[First published in Green, C.D., Shore, M., & Teo, T. (Eds.) (2001). The Transformation of Psychology: Influences of 19th-Century Philosophy, Technology, and Natural Science (pp. 133-152). Washington, DC: American Psychological Association.]

© 2001 by the APA

Charles Babbage, the Analytical Engine, and the
Possibility of a 19^th-Century Cognitive Science

Christopher D. Green
York University
christo@yorku.ca

Charles Babbage (1791-1871) is widely-known today as the inventor of several machines that were mechanical precursors of the modern electronic digital computer. He frequently receives mention in introductory computer science texts, and is often called the "inventor of the computer," or the "first computer scientist." Alongside of such celebratory blurbs about Babbage, one can often find brief accounts of Ada Lovelace (1815-1852), who is known primarily for having published a series of notes about one of Babbage's machines -- the Analytical Engine. In recent years, both figures have expanded their range from computer science textbooks to cognitive science textbooks as well. They are typically described as having foreshadowed the foundational article of faith of cognitive science, viz., that human brains are, in essence, biological computers, and that human thought is nothing more than the running of a program on such a computer.

In this paper I try to evaluate the claim that Babbage and Lovelace were cognitive scientists "ahead-of-their-time." In the first half I describe the historical events leading up to Babbage's invention of the Analytical Engine and the publication of Lovelace's notes about it. In the second half I turn to an examination of the contents of her notes, as well as the oft-forgotten article to which they were appended and to the writings of Babbage himself, in order to discover to what degree any of them had in mind what is commonly attributed to them by the cognitive scientists of today.

1. The Invention of the Analytical Engine

The September 1843 issue of Richard Taylor's Scientific Memoirs -- an English journal that specialized in communicating Continental European scientific activities to the British scientific community -- contained an anonymous translation of an article by an unknown Italian military engineer, Luigi Frederico Menabrea (1809-1896). The article had originally been published a year before in French in the Swiss journal, Bibliothèque Universelle de Genève. Menabrea would later go on to become a general in Garibaldi's army, and eventually Foreign Minister and Premier of the newly-unified Italian state, but in the early 1840s that was all still years away. A little ironically, the article was about a machine then being constructed in London by an Englishman, Charles Babbage, called the "Analytical Engine."

The article was based upon a series of lectures that Babbage had given about his invention in Turin, Italy, in 1840 at the invitation of the prominent Italian scientist Baron Giovanni Plana (1781-1864). The machine was not yet built -- indeed it would never be built -- but Babbage had come equipped with reams of drawings, diagrams, and other documents hoping to generate excitement about his new project on the Continent that he had found himself utterly unable to generate in his native land. Babbage's expectation seems to have been that the highly-respected Baron Plana himself would write an article about the lectures, thereby giving Babbage and his new Engine a stamp of legitimacy that even the nationalistic English would have to recognize, but this was not to be. Plana -- then over 60, 10 years Babbage's senior -- begged off the job, pleading ill-health, and gave it to his younger colleague, Menabrea, who was then about 30, 20 years Babbage's junior.

The article was an enthusiastic endorsement of the Analytical Engine and its prospective powers. It began, however, with a strong warning to the reader not to confuse it with Babbage's earlier, better-known project, the "Difference Engine." The warning was well-placed. Everyone who mattered in England knew of the fiasco surrounding the attempt to build that machine, and it was important, if Babbage was to earn back the confidence of the his own scientific community, and ultimately of the British Government, that the two be distinguished from each other.

Babbage's reputation as a man of science to be watched was established early, when as a student at Cambridge he and two of his friends -- John Herschel (1792-1871), son of the discoverer of Uranus (1781) William Herschel (1738-1822), and George Peacock (1791-1858), who would later become Dean of Ely -- formed the Cambridge Analytical Society in 1812. The primary mission of the Society was to replace the calculus notation entrusted to the British mathematical community by Isaac Newton (1642-1727) just over a century before with the notation developed by Leibniz (1646-1716). The upholding of the Newtonian notation was a matter of some national pride for the British, for the nasty priority dispute between Newton's and Leibniz's partisans over the discovery of calculus still echoed in the very traditional halls of Cambridge. Unfortunately for the British, Newton's notation was difficult to manipulate algebraically, and they were now some 50 years behind the mathematical developments of their Continental colleagues, who had of course used Leibniz's notation from the first. Babbage, Herschel, and Peacock aimed to put a stop to what they called the "dot-age" of Cambridge (a satirical reference to the dots used to indicate derivatives in the Newtonian notation) and replace it with the "pure d-ism" of Leibniz (who used the letter "d" to indicate the same).[1]

In 1816 they published a translation of a Continental textbook on calculus, Sylvestre-François Lacroix's Traité du Calcul Différentiel et du Calcul Intégral (1810), and with the help of William Whewell (1794-1866) -- who, though an ally, never seems to have been an actual member of the Analytical Society -- managed to change the notation used in the Cambridge math exams. By the 1820s, in the wake of a slew of new papers demonstrating the power of the Leibnizian notation, the revolution was complete. 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, Herschel, and a number of other "entrepreneur-scientists" (see Ashworth 1994; Fancher, this volume [p. 5 of ms.]) formed the rival Astronomical Society in 1820. Sir Joseph Banks (1743-1820), then President of the Royal Society for over 40 years, opposed them as he opposed the establishment of most scientific societies dedicated to special topics within science. He would die within the year, however, and the nascent Astronomical Society had access to old William Herschel's giant 40-foot reflector telescope, so there was no stopping the upstart group. 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. Although the Astronomical Society won the debate (the Board, headed by physicist Thomas Young, folded in 1828), they managed to alienate many in the Royal Society, and Babbage's career as an irritant to the establishment, as well as his reputation as a bit of a crank, was underway.

While busy discovering the 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 which he won the Astronomical Society's "Gold Medal" for the year 1823. He applied for assistance to the Royal Society, the Presidency of which had been assumed by Humphrey Davy (1778-1829), to build a full-scale version of the Engine. Davies Gilbert, the Royal's treasurer, lobbied the government on Babbage's behalf. Tory Robert Peel, then Home Secretary, likened the machine to the Trojan horse and refused to support it. The Duke of Wellington, however, recognized its potential, and requested the Chancellor of the Exchequer to supply £1000 for its construction in 1823 (Hyman, 1982, p. 52).

The money was long in coming, but was eventually received. 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), so the Government, exasperated, finally suspended the project (officially withdrawing their support in 1842). Peel is reported to have quipped that, if ever completed, the Engine should first be set to calculating how much money went into its construction.

The difficulties had not been entirely Babbage's fault. The Engine had turned out to be far more difficult to engineer than he had expected. He had toured the factories of England, researching the means to make its construction more efficient. Then, in 1827, his wife of 13 years had died suddenly, as did his father and one of his children. In his grief he had toured Europe through much of the next year. Never one to stop working completely, however, he devoted much of his travel to studying Continental means of industry and manufacture. While in Europe he was awarded the Lucasian Chair in mathematics at Cambridge, Newton's old position.

The early 1830s were, of course, a time of great political upheaval in England. The first of the Great Reform Bills was passed in 1832, transferring the bulk of the vote from the outlying boroughs to the urban industrial centers, and enfranchising nearly a quarter of a million middle class citizens. Babbage, a banker's son, was naturally on the side of reform, chairing the election committee of reform-advocate William Cavendish in Cambridge in 1829 and 1831, and standing for parliament himself in north London (Finsbury) in 1832 and 1834. He saw himself as attempting to engineer similar "liberalizing" reforms within science as well. In 1830 he published Reflections on the Decline in Science in England, an overt attack on the Royal Society, and in particular on its new president, Davies Gilbert, the very man who had lobbied the government on behalf of the Difference Engine a decade before (see, e.g., Patterson, 1983, pp. 55-68).

In 1832, he published On the Economy of Machinery and Manufactures. The relation of this book to his work on the Difference Engine is made clear in the very fist sentence:

The present volume may be considered as one of the consequences that have resulted from the calculating engine, the construction of which I have been so long superintending. Having been induced, during the last ten years, to visit a considerable number of workshops and factories, both in England and on the Continent, for the purpose of endeavouring to make myself acquainted with the various resources of mechanical art, I was insensibly led to apply to them those principles of generalization to which my other pursuits had naturally given rise.

That would not be the end of his discussion of the Engine either. In Chapter 20 he described, in very approving terms, the system set up by Marie de Prony (1755-1839) in Revolutionary France for the calculation and publication of new logarithmic and trigonometric tables. Faced with this monumental task, De Prony had applied Adam Smith's (1723-1790) analysis of the division of labor (Wealth of Nations, 1776, Chap. 1) to what was a mental task, rather than to traditional manual labor. He established three divisions of 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 sixty or eighty people who could only add and subtract, would do the actual computations, and return the results to the second section for checking. This procedure, Babbage famously concluded,

enables us to purchase and apply to each process precisely the quantity of skill and knowledge which is required for it: we avoid employing any part of the time of a man who can get eight or ten shillings a day by his skill in tempering needles, in turning a wheel, which can be done for sixpence a day.

The middle third of the same chapter consists of Babbage's description of his Difference Engine and hints that alone it could replace the whole third division of laborers in De Prony's system. He closes with a brief comparison to the way in which labor is divided in a mine, leaving no doubt of his intentions -- even when the "raw materials" and "finished products" are mental the same industrial principles apply as would in a factory. It is notable as well that throughout the chapter the emphasis is on efficiency and economy; the nature of mental processes themselves is never at issue. As we shall see, Babbage seems to have assiduously and subtly dodged the question of the nature of the mind throughout his career.

The Economy of Machinery was probably the most important work of Babbage's career. Its publication was instrumental in his being asked to run for Parliament in 1832. It was read by Karl Marx in 1847, the year before the publication of the Communist Manifesto (1848), and Marx would cite it in both The Poverty of Philosophy (1847) and in Das Kapital (1867). It was also quoted extensively in John Stuart Mill's Principles of Political Economy (1848).

It was in the following year, in 1833, that he first met Ada Byron, the only legitimate child of the poet Lord Byron, who had died in fighting for the freedom of Greece nine years earlier. Ada had never known her father. He had left Lady Byron when Ada was only a month old, and had left England forever five months later. Nevertheless, her father's shadow preceded her wherever she went, and in 1833, at the age of 17, she was enjoying her first London season. Among other things, Babbage was well known for his Saturday soirées, and Lady Byron and her daughter were invited along with much of London Society. Babbage's scale model Difference Engine was displayed along with other mechanical devices of a more obviously entertaining nature.

Lady Byron recorded that in mid-June 1833 they went to see what she called "the thinking machine (for so it seems)" at Babbage's house (cited in Stein, 1985, p. 42). This is particularly interesting because Babbage seems to have always carefully avoided saying that his machine could actually think. What Lady Byron's remark shows, though, is that the idea was "in the air" even if Babbage had not put it there, or even wanted it there. Lady Byron also recorded that Babbage demonstrated the machine calculating squares and cubes for his guests, and then showed how it could count up to 10,000 by ones, but without any apparent change in its operation, suddenly start increasing the gap between numbers by one at each count: 10,002, 10,005, 10,009, etc. He would later use a very similar example in his Ninth Bridgewater Treatise (1837) to argue, contra Hume and others, that miracles could be "programmed" into the mechanism of nature (i.e., that they need not be truly "supernatural" -- except in as much as God had "programmed" the mechanism in the first place).

Another of Babbage's guests, Sophia Frend, records in her memoirs:

I well remember accompanying [Ada Byron] to see Mr. Babbage's wonderful analytical engine. While other visitors gazed at the working of this beautiful instrument with the sort of expression, and I dare say the sort of feeling, that some savages are said to have shown in first seeing a looking-glass or hearing a gun … Miss Byron, young as she was, understood its working, and saw the great beauty of the invention. She had read the Differential Calculus to some extent. (cited Stein, 1985, p. 41)

This passage is often trotted out to demonstrate Ada Byron's precocity, but it is not to be trusted. It was written nearly 50 years after the events took place, and given that Babbage had not yet even conceived of the Analytical Engine, much less built one, it is clear that she is mistaken about some of the details. Moreover, Lovelace had not yet begun to study calculus, and would not until 1840.

Sophia Frend was, however, one these "nexus people" who, although not eminent in her own right, had strong connections to virtually all the major players in this story. She was a lifelong friend of Lady Byron's, and the daughter of the mathematician, William Frend, who had tutored Lady Byron in basic mathematics when she was just young Annabella Milbanke (the tutoring that had led Lord Byron to refer to her endearingly as his "Princess of Parallelograms" when courting her and, not so endearingly, as the "Mathematical Medea" when leaving her). William Frend had later been hired by Lady Byron herself to teach Ada mathematics for a time as well, but he had not taught her any calculus. His mathematical views were quite old-fashioned. He had not been a participant in the revolution wrought by Babbage and his Cambridge colleagues. Sophia Frend would soon marry one of the prime inheritors of the new mathematical landscape, however -- Augustus De Morgan (1806-1871), the man more responsible than anyone but perhaps George Boole (1815-1864) for developing the abstract algebra that is the conceptual foundation not only of modern mathematics and logic, but also of modern computational theory. What is more, it was DeMorgan who, between 1840 and 1842, would actually teach Ada calculus.

Ada was a regular guest in Babbage's home, often accompanied by Mary Somerville (1780-1872), a family friend and the most accomplished British woman scientist of her day. Somerville was so highly respected by the Royal Society for her translation of Laplace's Méchanique Céleste (trans. 1831) and for her own book On the Connexion of the Physical Sciences (1835), that a bust of her was placed in the Royal's entrance hall. They never let her officially join the Society, however, because of her sex. In any case, there is no indication of any intellectual collaboration between Ada Byron and Babbage at this time. Babbage was just on the verge of conceiving of the Analytical Engine, and Ada's life was about to become very busy indeed.

In 1835 she married William King, an old school chum of Somerville's son, Woronzow Greig. In 1836 she had her first child, a son. In 1837 she had her second child, a daughter. During the first half of 1838 she was struck down with a serious illness, possibly cholera. In the summer of 1838, her husband was raised to Earl of Lovelace by the newly-crowned Queen Victoria, and she to Countess of Lovelace. In 1839, she had her third and final child, a second son. Only then, in the fall of 1839, looking to return to the mathematical studies of her youth (and strongly encouraged to do so by her mother and husband, who both thought it would act suppress her supposed "Byronic tendencies"), did she write to Babbage, asking if he knew someone who might be able to teach her calculus. Ignoring the implicit invitation, he said he did not but that he would keep an eye out. Finally, in June of 1840, Augustus De Morgan, who had since married Sophia Frend, and who was just then in the process of publishing his own calculus textbook in serial form, agreed to tutor her by correspondence.

At the time De Morgan was also a leading figure in a mathematical revolution of perhaps even greater magnitude than that led by Babbage, Herschel, and Peacock more than two decades before. He, along with Peacock, Whewell, and a few others were putting forward the argument that algebra, far from being merely a technique for manipulating mathematical expressions, is a discipline of its own concerned with formal relations among symbols in general, and not necessarily mathematical at all. The issues were quite intricate (see e.g., Fisch, 1994, Richards, 1987, 1991, 1994), but John Passmore captured the gist of the debate extraordinarily clearly when he wrote:

They denied, in the first place, that in such an algebraic law as

a+b = b+a

a and b need stand for quantities. Anything whatever could be substituted for a and b, they said, provided only that it satisfy this law. And to the contention that only quantities could satisfy it, since only quantities are addible, they replied that the plus sign need not stand for addition: it could signify any relation of such a kind that when it is substituted for the plus sign this law still holds. To take De Morgan's example, the plus sign could mean 'tied to', since if a is tied to b, then also b is tied to a. Thus a+b is still equal to b+a. (Passmore, 1957, p. 122)

During the middle and late 1830s, Babbage began developing a design for a new machine he called the Analytical Engine. Unlike the Difference Engine, which could only calculate functions reducible to the method of differences, the Analytical Engine would be able to calculate any function whatsoever. Indeed, he often claimed that ultimately it would be able to carry out symbolic algebra, then considered to be one of the highest forms of rational thought known. To accomplish this extraordinary task, Babbage adapted the technology developed by Joseph-Marie Jacquard (1752-1834) in his famous automated loom of 1801: he would lash cards together end-to-end and punch holes in them that could be "read" by a number of moveable pins in the machine. The holes would "encode," as we would now say, information about which operations to employ over which symbols. Given a sophisticated enough control system for the cards, one would be able to repeat the same set of cards an indeterminate number of times (now called "looping", but he called it "backing" the cards), and one would be able to decide which cards to execute on the basis of intermediate results obtained during the computational process (now known as "conditional branching"). Both processes are central to modern computing theory.

Babbage attempted to obtain support for his new project, but found it impossible to do so. Few understood the potential of the new invention. Few of those who did, thought it would be practicable to build a machine so complex. Fewer still believed that Babbage was the man to finish the project, given the fiasco with the still-unfinished Difference Engine, even if the machine were buildable in principle. Babbage began on his own nevertheless. He hired draftsmen and engineers, and converted his own coach house to a workshop so he could oversee the work more closely than he had with the Difference Engine. Then, in 1840, Babbage received the invitation from Plana to lecture on the new Engine in Turin. He jumped at the chance to earn the endorsement of a prominent European scientist. After returning to England in November of 1840, Babbage spent a good deal of 1841 corresponding with Menabrea about the article he would write based on Babbage's lectures, prompting the young Italian to entirely rewrite his article at one point (Hyman, 1982, p. 190). In short, Babbage's hand was not far from the article written under Menabrea's name. Babbage's involvement was well-known at the time as well. So closely was his connection with the Menabrea paper thought to be that more than a decade later, William Parsons, Earl of Rosse (1855), described it in his 1854 Presidential Address to the Royal Society as explaining Babbage's views.[3]

In January of 1842 Menabrea wrote to Babbage that the final version of the article was ready to go to the Bibliothèque Univeselle, and, as mentioned at the beginning of this paper, it appeared in October of that year. Being written in French, and in a Swiss journal, however, it was not destined to have much impact on the English scientific community nor on the government on which Babbage depended.

In February of 1843, Charles Wheatstone -- co-inventor of the telegraph, and a friend of both Babbage and the Lovelaces -- suggested to Ada that she produce an English translation of Menabrea’s article for Taylor’s Scientific Memoirs. According to Babbage, when Ada presented him with the completed translation, the preparation of which he had not been previously aware, he asked why she had not written, instead, an original article of her own. She is said to have replied that the idea had never occurred to her. He reports that he then suggested that she write some notes explicating parts that Menabrea had left vague or that had been since superseded by new developments. He and Lovelace worked closely on the notes throughout the spring and summer of 1843. Dozens of letters and drafts flew back and forth between Lovelace and Babbage, and personal meetings were frequent. The question of how much of them, in the final analysis, is original to Lovelace and how much is really Babbage’s ideas communicated through her is a subject of continuing controversy. The notes, more than twice as long as the article to which they were appended, were completed by August of 1843, and were published the following month. Although the translation was anonymous (as was common for translators of the day, both male and female), each note was followed by the initials "A.A.L." Their authorship, however, was an open secret in the London scientific community.

2. Was the Analytical Engine Thought to be Cognitive?

Ada Lovelace's translation of, and notes to, Menabrea's article did not have the impact that Babbage must have hoped they would. Although Lovelace was a bright person, to be sure, she was not a serious scientist or mathematician. She had never before published a scientific article, nor would she publish another in the remaining nine years of her tragically short life. There can be little doubt that Babbage's main goal in working with Lovelace was to have a public show of support from a member of the nobility who might have some influence on the government. There was talk at the time, apparently begun by Wheatstone, of having Lovelace tutor Prince Albert in the sciences. What better influence over governmental science policy could there have been? It came to nothing, however.

The article, though received well in its day, was soon forgotten, as was Babbage for the most part. It was not until modern computers began to be developed that his work was really "rediscovered." Howard Aiken, the designer of the Harvard Mark I computer in the 1940s repeatedly paid homage to Babbage, and claimed to have been the one to finally fulfil "Babbage's Dream," as he often put it, but it is reasonably certain that he knew little of Babbage's actual designs, nor did the architecture of the Mark I owe anything to that of the Analytical Engine (indeed, the Mark I was not capable of conditional branching, and thus was really a giant calculator rather than a true computer). It was simply a way of lending historical legitimacy to the Mark I project (Cohen, 1988). He seems to have not even been aware of the Lovelace translation and notes until well after the project was complete. There is a brief mention of Lovelace in Douglas Hartree’s (1949) Calculating Instruments and Machines, but it was Alan Turing’s classic article “Computing machinery and intelligence” (1950) that put her back in the public mind, claiming that she had been the first to object that computers can never be truly original, but can only do what we program them to do. Soon thereafter, Bertram Vivian Bowden used her image in the frontispiece of his edited volume, Faster Than Thought; A Symposium on Digital Computing Machines (1953), as well as presenting the first modern account of Lovelace's work, and reprinting her full translation and notes for the first time in almost 70 years. He seems to have inspired the now-common claim that she was the first computer programmer (though he didn't quite make it himself), an honor which almost certainly should fall to Babbage.

Since then, she and Babbage have been frequently made to play the role of "trail-blazers" in books and articles not only about computer science, but in those about cognitive science as well (e.g., Gardner, 1985; Garnham, 1987; Haugeland, 1985; Hofstadter, 1979; Pylyshyn, 1984). The question is, then, whether this status is really justified. Were either Babbage or Lovelace of the opinion that the Analytical Engine really would have been able to think -- like humans think -- if it had been completed. In this half of the paper I try to show that Babbage seems to have been wary of answering this question straightforwardly throughout his life. Lovelace sometimes wrote as if she believed it to be true, but at other times makes what appear to be forthright denials of the possibility. Given that Babbage had so much influence over her writing, it is interesting to speculate about why he allowed her to occasionally stray over this line if he was unwilling to do so himself. One reason he restrained himself may have been, or so I will argue, that for him to have done so would have made him appear to endorse mechanistic materialism. To this his religious convictions would seem to have been opposed, and it would likely have been tantamount professional suicide in early Victorian England (see, e.g., Winter, 1997). First I will examine the Menabrea/Lovelace paper for indications of the kind of cognitive theory, if any, that is contained therein. Then I will survey Babbage's comments on the topic, and offer an interpretation of them.

Menabrea opens his paper by claiming that the tasks of mathematics may be divided into two parts, "one of which may be called the mechanical,…while the other demanding the intervention of reason, belongs more specially to the domain of the understanding" (Morrisons' 1961 edition, p. 225). Machinery, he went on almost analytically, may be employed to execute the mechanical portion of mathematics. After a brief mention of Pascal's mechanical adding machine, Menabrea then reviewed the portion of Babbage's Economy of Machinery in which De Prony's scheme for producing mathematical tables was discussed, and stated outright that the third section of workers could be replaced by the Difference Engine (which he described in terms very much like those in Babbage's earlier treatise). Here Lovelace inserts her first note. She first takes pains to deny that the Analytical Engine has any relation whatever to the Difference Engine -- a claim that Babbage needed to make stick if he were to have people take seriously his pleas for support for the new project. She then goes on to describe the difference between them as follows:

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated….

It may be desirable to explain that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may…. In abstract mathematics, of course operations alter those particular relations which are involved in the consideration of number and space…. But the science of operations … is a science of itself and has its own abstract truth and value; just as logic has its own particular truth and value, independently of the subjects to which we apply its reasonings and processes. (pp. 247-248)

Here we have a fairly standard formulation of the new formal approach to algebra then being pioneered by Lovelace's calculus teacher, De Morgan. One would expect that Lovelace learned this orientation toward algebra from De Morgan himself, but there is little discussion of such theoretical issues in the letters between them dating from the time he was teaching her calculus. One of the books De Morgan assigned her to read, however, was George Peacock's Treatise on Algebra (1830) in which the revolutionary distinction was first made between "arithmetical algebra" -- the traditional manipulation of numerical expressions via symbols -- and "symbolic algebra" -- a new general discipline of abstract symbol manipulation, of which the arithmetical form was but a single application. Even more interestingly, Babbage himself had written a manuscript in 1821 entitled "The Philosophy of Analysis" which anticipated many of the algebraic ideas put forward by Peacock almost decade later. Why Babbage never published "The Philosophy of Analysis" remains unknown -- he seems to have become distracted by other projects such as the building of the Difference Engine -- but it is known that Peacock, a core member of Babbage's "Analytical Society" at Cambridge, read the manuscript in May of 1822 and found it to be "of very great interest" (see Dubbey, 1978, chapter 5, esp. pp. 95-107).[4]

Returning to consideration of Lovelace's Note A, she moves on to exemplify her claims about abstract algebra with what would become one of her most quoted claims:

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

The Analytical Engine is an embodying of the science of operations…(p. 249)

Today this passage is often mistaken for the claim that the Engine would be "intelligent" enough to compose music, but that is not really its thrust at all. The aim is to drive a wedge between abstract algebra -- the "science of operations" -- and mathematics; to show that the operations can operate over symbols representing objects other than numbers, such as musical notes (however, see Anderson, this volume, on the use of musical metaphors with respect to the mind during this era).

After describing the differences between the two Engines even more fully, she then makes a claim that might seem to virtually commit her, and perhaps Babbage, to mechanistic materialism with respect to the mind (at almost the very moment that Helmholtz, Brücke, Bois-Reymond, and Virchow were declaring themselves to be mechanists in Berlin):

In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental process of the most abstract branch of mathematical science…. We are not aware of its being on record that anything partaking in the nature of what is so well designated the Analytical Engine has been hitherto proposed, or even thought of, as a practical possibility, any more than the idea of a thinking or of a reasoning machine.

Notice how she seems to claim outright that the Analytical Engine serves as a "uniting link" between mind and matter, but then at the end of the passage seems to back away, saying that no one had else had yet proposed a machine like the Analytical Engine any more than they had proposed a thinking machine: an apparently literal claim is reduced to a mere analogy. The last third of Note A is devoted almost exclusively to defending Babbage's actions with respect to the still-unbuilt Difference Engine over the previous decade.

Returning to Menabrea's original text, having just stated that the Difference Engine could replace De Prony's third section of workers -- those who actually carry out the calculations -- he goes on then to virtually claim -- though he is not completely explicit -- that the new Analytical Engine could replace the second section as well -- those who plug the numbers into the formulas produced by the expert mathematicians in the first section. He is careful to point out, however, that the machine, "must exclude all methods of trial and guess-work, and can only admit the direct process of calculation." This is necessarily the case, he goes on to say, because "the machine is not a thinking being, but simply an automaton which acts according to the laws imposed upon it" [emphasis added] (p. 230). This would seem to close the matter definitively, but Lovelace added a footnote to this passage, saying that "this must not be understood in too unqualified a manner. The engine is capable, under certain circumstances, of feeling about to discover which of two or more possible contingencies has occurred…" [emphasis added]. What exactly she meant by this is not entirely clear, but she appears to be referring to the Engine's conditional branching ability. Why she takes this to manifest itself as a "feeling" is anyone's guess, though Babbage's occasional picturesque references to this power as "foresight" may be the cause.

So already we can see a tension between two different ways of viewing the machine. On the one hand, according to Lovelace, it "unites" matter and mentality. She cannot quite bring herself to calling it a "thinking machine," but she's willing to say that it "feels" in some sense. On the other hand, according to Menabrea, it is definitely not a "thinking being"; just an automaton. Under other circumstances one might regard this simply as a difference of opinion, but since both these writers had one and the same mentor -- Charles Babbage -- a more interesting dynamic may be at play.

Menabrea says nothing more about the possible relation between the operation of the Analytical Engine and that of the human mind in the rest of his article, but Lovelace includes one more major speculation in her notes -- the passage Turing would call, over a century later, the "Lovelace Objection" to artificial intelligence:

It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine. In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable.

The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. (p. 284)[5]

If there were ever a question of Lovelace's believing that the machine would actually be able to think, this passage would seem to scotch it -- certainly Turing thought so -- but in combination with her earlier statements about it unifying mind and matter, and its being able to feel, it is hard to know exactly what opinion to attribute to her, or to her mentor, Babbage.

Babbage's comments on the topic were usually very careful. He almost invariably referred to the machine's activities as being able to "replace" or "substitute for" mental activities, or as being "analogous" to mental activities, but only very rarely as being able to carry them out itself. For instance, in his autobiography (Babbage, 1864/1994), in the midst of a discussion of his problems with mechanizing the process of "carrying" from one column of numbers to another in addition problems, he says, "the mechanical means I employed to make these carriages bears some slight analogy to the operation of the faculty of memory" (p. 46).[6] With this deflationary statement in place, he says later on the same page that "it occurred to me that it might be possible to teach mechanism to accomplish another mental process, namely -- to foresee" (p. 46). He then goes on to explain what we would call conditional branching.

What are we to think of Babbage's "true" beliefs on the matter? Was the first comment about memory a mere "foot in the door" that would allow him to slide to the stronger claim about foresight, or is the claim about foresight to be regarded as a mere "shorthand" for his real position, given just above it, that the activities of the machine are only "slightly analogous" to mental activities? In a paper of 1837 entitled "On the mathematical powers of the calculating engine" (that went unpublished until 1973) he wrote in a footnote,

In substituting mechanism for the performance of operations hitherto executed by intellectual labour it is continually necessary to speak of contrivances by which certain alterations in parts of the machine enable it to execute or refrain from executing particular functions. The analogy [emphasis added] between these acts and the operations of mind almost forced upon me the figurative [emphasis added] employment of the same terms. They were found at once convenient and expressive and I prefer continuing their use rather than substituting lengthened circumlocutions.

For instance, the expression 'the engine knows, etc.' means that one out of many possible results of its calculations has happened and that a certain change in its arrangement has taken place by which it is compelled to carry on the next computation in a certain appointed way. (Babbage, 1989, vol. 3, p. 31)

An even more interesting passage occurs in the posthumous biography of Babbage written, at his direction, by his long-time friend Harry Wilmot Buxton (not published until 1988). It begins as though a profound claim concerning the intelligence of the Engine is about to be defended:

It is manifest that the language of algebra is more simple and precise than the symbols of language expressed by sound, and it would seem therefore within the range of our intelligence to be able to reduce our thoughts in most cases into the form of mathematical language, and thus adapt the subject of our enquiry to the operations of the Analytical Engine. (Buxton, 1988, p. 155)

Buxton then goes on, however, to make a rather vague claim about Babbage's aspirations in this regard -- "Mr. Babbage entertained no doubt of the possibility of extending the powers of the Analytical Engine, far beyond the domain of abstract analysis" (p. 155) -- and then he immediately shifts to a very long quotation from Hobbes in which it was claimed that reasoning is nothing more than calculation. Buxton then suggests that the Analytical Engine could have established Hobbes' claim if only it had been equipped with letters of the alphabet and the plus and minus signs, in addition to numerals. Having gotten this far, however, he closes with the admission that "as Mr. Babbage himself has not recorded his views upon the subject, it might be deemed presumptuous to indulge in speculations or enter into details which he did not deem necessary" (p. 156). So it would appear that even Babbage's closest friends were not of the opinion that he believed his machines to be literally intelligent.

Conclusion

In this paper I have attempted to establish that, contrary to what is often found in textbooks, Babbage did not believe the Analytical Engine to have been a contribution to what we would now call cognitive science. Why might Babbage have refrained from taking such a step? Such speculation was rampant about him: Lady Byron had called even the lowly Difference Engine a "thinking machine"; Buxton certainly entertained the idea that human reasoning might be nothing more than what the Analytical Engine was intended to do; even Ada Lovelace intermittently raised the possibility. What held Babbage back?

Two things come immediately to mind. The first is that in Regency and early Victorian England, declaring oneself to be a mechanist materialist with respect to the mind would have been professionally foolish in the extreme. Allison Winter (1997) has written a fascinating chapter on the philosophical traps of this sort that the physiologist William Benjamin Carpenter -- who, incidentally, briefly served as tutor to the Lovelace's children -- had to avoid in launching his career during the 1830s and 1840s; dangers that, for instance, John Eliotson, the famed mesmerist, had failed to negotiate effectively, leading to his resignation from University College in 1838.

Tempting as it might be, however, one should not conclude that Babbage somehow "secretly" believed the Analytical Engine to be truly intelligent, but would not say so publicly for fear of the censure of his community. Babbage, though liberal, appears to have been a sincerely religious man, as were his closest colleagues: Whewell was a minister, Peacock was ordained and turned explicitly to questions of theology in the 1830s, and even Herschel's work has been described as evincing an attitude of "steadfast piety" (Richards, 1992, p. 55; also, contrast this with the attitude, described in Fancher (this volume) of the English scientist who reached intellectual maturity in the wake of Darwin's Origin of Species). When Whewell's Bridgewater treatise was published in 1833, the first in a series of works commissioned explicitly to defend the thesis (primarily against Hume) that God's hand can be discovered in the organization of the natural world, Babbage felt compelled to write a book-length response, his so-called Ninth Bridgewater Treatise (1837). Significantly, Babbage's objection to Whewell was not that he defended "natural theology" as it was then called, but rather that Whewell had argued that nothing of the divine could be found in the "deductive" sciences, but only in "inductive" forms of knowledge. Babbage was incensed, not only because this excluded the truths of mathematics from the realm of "divine truths" -- a position Babbage was keen to defend -- but also because the intent of Whewell's remarks was to devalue the work of recent Continental scientists (e.g., Euler, Laplace, Lagrange). Babbage thought these to be the very examples to which the English should look to improve their science. Whewell, however, favored the work of much earlier "divinely inspired" (in Whewell's opinion) scientists such as Copernicus, Kepler, and more importantly -- because more British -- Boyle and Newton (Richards, 1992, pp. 60-61). Although Babbage argued that miracles might be the result of a "divine mechanism" the underlying principles of which we humans can only partially comprehend, his suggestion was not that God Himself is such a mechanism; it was, by contrast, that only a divine intelligence could craft a mechanism so intricate as that found in nature.

To conclude then, Babbage does not seem to have regarded the Analytical Engine as a kind of intelligence, or even as revealing anything of particular significance about the nature of the human mind. Attributions of such opinions to him by modern cognitive scientists and their intellectual kin are primarily anachronistic. His primary interests in his Engines were industrial and economic. He saw them as bringing the very same principles of division of labor to the realm of mental work that he supported in the realm of manufacture. Indeed, one might argue that the powers of his Engines served to distinguish precisely between those aspects of the human mind that were thought to be merely mechanical and those that were regarded as being truly original, creative, rational, and ultimately divine in character.

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Footnotes

[1] Cambridge mathematician Robert Woodhouse has earlier used the Continental notation in his Principles of Analytical Calculation (1803), in which he attempted to reformulate Lagrange's (1797) approach to the foundations of calculus (see Dubbey, 1978, chap. 2), but his work had little impact on the practices of English Mathematicians of the day. Indeed Woodhouse moderated four mathematics examinations at Cambridge between 1804 and 1808, employing the old Newtonian fluxionary notation in each (Dubbey, 1978, p. 37).

[2] A point often glossed over is that the revolution Babbage instigated in mathematical notation was grounded in a Lagrangian approach to the foundations calculus, under which "evanescent" quantities, such as Newton's "fluxions," Leibniz's "infinitesimals," and D'Alembert's "limits," were replaced by the less controversial polynomial approximations of continuous functions made possible by Taylor's Theorem -- precisely what the Difference Engine used for its computations. Thus, Babbage's first calculating machine and his earlier work on calculus were closely connected conceptually.

[3] Indeed, the French translator of the speech for the journal Cosmos, rendered the passage such that Babbage himself had written it under the pseudonym of "Menabrea." Menabrea (1855/1989) himself felt compelled to respond insisting that he was, in fact, the true author.

[4] Beecher (1980) has argued that the algebraical innovations of both Babbage and Peacock were prefigured in the work of Robert Woodhouse (1803), with which they were both very familiar. Woodhouse preceded Babbage as Lucasian Professor of Mathematics at Cambridge (Newton's old chair), and died in 1827, less than three years before the publication of Peacock's Algebra.

[5] It is interesting to compare these words to some written by Babbage about the Analytical Engine two years earlier, in 1841: "It cannot invent. It must derive from human intellect those laws which it puts in force in the developments it performs. It cannot, in fact, do anything more than perform with absolute precision and in much shorter time those series of operations which the hand of man might itself much more imperfectly accomplish" (cited in Collier 1990, p. 178 from Vol. VII the papers deposited by H.M. Buxton at the Museum of the History of Science, Oxford).

[6] Note the relation here to the concepts of memory employed in later decades by Wundt and Ebbinghaus, described by Danziger (this volume). Ebbinghaus might have been quite happy to call this actual memory, whereas Wundt would likely have scoffed at the idea.