January 20, 2005
Pray, Mr Babbage
I found the intriguing extract below in Babbage's Intelligence by Simon Schaffer. The article is mainly about how Babbage's theories fit in with the development of Victorian machinofacture and the alienation of labour consequent on the emergence of industrial capitalism, so I wouldn't recommend you read the whole thing unless you are particularly interested in such matters, but these paragraphs on the Difference Engine and Babbage's notion of the miraculous caught my eye:
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". Unsurprisingly, I thought of this:
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".
On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.Recognising that the behaviour of the Difference Engine is the natural consequence of its structure and settings and nothing else, Babbage's preprogrammed miracles are merely an artifact of the audience's ignorance of the rules that ordained the event. With Babbage's approach, there is no reason, necessarily, the rules behind other miracles should be no less learnable. Babbage's problem in reconciling a machine universe with miracles remains unchanged - if there are rules, there need not be God.