevitable that Babbage should ultimately teach the supreme value of machines possessed of foresight and memory by attributing these powers to the Deity. Natural theology was the indispensable medium through which early Victorian savants broadcast their messages. The dominant texts of this genre were the Bridgewater Treatises produced in the early 1830s by eminent divines and natural philosophers under the management of the Royal Society's presidency. The treatise produced by William Whewell, then mathematics tutor at Trinity College Cambridge, was among the most successful of these works and included a claim about the relation between mathematics, automatism and atheism which Babbage decided he had to answer. His machine philosophy was here assailed from a perspective in complete contrast to those of the radical artisans. Whewell, a moderate evangelical and follower of Coleridgean politics, argued that whereas the great scientific discoverers were men of faith, because their acts of induction would inevitably prompt them to identify divine intelligence in the creation, mathematical deductivists might falsely hold that the laws of the world could be spun out by analysis and that the world itself might seem to be an automatic system. Whewell maintained a consistent hostility to the implications of mechanised analysis: "we may thus deny to the mechanical philosophers and mathematicians of recent times any authority with regard to their views of the administration of the Universe". Worse was to follow. Whewell brutally denied that mechanised analytical calculation was proper to the formation of the clerisy. In classical geometry "we tread the ground ourselves at every step feeling ourselves firm" but in machine analysis "we are carried along as in a railroad carriage, entering it at one station and coming out of it at another.....it is plain that the latter is not a mode of exercising our own locomotive powers...It may be the best way for men of business to travel but it cannot fitly be made a part of the gymnastics of education". 
These remarks were direct blows to Babbage's programme. He called the reply to Whewell he produced in 1837 the Ninth Bridgewater Treatise and labelled it "a fragment". It contained a series of sketches of his religious faith, his cosmology and his ambitions for the calculating engines. It amounted to a confession of his faith that the established clerisy was incompetent, dangerous and innumerate. Babbage had shown that memory and foresight were the two features of intelligence represented in his machines. He now showed, using resources from his calculating engines and from Hume's notorious critique of miracles and revelation, that these features of machine intelligence were all that was needed to understand and model the rule of God, whether based on the miraculous work of the Supreme Intelligence or on His promise of an afterlife. "Foresight" could be shown to be responsible for all apparently miraculous and specially providential events in nature. Throughout the 1830s Babbage regaled his guests with a portentous party trick. He could set the machine to print a series of integers from unity to one million. Any observer of the machine's output would assume that this series would continue indefinitely. But the initial setting of the machine could be adjusted so that at a certain point the machine would then advance in steps of ten thousand. An indefinite number of different rules might be set this way. To the observer, each discontinuity would seem to be a "miracle", an event unpredictable from the apparent law-like course of the machine. Yet in fact the manager of the system would have given it foresight. Whewell's Bridgewater Treatise appeared at the start of March 1833. Less than two months later Babbage had already worked out an experiment using the Difference Engine to print the series of even integers up to ten thousand and then increase each term in steps of three. The sudden discontinuity was both predictable to the analyst and yet surprising to the audience. Babbage drew the analogy with divine foresight, whether in the production of new species or in miraculous intervention. In May 1833, therefore, Babbage was ready to show a mechanical miracle.
His onlookers were almost always impressed. The dour Thomas Carlyle was predictably sceptical, and thundered his complaint about Babbage's analogy between thought and steam power. But as early as June 1833 Lady Byron and her daughter "both went to see the thinking machine (for such it seems) and were treated to Babbage's miraculous show of apparently sudden breaks in its output. "There was a sublimity in the views thus opened of the ultimate results of intellectual power", she reported. Two years later George Ticknor was treated to a lecture of three hours on the topic of programmed discontinuities: "the whole, of course, seems incomprehensible, without the exercise of volition and thought". Here, then, was the theological equivalent of the systematic gaze. In answer to Whewell's boast that only induction might reveal the divine plan of the world, and that machine analysis could never do so, Babbage countered that the world could be represented as an automatic array only visible as a system from the point of view of its manager. The world-system was a macroscopic version of a factory, the philosophy of machinery the true path to faith, and the calculating engines' power of "volition and thought" demonstrated to all. 
The mechanical metaphor for miracles, creations and extinctions was, of course, profoundly influential on the actualist naturalists among Babbage's friends, including Charles Lyell and Charles Darwin. In the Ninth Treatise Babbage reproduced his own views on crustal elevation and stratigraphy and two crucial letters from John Herschel on the uniformity of earth history and the production of life. He sent copies to figures of political eminence, including both the new Queen Victoria and the Piedmontese premier Cavour. He also sent the text to the gentlemen of science. Lyell predicted that "some people would not like any reasoning which made miracles more reconcilable with possibilities in the ordinary course of the Universe", while the American mathematician Nathaniel Bowditch told Babbage that "when you carried me from the simple machine made by a man to the grand machine of the Universe I wish I could express to you one half of the enthusiasm I felt....I want no priestcraft, but I want high feelings always to exist in men's minds in regard to God".  Babbage was not content with making mechanizable foresight responsible for all apparently miraculous and specially providential events. Mechanizable memory was to be associated with the doctrine of a future state of rewards and punishments. "We must possess the memory of what we did during our existence in order to give them those characteristics. In fact, memory seems to be the only faculty which must of necessity be preserved in order to render a future state possible". Babbage even managed to offer a material cause for the preservation of memory, for since all sound, and thus all speech, was preserved in aerial vibrations, the memory of all previous consciousness would be preserved in the atmosphere. However hypothetical, with this model Babbage managed to show that just those features of intelligence displayed in his machine were also required for religion. Without memory, there could be no heaven nor hell, and without foresight, no providence. 
The apotheosis of the intelligent machine was an integral part of Babbage's ambitious programme. This programme has been used here to illuminate the complex character of systematic vision in the Industrial Revolution. In the Ninth Bridgewater Treatise, the system was coextensive with the universe, and Babbage explained that its order and logic would only be visible from a privileged point of view. In his surveys of the factories and workshops, Babbage set out to reveal the systematic character of the machine economy by pointing out the rationale of the production, distribution and deployment of power in the workshops of industrial Britain. In his project to build intelligent calculating engines, he attempted to represent himself as the intellectual manager of the complex labour relations of the machine-tool industry, initially disastrously, and then as part of his overall vision of a newly rational system of automatic precision engineering. In the setting of early Victorian society, the connections between these spheres of theological, political and technological work cannot be seen as merely metaphorical. These techniques helped make a new social order and a new form of knowledge. The systematic gaze was designed to produce the rational order it purported to discover. This is to place Babbage's project alongside those of Bentham, whose panoptic schemes have been associated with the production of the docile body, and of Smiles, whose hagiographies cleverly connected the self-fashioning of the Victorian engineers with the transformations they wrought on the material world.  A third, and highly suggestive, contemporary is Henry Mayhew, the surveyor of the unproductive bodies of the London poor in a four volume work of 1861 subtitled A Cyclopaedia of the condition and earnings of those that will work, those that cannot work, and those that will not work. In Mayhew's ghastly and obsessive stories, the apparent nomadic disorder of the diseased bodies of the London streets is inexorably revealed as systematic and possessed of its own rationality, and thus, paradoxically, its own productivity. Mayhew cites Babbage directly at this key point in his work - the discussion of waste. In Babbage's Economy of Machinery the reader is regaled with details of the admirable system for slaughtering horses at the factories in Paris. Even the rats which live off rotting horse carcasses could be systematically caught, killed and sold. With an exhaustive and exhausting tabulation of data, Babbage showed that a twelve shilling horse carcass could produce more than four pounds of income. Mayhew went one better, by linking the statistics of dead horses to the entire economy of productive waste and waste- sellers on the London streets. As Catherine Gallagher has remarked, Mayhew here effects the "conversion of economic into physiological categories".  This interconversion holds the key to the systematic vision. Under Babbage's productive gaze, the powers of the body were simultaneously rendered mechanical and thus profitable, or wasteful and thus consigned to oblivion.