Was
Babbage's Analytical Engine an
Instrument of Psychological Research?
christo@yorku.ca
This paper is an abridgement of "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 (pp. 133-152).
Abstract
Charles Babbage
(1791-1871) began work on a mechanical computer that he dubbed the Analytical
Engine in the mid-1830s. The machine was
to constitute a dramatic improvement on his earlier Difference Engine, which he
had originally conceived primarily as a way of automating the process of
computing and printing accurate mathematical tables. Almost from the beginning, however, people
around Babbage described his inventions in ways that suggest they believed the
machines to be endowed with, or at least to closely model, authentic mental powers.
Even today, one regularly sees the Analytical Engine cited as an early attempt
at computational cognitive science.
Babbage himself, however, seems to have steadfastly refrained from
making public claims regarding the putative mentality of his machines. Despite his own reluctance to publicly
endorse the idea that he had developed a "mechanical mind," he does
not seem to have prevented, or even discouraged, those who worked with him from
mooting the idea in their own publications on the topic. This paper
investigates whether (1) the Analytical Engine was indeed the focus of a covert
research program orchestrated by Babbage into the mechanism of mentality, (2)
Babbage personally opposed the idea that the Analytical Engine was kind or
model of mentality but allowed his colleagues to speculate as they saw fit, or
(3) Babbage personally believed such claims to be fanciful, but cleverly used
the publicity they engendered as a means of drawing 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. 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 and a Swede named Georg
Scheutz, built a cut-down version of the Difference Engine in the 1850s.
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
"forefathers" of computer science.
This trend began with the public pronouncements 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 fulfil "Babbage's Dream," as he often put it.
More recently there has been a trend to cite Babbage as a father of
computational cognitive science as well (e.g., Gardner, 1985; Garnham, 1987;
Haugeland, 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 paper 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.
1. The Origins of the Engines
Babbage had first made a name for himself in the late-1810s when he led a
mathematical revolution at
In the late 1820s, Babbage toured
It was in 1833 that he first met the future Ada Lovelace, then known as Ada
Byron, the only legitimate child of the poet Lord Byron. Then aged 17,
During the middle and late 1830s, Babbage began developing a design for 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. Babbage began on his own nevertheless. In 1840 he was invited by the
well-known Italian scientist Giovanni Plana to give series of lectures on the
Analytical Engine in
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 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
royal court. It came to nothing, however.
2. Was the Analytical Engine Thought to be Cognitive?
As mentioned above, in recent years Babbage has been frequently put in the
role of "trail-blazer" in books and articles not only about computer
science, but in those about cognitive science as well. The question is, then,
whether this status is really justified. Were either
Babbage, Menabrea, 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. Menabrea denied the possibility
outright. Lovelace often wrote as if she believed it to be true, but at other
times made 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, which would likely
have been tantamount professional suicide in early Victorian England (see,
e.g., Winter, 1997). But if this was his fear, then
his reasons for not dissuading Lovelace from doing so remain obscure. 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
Blaise 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. 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, Augustus De
Morgan. Lovelace likely learned this orientation toward algebra from De Morgan
himself, and from the textbook he assigned to her, 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.
Lovelace then moves on to exemplify her claims about abstract algebra:
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.
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 (very close to the
time 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.
Here she claims outright that the Analytical Engine serves as a
"uniting link" between mind and matter, and then says that no one had
else had yet proposed a machine like the Analytical Engine any more than they
had proposed a thinking machine. Although she stops somewhat short of the
explicit claim that the Analytical Engine is itself such a thinking machine,
the clear intent appears to be to raises the possibility for serious
discussion.
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 that the
new Analytical Engine would be able 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
adds a footnote here, 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 took
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 source.
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
that Alan Turing, over a century later, would dub 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)
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 indeed to her mentor,
Babbage.
Babbage's comments on the topic were always very careful. He almost
invariably referred to the machine's activities as being able to
"replace" or "substitute for" mental activities, or
occasionally as being "analogous" to them, 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 difficulties in
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). 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? Babbage seems to
have clarified his position in a paper entitled "On the Mathematical
Powers of the Calculating Engine" that had been authored in back in 1837 (but
that went unpublished until 1973):
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)
Thus, it seems to have simply been a matter of verbal shorthand for Babbage,
not a literal claim of mentality.
One other 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) -- but then he immediately shifts to
a 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 famed physiologist William Benjamin Carpenter -- who,
incidentally, briefly served as tutor to Ada Lovelace's children -- had to
avoid in launching his career during the 1830s and 1840s; dangers that, for
instance, the notorious mesmerist John Eliotson 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 censure. Babbage, though liberal,
appears to have been a sincerely religious man.
When William Whewell published in 1833 the first in a series of works
commissioned to defend the thesis that God's "design" 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 the
"divine" -- 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
(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 truly 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.
References
Ashworth, William J. (1994). The calculating eye: Baily, Herschel, Babbage
and the business of astronomy. British
Journal of the History of Science, 27,
409-441.
Babbage, Charles. (1832). On the economy of
machinery and manufactures.
Babbage, Charles. (1837). Ninth
Babbage, Charles. (1989). On the mathematical
powers of the calculating engine. In Martin Campbell-Kelly (Ed.), The works of Charles Babbage (vol. 3, pp.
15-61).
Babbage, Charles. (1994). Passages from the life of a philosopher.
Becher, Harvey W. (1980). Woodhouse, Babbage, Peacock, and
modern algebra. Historia
Mathematica, 7, 389-400.
Bowden, B. V. (Ed.) (1953). Faster
than thought: A symposium on digital computing machines.
Buxton, Henry Wilmot (1988). Memoir of
the life and labours of the late Charles Babbage Esq., F.R.S. Cambridge,
MA: MIT Press.
Cohen,
Collier, Bruce. (1990). The little engines
that could've: The calculating machines of Charles Babbage.
Dubbey, J. M. (1978). The mathematical
work of Charles Babbage.
Fisch, Menachem. (1994). 'The emergency which has arrived': The problematic
history of nineteenth-century British algebra -- a programmatic outline. British Journal of the History of Science,
27, 247-276.
Garnderm Howard. (1985). The mind's new science.
Garnham, Alan. (1987). Artificial
intelligence: An introduction.
Haugeland, John. (1985). Artificial
intelligence: The very idea.
Hofstadter, Douglas R. (1979). Gödel,
Escher Bach: An eternal golden braid.
Hartree, Douglas R. (1949). Calculating instruments and machines.
Lagrange, Joseph Louis. (1797). Théorie des fonctions analytique.
Menabrea, Luigi Frederico. (1842). Notions sur la machine
analytique de M. Charles Babbage. Bibliothèque
Universelle de Genève, 41,
352-376. (Translation
by Augusta Ada Lovelace published 1843 in Scientific
Memoirs, 3, 666- ???)
Menabrea, Luigi Frederico. (1989). Letter to the Editor of
Cosmos. In Martin
Campbell-Kelly (Ed.), The works of Charles Babbage (vol. 3, pp.
171-174).
Morrison, Philip & Morrison, Emily (Eds.). (1961). Charles Babbage and
his calculating engines; selected writings by Charles Babbage and others.
Patterson, Elizabeth Chambers. (1983). Mary Somerville and the cultivation of
science, 1815-1840.
Peacock, George. (1803). A treatise on algebra.
Pycior, Helena M. (1981). George Peacock and the British
origins of symbolical algebra. Historia
Mathematica, 8, 23-45.
Pycior, Helena M. (1982). Early criticism of the
symbolical approach to algebra. Historia
Mathematica, 9, 392-412.
Pycior, Helena M. (1983). Augustus De Morgan's algebraic work: The three
stages.
Pylyshyn, Zenon W. (1984). Computation
and cognition: Toward a foundation for cognitive science.
Richards, Joan L. (1980). The art and science of British algebra: A study in
the perception of mathematical truth. Historia
Mathematica, 7, 343-365.
Richards, Joan L. (1987). Augustus De Morgan, the history
of mathematics, and the foundations of algebra.
Richards, Joan L. (1991). Rigour and clarity: Foundations of mathematics in
Richards, Joan L. (1992). God, truth, and mathematics in
nineteenth century
Rosse, William Parsons, Earl of (1855). Address of the
President. Proceedings of the
Royal Society, 7, 248-263.
Stein, Dorothy. (1985).
Turing, Alan M. (1950). Computing machinery and
intelligence. Mind, 59, 433-460.
Winter, Alison. (1997). The construction of
orthodoxies and heterodoxies in early Victorian England. In
Bernard Lightman (Ed.), Victorian science
in context (pp. 24-50).
Woodhouse, Robert. (1803). Principles of analytical calculation.