History of Psychology Copyright 2005 by the Educational Publishing Foundation 2005, Vol. 8, No. 1, 35–45 1093-4510/05/$12.00 DOI: 10.1037/1093-4510.8.1.35 WAS BABBAGE’S ANALYTICAL ENGINE INTENDED TO BE A MECHANICAL MODEL OF THE MIND? Christopher D. Green York University In the 1830s, Charles Babbage worked on a mechanical computer he dubbed the Analytical Engine. Although some people around Babbage described his invention as though it had authentic mental powers, Babbage refrained from making such claims. He does not, however, seem to have discouraged those he worked with from mooting the idea publicly. This article investigates whether (1) the Analytical Engine was the focus of a covert research program into the mechanism of mentality; (2) Babbage opposed the idea that the Analytical Engine had mental powers but allowed his colleagues to speculate as they saw fit; or (3) Babbage believed such claims to be fanciful, but cleverly used the publicity they engendered to draw public and political attention to his project. Charles Babbage (1791–1871) was the inventor of a number of mechanical devices that were intended to compute mathematical and logical functions.1 The two most famous are the Difference Engine, dating from the 1820s, which was to have calculated and printed basic mathematical tables of various kinds, and the Analytical Engine. The Analytical Engine, for which designs began in the mid- 1830s, was a much more ambitious project because it was to have employed then-recent developments in abstract symbolic algebra, thereby extending its range into the logical realm rather than being limited to the strictly mathematical. Neither machine was ever completed, though Babbage built two small models of the Difference Engine. For many decades now, it has not been uncommon to find Charles Babbage named in both popular and scholarly publications as one of the primary “forefa- thers” of computer science. This trend began with the public pronouncements of Howard Aiken, the designer of the Harvard Mark I “computer” in the 1940s, who repeatedly paid homage to Babbage and claimed to have been the one to finally fulfill “Babbage’s Dream,” as he often put it. More recently, there has been a trend to cite Babbage as a father of compu- Christopher D. Green is a professor in the History & Theory of Psychology program at York University, Toronto, Ontario, Canada. He holds PhDs in psychology (1992) and philosophy (2004) from the University of Toronto. In January 2006 he will become Editor of the Journal of the History of the Behavioral Sciences. Correspondence concerning this article should be addressed to Christopher D. Green, Depart- ment of Psychology, York University, Toronto, Ontario M3J 1P3, Canada. E-mail: [email protected] 1 Much of the material presented here previously appeared in “Charles Babbage, the Analytical Engine, and the Possibility of a 19th-Century Cognitive Science.” In C. D. Green, T. Teo, & M. Shore (Eds.), The Transformation of Psychology: Influences of 19th-Century Philosophy,Technol- ogy,and Natural Science (pp. 133–152). Washington, DC: American Psychological Association. 35 36 GREEN tational cognitive science as well (e.g., Gardner, 1985; Garnham, 1987; Hauge- land, 1985; Hofstadter, 1979; Pylyshyn, 1984). Though it has received little serious consideration, this is a striking attribution, for it implies that Babbage not only intended his machines to compute useful functions, but that he also thought the operation of his machines in some way closely paralleled the operations of the human mind. In this article I examine this claim. What I ultimately discover is that Babbage himself was reluctant to associate the activities of his machines with the operations of the mind, but he seems to have been happy to allow others, even some who worked closely under his guidance, to come very close to attributing to them actual mental powers. The question we are left with, then, is whether he did this because (1) he was indeed engaged in covert psychological research, (2) he was simply so liberal minded that he allowed even his closest associates to publicly speak their minds even when their opinions of his work conflicted with his own, or (3) he allowed his assistants to risk their own reputations by making controversial claims in the hope that it would draw public attention to his project which he could then use to his advantage. The Origins of the Analytical Engine Babbage had first made a name for himself in the late 1810s when he led a mathematical revolution at Cambridge to switch from the clumsy Newtonian notation for calculus to the more easily manipulated Leibnizian notation. For his efforts, Babbage was made a fellow of the Royal Society at the age of only 24. His “revolutionary fervor” was not spent, however. Frustrated with the stodgy and aristocratic Royal Society, Babbage and a number of other “entrepreneur-scien- tists” (see Ashworth, 1994) formed the rival Astronomical Society in 1820. The Astronomical Society began life by attacking the Royal Society-endorsed Board of Longitude, which was then making up a set of new astronomical tables. While busy discovering errors in the Board of Longitude’s tables (and just about everyone else’s), Babbage hit upon the idea of developing a machine that would calculate and print the required numbers automatically, so that there could be no mistakes either in computation or copying. The machine he designed implemented a then-common mathematical technique for calculating polynomials, from which the values of a wide array of other functions could be approximated. The technique was called the “method of differences,” and thus the machine was dubbed the “Difference Engine.”2 He built a small working model in 1822, for 2 The method of differences allows complicated problems to be turned into simple addition problems by relying on the fact that polynomials have certain constant relations to each other. For instance, the square of the numbers 0, 1, 2, 3, 4, 5,...are0,1,4,9,16,25,...Bysubtracting each square from the square above it in the series (e.g.,1–0,4–1,9–4, . .), one gets 1, 3, 5, 7, 9,. These are called the “first differences” of the squares. If one subtracts each of these differences from the one above it in the series (e.g.,3–1,5–3,7–5, . .), the outcome is 2 in every case. These are called “second differences.” Once one knows that the second differences between any square in the series is 2, one can use the process in reverse to obtain a square simply by adding. For instance, what is the square of 7? It is 2 more distant from the square of 6 than the square of 6 is from the square of 5. The square of 6 is 2 more distant from the square of 5 than the square of 5 is from the square of 4, and so on down to 0. Of course, this is a fairly cumbersome procedure for a human (who can multiply), but for a machine that can only add (and that can do so extremely quickly and accurately) it is a virtually ideal algorithm. Of course, figuring out the square of 7 is not going to SPECIAL ISSUE: BABBAGE’S ANALYTICAL ENGINE 37 which he won the Astronomical Society’s “Gold Medal.” He then applied for assistance to build a full-scale version of the Engine to the Royal Society itself. Davies Gilbert, the Royal’s treasurer, lobbied the government on Babbage’s behalf. The Duke of Wellington, then Prime Minister, approved £1,000 for its construction in 1823 (Hyman, 1982, p. 52). Babbage found that the machine was more expensive to build than he had expected, so he asked for and received more money from the government, and then more, and still more. By 1833, a decade later, he had received over £17,000, and still no working machine had been completed (but for a new scale model that he kept in his house as a showpiece). The government finally suspended the project in the mid-1830s, officially with- drawing their support in 1842. Then-Prime Minister Robert Peel is reported to have quipped that, if ever completed, the Difference Engine should first be set to calculating how much money went into its construction. In the late 1820s, Babbage toured Europe, devoting much of his travel to studying Continental means of industry and manufacture. One of the things he discovered was the system set up by Marie de Prony (1755–1839) in Revolution- ary France for the calculation and publication of new logarithmic and trigono- metric tables. Faced with this monumental task, De Prony had innovatively applied Adam Smith’s (1723–1790) analysis of the division of labor (Smith, 1776, chap. 1), developed for traditional manual work, to what was a mental task. He established three sections of mental laborers: The first section was to consist of the best mathematicians in the land, who would seek out or develop the easiest methods of calculating the functions desired; the second section, consisting of six or eight junior mathematicians, would take the formulae developed by the first section and plug in the actual numbers required; the third section, made up of 60 or 80 people who could only add and subtract, would do the actual computations and return the results to the second section for checking. Babbage, in chapter 20 of his 1832 book On the Economy of Machinery and Manufactures, hints that his Difference Engine could replace the whole third section of laborers in De Prony’s system. It is notable, however, that throughout the chapter the emphasis is on efficiency and economy; the nature of mental processes themselves is never at issue.