(b. Walworth, Surrey, England, 26 December 1791; d. London, England, 18 October 1871)
mathematics, computing, statistics, economics, philosophy of science. For the original article on Babbage see DSB, vol. 1.
Babbage is generally remembered as the nineteenth-century prophet of the modern computer. He was a mathematician who designed two distinct types of mechanical computing devices that were rediscovered in the late 1930s, a time when American and European engineers were building electronic computing machines. Since that period, the story of Babbage served as a starting point for the computer age, the distant founder of a modern discipline. Many a discussion of the field began with a brief treatment of Babbage’s computing engines. The London Science Museum constructed one of his computing machines from the original plans in order to demonstrate the validity of Babbage’s ideas.
After the first major biography of Babbage appeared in 1982, scholars developed a broader understanding of Babbage that places his computing machines in the context of his other scientific work. Babbage explored a number of fields, including geology, chemistry, economics, electricity, actuarial mathematics, astronomy, statistics, and mechanical engineering. In probing these different areas, he developed three basic themes that served as his foundation stones for the practice of science. The first was the importance of analysis, the dissection of ideas into their fundamental components. The second was the value of symbolism, the tool for recording and manipulating ideas. The last is need for well, democratic institutions to support scientific research. These themes are best seen in his efforts to reform the English scientific community and his writings on industrial management but they are also found in his work on computing machines.
Education and Early Career. Babbage was born into a middle-class family with rising fortunes. His father was a London banker, who made enough money to be able to purchase an estate in the country. Though he was educated at minor regional schools, Babbage was prepared for the Cambridge University entrance exam by a scholar from Oxford. In this preparatory work Babbage demonstrated a substantial skill in mathematics and a firm interest in the mathematical writings of continental mathematicians represented by Leonhard Euler, Joseph-Louis Lagrange, and Pierre-Simon Laplace, a group that was often identified as the “analytical school.”
Babbage entered Trinity College, Cambridge, in the fall of 1810. His first months at college were awkward as he struggled to find a place among the aristocratic students who had studied at England’s public schools. He shunned the ordinary course of study at Cambridge, which was focused on the mathematical ideas of Isaac Newton, and spent hours studying the analytical mathematicians. In the spring of 1812 he fell into a group of like-minded students and formed an organization known as the Analytical Society. The leader of this group was John Herschel, son of the astronomer William Herschel.
For the rest of Babbage’s life Herschel would be his best friend and closest confidant.
Over the next eighteen months Babbage and Herschel prepared a small volume of mathematical papers called the Memoirs of the Analytical Society (1813). After
Herschel graduated from college in May 1813, Babbage turned his attention from mathematics to chemistry. He created a small laboratory in his college rooms and started a program of experiments. Most of these experiments consisted of subjecting different substances to extremely high temperatures. His study was guided by England’s premier chemist of the time, Smithson Tennant, who had just taken an appointment at Cambridge. Babbage’s interest in the subject faded when his time at college came to an end, but he would later write that “I have never regretted the time I bestowed upon [chemistry] at the commencement of my career” (1864, p. 27).
In June 1814 Babbage left Cambridge with a bachelor’s degree, married Georgiana Whitmore, and moved to London. For the next seven years he returned to mathematical work and published more than a dozen papers. Though he is usually associated with the traditional ideas of calculus—the analysis of motions and forces—Babbage actually devoted most of his energies to a branch of algebra called the calculus of functions. This branch looks at broad classes of mathematical functions and tries to determine the properties of those functions.
During his time in London, Babbage became interested in geology and astronomy. He also traveled to France in search of scientific books. While in Paris he was likely introduced to the work of Gaspard de Prony, who had completed a large set of logarithm and trigonometry tables. De Prony had been able to divide the labor of computing these tables among ninety assistants. This work impressed Babbage, and he would draw upon it when he returned to England.
The Difference Engine. In 1820 he became a founding member of the Astronomical Society, a group of businessmen who were interested in revising the Royal Nautical Almanac, the annual volume that was used by navigators and surveyors. This book gave lengthy tables that showed the positions of the heavenly bodies on every night of the year. It needed to be prepared years in advance and required a substantial amount of calculation.
In preparing some ancillary tables for the Almanac, Babbage conceived of a machine that might assist with the calculation. The machine would calculate polynomial interpolations; it would draw curves through points on a graph. Babbage called this machine the Difference Engine, because it used the method of finite differences to compute the interpolations. For this idea he received a gold medal from the Astronomical Society and a grant of funds from the British government to complete the machine.
Though Babbage was quickly able to complete a prototype of his Difference Engine, he found that the full machine was considerably more complicated than he had anticipated. He spent seven years refining the design and developing new machining techniques. During this time he visited different English companies in order to learn how they engineered complicated machinery. He also became engaged in other activities. He became interested, for a time, in the new insurance industry. He wrote a treatise on the construction of mathematical tables. He experimented with electricity. He wrote papers on machinery and mechanical engineering. And he lobbied for an academic appointment at the new University of London.
In 1827 Babbage was confronted, in less than six months’ time, by the deaths of a son, his father, and his wife. Abandoning his Difference Engine, still unfinished, he retreated to Europe. During his travels he was introduced to many of Europe’s leading scientists and learned that he had been appointed to the Lucasian chair at Cambridge, the professorship that had once been held by Newton.
Babbage returned to England invigorated and filled with new ideas. He first became involved in the reform movement and stood for election to Parliament twice as a Liberal or Whig. He lost both times and turned from politics back to scientific projects. From the notes he made while visiting machine shops and factories he wrote a book titled On the Economy of Machinery and Manufactures (1832), which was probably his most influential work during his lifetime. It took the economic ideas of Adam Smith and updated them to the machinery age. The book showed not only how machines might be used in industry but how they might be used most economically.
Most of Babbage’s economics ideas were based upon the division of labor. He recognized that the division of labor could be applied not only to physical tasks such as manufacturing but also to mental tasks such as the computation of a trigonometry table. Furthermore, he recognized that the division of labor allowed factory owners to reduce the cost of manufacturing by assigning each individual task to the least expensive laborer capable of handling that task. This insight became one of the foundations of industrial management.
As one of the country’s leading experts on computation, Babbage was appointed to a committee reviewing the Royal Nautical Almanac. This group met in the offices of the Royal Astronomical Society and considered both the contents and means of producing the almanac. They recommended adding a substantial number of tables to the volume. They also urged that the British government use a more systematic form of management to compute the tables, though they stopped short of recommending that Babbage’s machine be used for the calculations.
During this period Babbage also became interested in the organization of scientific societies. In particular he became a champion of the modern, self-organized scientific institution. In an 1830 pamphlet, Reflections on the Decline of Science, he argued that “science has long been neglected and declining in England” (p. i). England’s major scientific society of the time, the Royal Society, was not entirely self-governed and had many members who were not scientists. Babbage, who had been a member of the Royal Society since his graduation from Cambridge, attempted to reform the society but found little assistance. Frustrated by the work, he and a small group of friends decided to found a new society, the British Association for the Advancement of Science, based on the principles of self-organization by scientists.
The Analytical Engine. In 1834, with his Difference Engine still unfinished, Babbage conceived a new, more general machine for the evaluation of functions. This machine resembled the modern computer in that it read operations from a string of punched cards and performed those operations on individual numbers. It also had a means of storing and retrieving numbers. He would name the new device the Analytical Engine after his interest in analytical mathematics. It was far more complicated than his Difference Engine, which could calculate only polynomials. It required him to prepare new designs, new plans, and new descriptions.
In his work on the Analytical Engine, Babbage was briefly assisted by Ada Lovelace, the daughter of the poet Lord Byron (George Gordon Byron). Lovelace played a
key role that moved Babbage’s idea beyond its inventor into the larger world: She translated and annotated a description of the Analytical Engine and wrote the instructions that would compute a set of values called Bernoulli numbers. In modern terminology the term program would be used to identify this set of instructions.
While Babbage was working on his design for his Analytical Engine he was also continuing to organize scientific institutions. He was a founding officer of the Royal Statistical Society. At the time, statistical science included most of the fields that have since devolved into social sciences: economics, sociology, psychology, and anthropology. Babbage was interested in the mathematical foundations of these fields and corresponded with most of the leading statisticians of the day, including the Belgian Adolphe Quetelet.
Though he worked on many different projects during the late 1830s, Babbage devoted most of his attention to his Analytical Engine. “My coach house was now converted to a forge,” he wrote, “whilst my stables were transformed into a workshop” (1864, p. 27). He refined the design of the machine, carefully describing the motion of each part in a notation that he had devised. Through these years his ideas about calculation drew the attention of individuals both in England and in Europe. In 1840 Babbage discussed his Analytical Engine at a scientific conference in Turin, Italy, which proved to be one of the more gratifying moments in his life. Two years later his workshop was visited by Prince Albert, the husband of Queen Victoria.
Through 1842 the British government had supported the development of Babbage’s computing machines and had given him fifteen thousand pounds to help pay for materials and the salary of a skilled machinist. However, the government had become impatient with Babbage’s progress. In twenty years of work he had failed to complete a full, working machine. In the fall of that year the chancellor of the exchequer informed him that the government would no longer provide him with funds. Babbage appealed to the prime minister, but he was unable to change the decision.
Babbage was angered by the action of the British government and was particularly stung by a report from the astronomer royal, George Airy, who wrote, “I believe the machine to be useless, and that the sooner it is abandoned, the better it will be for all parties” (George Airy to Henry Goulburn, September 16, 1842, Papers of the Royal Greenwich Observatory, Cambridge University). For the next twenty-five years Babbage would devote himself to erasing that verdict and establishing the value of his ideas. However, Airy probably made the correct judgment for the time. Babbage’s calculators would have had limited application. Within the nineteenth-century scientific community only astronomers might regularly have found a use for one of Babbage’s machines, and none of them could have kept it fully occupied.
In 1854 Babbage’s ideas came to the attention of George and Edvard Scheutz, a father and son from Sweden. After reading a description of the Difference Engine, they designed and built their own version. This machine was smaller and lighter than the engine conceived by Babbage. They used gears and levers that would have been suitable for the mechanism of a clock. In contrast, Babbage used technology that would have been appropriate for a steam engine. Babbage’s engine, if completed, would have filled a room. The Scheutz engine sat nicely on a table and looked like a complicated music box.
Babbage was pleased with Scheutz engine and praised it publicly. The machine was purchased by the Dudley Observatory in Albany, New York, and was given its test, in 1858, by the staff of the American Nautical Almanac. The Americans used it to compute part of an astronomical table that showed the position of the planet Mars. Though they ultimately completed the task, they found the machine difficult to set up and more trouble than it was worth. “The result thus far,” wrote one member of the staff, “has not been such as to demonstrate to my satisfaction that any considerable portion of the Almanac can be computed more economically by this machine” (U.S. Naval Observatory Annual Report for 1858, p. 7).
Later Years. At this time Babbage began to withdraw from scientific work. One author speculates that Babbage had a problem with his eyes that made it hard for him to work and exacerbated his difficult personality. Increasingly he turned to problems that were trivial and not worthy of his talents. He designed a system for coastal navigation and worked on minor problems of machining. However, he did complete a new, refined design for his Difference Engine and continued to promote his ideas on computation.
Babbage remained a key member of the scientific community. He knew Charles Darwin and had a brief correspondence with George Boole. Yet during the last years of his life he continued to return to his computing engines. In 1861 he wrote an autobiography, which is largely a defense of his ideas on computing machines. He also returned to his Analytical Engine, looking at calculations and seeing how he might do them with his machine. For the most part he went over old ground. He looked at different mathematical expressions and tried to write code for them. Only a few times did he begin to wander into fields that would really show the power of the computer, but he never pursued these ideas very far. He died in 1871 with his machines still unfinished.
In 1879 the British Association for the Advancement of Science considered the possibility of building an Analytical Engine from Babbage’s plans but concluded that such a project was beyond their ability and resources. A decade later Babbage’s son, Henry Prevost Babbage, constructed part of the machine, the section involved with the actual computation. The younger Babbage also collected and published his father’s papers on calculating machines.
A practical Difference Engine was demonstrated by the Royal Nautical Almanac in the 1920s. The superintendent of the Almanac, L. J. Comrie, discovered a commercial bookkeeping machine that had a structure similar to that of Babbage’s original computing machine. It can “be called a modern Babbage machine,” Comrie wrote, for “it does all that Babbage intended his difference engine to do and more” (Comrie, 1936, p. 94). Comrie showed how this machine could be used to compute some of the Almanac’s tables. The Almanac staff made regular use of this machine until it was replaced with an electronic computer in the 1950s.
Babbage is connected to the modern computer through the work of Howard Aiken, a Harvard University graduate student who built a computing machine in the early 1940s. Aiken discovered Babbage’s papers and a model of his computing machine while he was designing his own device. Aiken quickly grasped what Babbage had accomplished and identified him as one of the founders of the field of computation, “a radical inventor,” according to Aiken’s biographer, “who was not fully appreciated by his contemporaries” (quoted in Cohen, 1999, p. 72).
The major collections of Babbage’s papers are found at the British Library and at the Beinecke Library at Yale University.
WORKS BY BABBAGE
Reflections on the Decline of Science in England, and on Some of Its Causes. London: B. Fellowes, 1830.
On the Economy of Machinery and Manufactures. London: Charles Knight, 1832; New York: New York University Press, 1989.
Passages from the Life of a Philosopher. London: Longman, Green, Longman, Roberts and Green, 1864; New York: New York University Press, 1989. An autobiography largely devoted to defending his reputation as the designer of computing machines.
Memoirs of the Analytical Society. In Aspects of the Life and Thought of Sir John Frederick Herschel, edited by S. S. Schweber. Vol. 1. New York: Arno Press, 1981. The complete text of Babbage and Herschel’s mathematics volume.
Works of Charles Babbage. Edited by Martin Campbell-Kelly. New York: New York University Press, 1989. Most of his papers but not quite all.
Ashworth, William T. “The Calculating Eye: Baily, Herschel, Babbage, and the Business of Astronomy.” British Journal of the History of Science 27 (1994): 409–441.
Bromley, Alan. “Charles Babbage’s Analytical Engine, 1838.” IEEE Annals of the History of Computing4 (1982): 196–217. This paper and the three that follow are the definitive technical analyses of Babbage’s machines.
———. “The Evolution of Babbage’s Calculating Engines.” IEEE Annals of the History of Computing9 (1987): 113–136.
———. “Charles Babbage’s Analytical Engine, 1838.” IEEE Annals of the History of Computing 20 (1998): 29–45.
———. “Babbage’s Analytical Engine Plans 28 and 29A: The Programmer’s Interface.” IEEE Annals of the History of Computing 22 (2000): 5–19.
Campbell-Kelly, Martin. “Charles Babbage and the Assurance of Lives.” IEEE Annals of the History of Computing 16 (1994): 5–14.
Cohen, I. Bernard. Howard Aiken, Portrait of a Computer Pioneer. Cambridge, MA: MIT University Press, 1999.
Comrie, Leslie J. “Inverse Interpolation and Scientific Applications of the National Accounting Machine.”Supplement to the Journal of the Royal Statistical Society3, no. 2 (1936): 87–114.
Enros, Philip C. “The Analytical Society (1812–1813): Precursor of the Revival of Cambridge Mathematics.” Historica Mathematica 10 (1983): 24–27.
Grier, David A. “Biographies and Writings by Charles Babbage (1791–1870).”Communications Book Notes Quarterly 37 (2006): 7–13. Complete bibliography of biographies and other books about Charles Babbage.
Hyman, Anthony. Charles Babbage, Pioneer of the Computer. Princeton, NJ: Princeton University Press, 1982. The canonical biography. Largely based on Babbage’s autobiography.
IEEE Annals of the History of Computing. Including those articles listed here, this journal has published more than thirty papers on Charles Babbage and his machines.
Keller, C. R. “Babbage the Unfortunate.” British Journal of Ophthalmology88 (2004): 730–732.
Swade, Doron. The Cogwheel Brain: Charles Babbage and the Quest to Build the First Computer. London: Little, Brown, 2000. Published in the United States as The Difference Engine. New York: Viking, 2001.
Van Sinderen, Alfred W. “Printed Papers of Charles Babbage.” IEEE Annals of the History of Computing 2 (1980): 169–185. Contains a complete list of Babbage’s published works.
Williams, Michael M. “Babbage and Bowditch: A Transatlantic Connection.”IEEE Annals of the History of Computing 9 (1988): 283–290.
David Alan Grier
"Babbage, Charles." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/babbage-charles-0
"Babbage, Charles." Complete Dictionary of Scientific Biography. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/babbage-charles-0
(b. Teignmouth, England, 26 December 1792; d. London, England, 18 October 1871)
mathematics, computer logic, computer technology.
Babbage’s parents were affluent. As a child, privately educated, he exhibited unusually sharp curiosity as to the how and why of everything around him. Entering Cambridge University in 1810, he soon found that he knew more than his teachers, and came to the conclusion that English mathematics was lagging behind European standards. In a famous alliance with George Peacock and John Herschel, he began campaigning for a revitalization of mathematics teaching. To this end the trio translated S. F. Lacroix’s Differential and Integral Calculus and touted the superiority of Leibniz’s differential notation over Newton’s (then widely regarded in England as sacrosanct).
After graduation, Babbage plunged into a variety of activities and wrote notable papers on the theory of functions and on various topics in applied mathematics. He inquired into the organization and usefulness of learned societies, criticizing the unprogressive ones (among which he included the Royal Society) and helping found new ones—in particular the Astronomical Society (1820), the British Association (1831), and the Statistical Society of London (1834). He became a fellow of the Royal Society in 1816, and in 1827 was elected Lucasian professor of mathematics at Cambridge. He had not sought this prestigious chair (he described his election as “an instance of forgiveness unparalleled in history”) and, although he held it for twelve years, never functioned as professor. This is a little surprising, in that the position could have been used to further the pedagogic reforms he advocated. But Babbage was becoming absorbed, if not obsessed, by problems of the mechanization of computation. He was to wrestle with these for decades, and they were partly responsible for transforming the lively, sociable young man into an embittered and crotchety old one, fighting all and sundry, even the London street musicians, whose activities, he figured, had ruined a quarter of his working potential.
Babbage had a forward-looking view of science as an essential part of both culture and industrial civilization, and he was among the first to argue that national government has an obligation to support scientific activities, to help promising inventors, and even to give men of science a hand in public affairs.
Few eminent scientists have had such diversified interests as Babbage. A listing of them would include cryptanalysis, probability, geophysics, astronomy, altimetry, ophthalmoscopy, statistical linguistics, meteorology, actuarial science, lighthouse technology, and the use of tree rings as historic climatic records. Two deserve special mention: the devising of a notation that not only simplified the making and reading of engineering drawings but also helped a good designer simplify his “circuits”, and his insightful writings on mass production and the principles of what we now know as operational research (he applied them to pin manufacture, the post office, and the printing trade).
Computational aids began to haunt Babbage’s mind the day he realized that existing mathematical tables were peppered with errors whose complete eradication was all but infeasible. As a creature of his era—the machine-power revolution—he asked himself, at first only half in earnest, why a table of, say, sines could not be produced by steam. Then he went on to reflect that maybe it could. He was at the time enthusiastic about the application of the method of differences to tablemaking, and was indeed using it to compile logarithms. (His finished table of eight figure logarithms for the first 108,000 natural numbers is among the best ever made.) While still engaged in this work, Babbage turned to the planning of a machine that would not only calculate functions but also print out the results.
To understand his line of thought, we must take a close look at the method of differences—a topic in what later became known as the calculus of finite differences. The basic consideration is of a polynomial f(x) of degree n evaluated for a sequence of equidistant values of x. Let h be this constant increment. We next take the corresponding increments in f(x) itself, calling these the first differences; then we consider the differences between consecutive first differences, calling these the second differences. And so forth. An obvious recursive definition of the rth difference for a particular value of x, say xi, is
and it is not difficult to show that, specifically,
As r increases, the differences become smaller and more nearly uniform, and at r = n the differences are constant (so that at r = n + 1, all differences are zero). A simple example—one that Babbage himself was fond of using—is provided by letting the function be the squares of the natural numbers. Here n = 2, and we have
Two propositions follow. The first, perhaps not obvious but easily demonstrated, is that the schema can be extended to most nonrational functions (such as logarithms), provided that we take the differences far enough. (This is linked to the fact that the calculus of finite differences becomes, in the limit, the familiar infinitesimal calculus.) The second, originated by Babbage, is that the inverse of the schema is readily adaptable to mechanization. In other words, a machine can be designed (and it will be only slightly more sophisticated than an automobile odometer or an office numbering machine) that, given appropriate initial values and nth constant differences, will accumulate values of any polynomial, or indeed of almost any function. (For nonrational functions the procedure will be an approximation conditioned by the choice of r and h and the accuracy required, and will need monitoring at regular checkpoints across the table.)
This is what Babbage set out—and failed—to do. As the work progressed, he was constantly thinking up new ideas for streamlining the mechanism, and these in turn encouraged him to enlarge its capacity. In the end his precepts ruined his practice. The target he set was a machine that would handle twenty decimal numbers and sixth-order differences, plus a printout device. When he died, his unfinished “Difference Engine Number One” had been a museum piece for years (in the museum of King’s College, at Somerset House, London, from 1842 to 1862, and subsequently in the Science Museum, London—where it still is). What is more revealing and ironic is that, during his own lifetime, a Swedish engineer named Georg Scheutz, working from a magazine account of Babbage’s project, built a machine of modest capacity (eight-decimal numbers, fourth-order differences, and a printout) that really worked. It was used for many years in the Dudley Observatory, Albany, New York.
Aside from technicalities, two factors militated against the production of the difference engine. One was cost (even a generous government subsidy would not cover the bills), and the other was the inventor’s espousal of an even more grandiose project—the
construction of what he called an analytical engine.
Babbage’s move onto this new path was inspired by his study of Jacquard’s punched cards for weaving machinery, for he quickly saw the possibility of using such cards to code quantities and operations in an automatic computing system. His notion was to have sprung feeler wires that would actuate levers when card holes allowed them access. On this basis he drew up plans for a machine of almost unbelievable versatility and mathematical power. A simplified flow diagram of the engine is shown in the accompanying figure. The heart of the machine, the mill, was to consist of 1,000 columns of geared wheels, allowing up to that many fifty-decimal-digit numbers to be subjected to one or another of the four primary arithmetic operations. Especially remarkable was the incorporation of decision-making units of the logical type used in today’s machines.
Although the analytical engine uncannily foreshadowed modern equipment, an important difference obtains: it was decimal, not binary. Babbage, not having to manipulate electronics, could not have been expected to think binarily. However, his having to use wheels meant that his system was not “purely” digital, in the modern sense.
All who understood the plans expressed unbounded admiration for the analytical engine and its conceiver. But material support was not forthcoming, and it remained a paper project. After Babbage’s death his son, H.P. Babbage, sorted the mass of blueprints and workshop instructions, and, in collaboration with others, built a small analytical”mill” and printer. It may be seen today in the Science Museum, London.
I. Original Works. Babbage appended a list of eighty of his publications to his autobiographical passages From the Life of a Philosopher (London, 1864), and it is reproduced in P. and E. Morrison’s Charles Babbage and his Calculating Engines (New York, 1961). It is a poor list, with reprinted papers and excerpts separately itemized. Apart from translations and the autobiography and a few small and minor works, the only books of substance that Babbage published were Reflections on the Decline of Science in England (London, 1830); Economy of Manufactures and Machinery (London, 1832); and The Exposition of 1851 (London, 1851). His logarithms deserve special mention: they were originally published in stereotype as Table of the Logarithms of the Natural Numbers From I to 108,000 (London, 1827), with a valuable introduction dealing with the layout and typography of mathematical tables. A few years later he published Specimen of Logarithmic Tables (London, 1831), a 21-volume, single-copy edition of just two of the original pages printed in a great variety of colored inks on an even greater variety of colored papers, in order “to ascertain by experiment the tints of the paper and colors of the inks least fatiguing to the eye.” In the same “experiment” about thirty-five copies of the complete table were printed on “thick drawing paper of various tints.” In 1834 regular colored-paper editions were published in German at Vienna and in Hungarian at Budapest, by C. Nagy. Babbage’s formal scientific articles number about forty. The first publication dealing with his main subject is “A Note Respecting the Application of Machinery to the Calculation of Mathematical Tables,” in Memoirs of the Astronomical Society, 1 (1822), 309; the last is chs.5–8 of his entertaining autobiography (see above).
II.Secondary Literature. Practically all the significant material is either reproduced or indexed in the Morrisons’ book, the only one entirely devoted to Babbage (see above). The symposium Faster Than Thought (London, 1953) has a first chapter (by the editor, B.V. Bowden) that is largely concerned with Babbage. Both of these books carry reprints of a translation and annotation of an article on the analytical engine written by the Italian military engineer L.F. Menabrea (Geneva, 1842). The translator was Lady Lovelace, Lord Byron’s mathematically gifted daughter, and her detailed annotations (especially a sketch of how Bernoulli numbers could be computed by the engine) are excellent. It is in the course of this commentary that she finely remarks that “the Analytical Engine weaves algebraic patterns, Just as the Jacquard-loom weaves flowers and leaves.” The sectional catalog Mathematics, I. Calculating Machines and Instruments, The Science Museum (London, 1926), contains much useful illustrated information about Babbage’s engines, as well as about allied machines, such as the Scheutz difference engine.
Norman T. Gridgeman
"Babbage, Charles." Complete Dictionary of Scientific Biography. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/babbage-charles
"Babbage, Charles." Complete Dictionary of Scientific Biography. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/babbage-charles
Charles Babbage (1792–1871), English mathematician, did pioneering work on calculating machines and in operations research and was active in winning public support for science. A man far ahead of his time, he was generally recognized only long after his death. However, his work strikingly anticipated certain key developments in modern thought. The great electronic computers, whose uses have multiplied enormously since they were developed in the mid-twentieth century, are based on principles first stated by Babbage.
His dream was to mechanize the abstract operations of mathematics for use in industry. His first idea was that of the “difference engine,” a machine for integrating difference equations, which formed mathematical tables by interpolation and set them directly into type. Babbage pointed out the advantages such a machine would have for the government in preparing its lengthy tables for navigation and astronomy. With the enthusiastic approval of the Royal and Astronomical societies, the government of England agreed to grant funds for the construction of such a machine. Work proceeded for about eight years but stopped abruptly after a dispute between Babbage and his chief engineer. Shortly thereafter Babbage thought of another machine, the “analytical engine,” built on an entirely new principle—internal programming—and wholly superseding and transcending the difference engine. Babbage explained his new idea to the first lord of the Treasury and asked for an official decision on whether to continue and complete the original difference engine or to suspend work on it until the analytical engine was further developed.
The government had already spent £17,000 on the difference engine, and Babbage had contributed a large amount from his private fortune. After years of correspondence with various government officials, Babbage was advised that the prime minister, Sir Robert Peel, had decided the government must abandon the project because of the expense involved.
Babbage continued to work on his analytical engine. The machine he envisioned (which he called “the Engine eating its own tail”) was one that could change its operations in accordance with the results of its own calculations. The machine could make judgments by comparing numbers and then, acting on the result of its comparisons, could proceed along lines not specified in advance by its instructions. These notions are acknowledged as the backbone of modern digital computers. Bound by the technology of his time, Babbage had to translate his great idea into wholly mechanical form, using a mass of intricate clockwork in pewter, brass, and steel, with punched cards modeled on those of the Jacquard loom.
After some years of work on his analytical engine, Babbage decided to design a second difference engine, which would incorporate the improvements suggested by his work on the analytical engine. He again asked for government support but was again refused. Babbage completed only small bits of a working engine and did not publish any detailed descriptions of them other than the informal ones in the autobiography he wrote as a disappointed old man, Passages From the Life of a Philosopher (1864). After his death one of his sons, Major Henry P. Babbage, compiled and published a book including papers both by Babbage himself and by his contemporaries, entitled Babbage’s Calculating Engines.
While working on his engines, Babbage became deeply involved in the problems of establishing and maintaining in his machine shop and drafting room the new standards of precision that his designs demanded. Under his direction the machinists he employed developed tools and methods far ahead of contemporary practice; these developments alone might have justified the government’s expenditures. Babbage also invented a scheme of mechanical symbols that could make clear the action of all the complicated moving parts of his machinery. The detailed drawings of his engines were models for their day.
The son of a banker in Devon, who later left him a considerable fortune, Charles Babbage was educated mostly at home, with mathematics his favorite subject. At Cambridge University his closest friends were John Herschel (later the astronomer royal) and George Peacock (later the dean of Ely); with them Babbage solemnly entered into a compact to “do their best to leave the world wiser than they found it.” They began their mission by translating Sylvestre Lacroix’s An Elementary Treatise on the Differential and Integral Calculus and founding the Analytical Society, whose purpose was to put “English mathematicians on an equal basis with their continental rivals.” Babbage published a variety of mathematical papers after receiving his M.A. from Cambridge in 1817. His interest in mathematics led directly to a concern for accurate and readable mathematical tables. A chance conversation with Herschel, while the two were checking a table of calculations done for the Astronomical Society (which they had recently helped to found), led Babbage to his dream of a machine for calculating mathematical tables, a dream that was to become the obsession of his life.
Although he never abandoned the pursuit of his engines, his great curiosity and enthusiasm led him onto many other paths. The problems he encountered in the construction of his own machines aroused his interest in the general problems of manufacturing. After a tour of factories throughout England and the Continent, Babbage wrote his most popular book, On the Economy of Machinery and Manufactures (1832). The book included a detailed description and classification of the tools and machinery he had observed, together with a discussion of the “economical processes of manufacturing.” A pioneer work in the field that, one hundred years later, we call operations research, the Economy is still good reading.
In addition to pure and applied mathematics, Babbage wrote papers on physics and geology, astronomy and biology. He even ventured into the fields of archeology and apologetics and wrote one of the first clear popular accounts of the theory of life insurance. He also enjoyed making suggestions for practical inventions of all kinds, ranging from the cowcatcher on a railway locomotive to a system of flashing signals for lighthouses.
An enthusiastic conference man, Babbage was an active member of learned societies all over the world. He was instrumental, with Herschel, in founding the Royal Astronomical Society in 1820, the British Association for the Advancement of Science (BAAS) in 1831, and the Statistical Society in 1834. For years Babbage led an assault on the decline of science in England, attacked the neglect of science in the universities, and urged government support of scientists. He pointed out that only men with private fortunes could pursue abstract science and that “scientific knowledge today hardly exists among the higher classes.” The chief target of his book Reflections on the Decline of Science in England (1830) was the Royal Society, to which he had been elected while still at Cambridge. He attacked the autocratic misrule of the society by a social clique and pointed out that only a small proportion of the society’s members ever contributed papers to its Transactions. His book received a good deal of support from other members, and within the next twenty years the Royal Society did succeed in reorganizing itself in response to their criticisms. In an appendix to the Decline of Science, Babbage reprinted without comment an account of “an annual Congress of German naturalists meeting in each successive year in some great town.” This account probably inspired the first meeting of the BAAS in 1831, with Babbage taking a leading part in shaping its constitution.
Babbage was deeply committed to the belief that careful analysis, mathematical procedures, and statistical calculations—using high-speed computation—could be reliable guides in practical and productive life. This conviction, combined with the wide range of his organizational and scientific interests, gives him still a wonderful modernity.
Philip Morrison and Emily Morrison
1830 Reflections on the Decline of Science in England, and on Some of Its Causes. London: Fellowes.
(1832) 1841 On the Economy of Machinery and Manufactures. 4th ed. enl. London: Knight.
1864 Passages From the Life of a Philosopher. London: Longmans.
Babbage’s Calculating Engines: Being a Collection of Papers Relating to Them; Their History and Construction. Edited by Henry P. Babbage. London: Spon. 1889.
Charles Babbage and His Calculating Engines: Selected Writings by Charles Babbage and Others. Edited with an introduction by Philip and Emily Morrison. New York: Dover. 1961.
Bowden,, Bertram V. (editor) (1953) 1957 Faster Than Thought: A Symposium on Digital Computing Machines. London: Pitman.
Mullett, Charles F. 1948 Charles Babbage: A Scientific Gadfly. Scientific Monthly 67:361–371.
"Babbage, Charles." International Encyclopedia of the Social Sciences. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/babbage-charles
"Babbage, Charles." International Encyclopedia of the Social Sciences. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/social-sciences/applied-and-social-sciences-magazines/babbage-charles
British Inventor and Mathematician
A mathematician, philosopher, and inventor, Charles Babbage is best remembered for his concept of the Analytical Engine—a calculating machine that was not actually built during his lifetime.
Being born into a wealthy family on December 26, 1791 allowed Babbage to pursue his interests free from financial worries through most of his life. The oldest child of a successful Devonshire banker, Babbage spent the greater part of his early childhood relieved of study due to poor health. Deprived of formal study, the young Babbage used experiments to find answers to his questions. For example, he would take toys apart to see what was inside. On another occasion, he tried, unsuccessfully, to summon the devil to confirm the creature's existence. His failure to do so led him to reason that devils and ghosts were not real.
Babbage's formal education began at a boarding school in London, England. Algebra interested him to such an extent that he and another student would wake at 3 A.M. to study for a few hours. In 1814 Babbage entered Cambridge University to study mathematics. As a result of his late-night algebra studies and knowledge of European mathematical advances, he knew more than his tutors. Babbage and his equally mathematically talented friends, John Herschel and George Peacock, formed the Analytical Society to promote European mathematics as a more advanced subject than the mathematics of English physicist Isaac Newton (1642–1727). On the lighter side, he joined friends to form the Ghost Club.
Upon completing a master of arts, Babbage continued to work for mathematical reform through the translation of a paper by Sylvestre François Lacroix. This and further works on calculus were recognized by Cambridge University in 1828 when Babbage was elected as Lucasian Professor of Mathematics. During his ten years as professor, Babbage gave no lectures; however he participated in the examination of students for the Smith prizes given for excellence in mathematics.
A major outcome of his mathematical studies was the idea for a calculating machine—the Difference Engine—which would calculate and print numbers in a sequence based on the principle of differences. The sequences of the calculations can be described by a theorem or as a polynomial and the succeeding values are calculated by addition and subtraction rather than by multiplication. The Difference Engine produced tables of logarithmic and trigonometric functions to six decimal places. This machine would have a mechanical memory and the capability of producing printed tables. To get funding to build a large Difference Machine, Babbage used a small working model to demonstrate the machine's potential to the British government. The machine was designed to a second-order difference and six decimal places. All parts of the machine were hand tooled or cast. Babbage built a foundry and forge on his land to facilitate and oversee the creation of the components.
In 1824 Babbage was awarded a grant to build his machine. As work progressed on the machine, he was making changes on the design and eventually scrapped the original model for a more complex one, the Analytical Engine. He again petitioned the government for more funding but was denied. Despite the lack of funding, he continued to design and construct parts for the Analytical Engine using his own funds.
The Analytical Engine design incorporated the following functions. Variables and detailed instructions would be read into the machine from punched cards. These cards were based upon the card coding method used in Jacquard weaving. The variables would be placed in a 'store,' memory, as would intermediate calculations. The 'mill,' processor, would carry out the instructions thereby performing the calculations. Based on calculation results, the engine could determine which instruction should be used next. Babbage had developed a decision function. The results would be printed out. This design has all the characteristics of a computer.
Despite his accomplishments, Babbage could not get financial support for the Analytical Engine and did not have the resources to complete a working model. He did leave detailed drawings for the internal mechanism and notes for the design and construction.
In the early 1840s, Babbage came in contact with Ada Byron King, Countess of Lovelace, a female contemporary mathematician and theoretician. Lovelace had translated a summary of Babbage's achievements from an original Italian account. When she showed Babbage her translation, he suggested that she add her own notes, which turned out to be three times the length of the original article. Letters between Babbage and Lovelace raced back and forth. When Lovelace eventually published the article in 1843, it included her predictions that Babbage's machine might be used to compose complex music and to produce graphics, and it might be used for both practical and scientific use. She was correct. It was Lovelace who also suggested to Babbage the idea of writing a plan on how his engine might calculate Bernoulli numbers . This plan is now regarded as the first "computer language."
When not completely involved with the calculating engines, Babbage turned his attention to other pursuits. He was avidly interested in all kinds of statistics, from the heartbeat of a pig, to the quantity of wood that a man could saw in a specific amount of time. Babbage would put himself into danger to learn more. Once he spent time in a large drying machine to test the human body's reaction to heat. On another occasion, he spent five to six minutes inside a 129ºC (265ºF) oven, noting his pulse and the quantity of his perspiration. Another venture was to explore the inside of an active volcano. Babbage descended into Italy's Mount Vesuvius to observe the occurrence of mini eruptions. Having determined that the time between eruptions was about ten minutes, Babbage proceeded to descend further and closer to the eruption site to see liquid lava and note its movement. He remained for six minutes allowing four minutes to retreat from his position before the next eruption.
In 1837 Babbage conducted experiments which determined that the Brunel wide gauge track (railway) was safer and more efficient than narrower gauge tracks. Plus, his calculations of mail delivery showed that the most costly aspect of the mailing process was the distance traveled, and not the time or labor involved. This analysis resulted in the introduction of uniform postal rates.
Babbage's book, Economics of Manufactures and Machinery, set out the mathematics for the manufacturing processes. The book became a basis for operations research. Babbage published numerous papers covering a wide range of topics, from science to religion. He founded the British Association's Statistical Society and the British Association for the Advancement of Science; was elected a fellow of the Royal Society; and was a member of the Astronomical Society. Babbage's The Ninth Bridgewater Treatise details his ideas that science could explain religion. Babbage died in London on October 18, 1871.
see also Analytical Engine; Lovelace, Ada Byron King, Countess of.
Bertha Kugelman Morimoto
Morrison, Philip, and Emily Morrison, eds. Charles Babbage and his Calculating Engines. New York: Dover Publishing Inc., 1961.
Charles Babbage Institute. <http://www.cbi.umn.edu/exhibits/cb.html>
The Babbage Pages. <http://www.ex.ac.uk/BABBAGE/welcome.html>
"Babbage, Charles." Computer Sciences. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/computing/news-wires-white-papers-and-books/babbage-charles
"Babbage, Charles." Computer Sciences. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/news-wires-white-papers-and-books/babbage-charles
Born: December 26, 1791
Died: October 18, 1871
English mathematician and inventor
Charles Babbage was an English inventor and mathematician whose mathematical machines were based on ideas that were later put to use in modern computers. Indeed, Babbage is sometimes even called the inventor of the computer. He was also a pioneer in the scientific understanding of manufacturing processes.
A bright, curious child
Charles Babbage was born on December 26, 1791, in London, England. His father, Benjamin Jr., was a banker and merchant. One of his grandfathers, Benjamin Sr., had been mayor of Totnes, England. Babbage was always curious—when he would receive a new toy, he would ask his mother, Elizabeth, what was inside of it. He would then take apart the toy to figure out how it worked. Babbage was also interested in mathematics at a young age, and he taught himself algebra.
The Babbage family was wealthy, and Charles received much of his early education from private tutors. In 1810 he entered Trinity College at Cambridge University. He found that he knew more about mathematics than did his instructors. Very unhappy with the poor state of mathematical instruction there, Babbage helped to organize the Analytical Society, which played a key role in reducing the uncritical following of Sir Issac Newton (1642–1727; English scientist, mathematician, and astronomer) at Cambridge and at Oxford University.
In 1814, the same year of Babbage's graduation from Cambridge, he married Georgiana Whitmore. They had eight children together, but only three lived beyond childhood. Georgiana herself died in 1827.
In 1822 Babbage produced the first model of the calculating engine, which would become the main interest of his life. The machine calculated and printed mathematical tables. He called it a "difference engine" after the mathematical theory upon which the machine's operation was based. The government was interested in his device and made a vague promise to fund his research. This encouraged Babbage to begin building a full-scale machine.
But Babbage had underestimated the difficulties involved. Many of the machine tools he needed to shape the wheels, gears, and cranks of the engine did not exist. Therefore, Babbage and his craftsmen had to design the tools themselves. The resulting delays worried the government, and the funding was held back.
Meanwhile, the idea for a far grander engine had entered Babbage's ever-active mind: the "analytical engine." This machine would be able to perform any mathematical operation according to a series of instructions given to the machine. Babbage asked the government for a decision on which engine to finish. After an eight-year pause for thought, the government decided that it wanted neither.
Babbage managed to squeeze in an incredible variety of activities between dealing with the government and working on his engines. In addition to other subjects, he wrote several articles on mathematics, the decline of science in England, the rationalization of manufacturing processes, religion, archeology, tool design, and submarine navigation. He helped found the Astronomical Society, which later became the Royal Astronomical Society, as well as other organizations. He was Lucasian professor of mathematics at Cambridge for ten years. He was better known, though, for his seemingly endless campaign against organ-grinders (people who produce music by cranking a hand organ) on the streets of London.
He always returned to his great engines—but none were ever finished. He died on October 18, 1871, having played a major part in the nineteenth-century rebirth of British science.
For More Information
Campbell, Kelley Martin, ed. The Works of Charles Babbage. New York: New York University Press, 1988.
Collier, Bruce. Charles Babbage and the Engines of Perfection. Oxford, England: Oxford University Press, 1998.
Moseley, Maboth. Irascible Genius: A Life of Charles Babbage, Inventor. London: Hutchinson, 1964.
"Babbage, Charles." UXL Encyclopedia of World Biography. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/babbage-charles-0
"Babbage, Charles." UXL Encyclopedia of World Biography. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/babbage-charles-0
British Mathematician and Inventor 1791–1871
Babbage was the son of a wealthy banker and attended Cambridge University. A brilliant man, he was elected to membership in the Royal Society before receiving his master's degree in 1817. He was appointed to the Lucasian Chair of Mathematics at Cambridge in 1828, a position also held by such great scientists as Sir Isaac Newton and today's Stephen Hawking.
As an authentic Newtonian , Babbage advocated the reduction of all things to numerical terms and believed that they could then be understood and controlled. He was particularly attracted to the use of statistics .
Babbage is often regarded as the "father of computing." In 1823, with financial support from the British government, he began work on what he called the Difference Engine, a steam-powered machine that would calculate mathematical tables correct to twenty decimal places. He built prototypes that produced tables of logarithms correct to eight decimal places but was never successful in constructing a full-size version.
Instead, in 1833, Babbage became interested in designing and building an Analytical Engine. This device was to be a mechanical apparatus that could perform any mathematical calculation. It would be controlled by a "program" of instructions that the machine would read from punched paper cards. Although his Analytical Engine has never been constructed, Babbage's basic design was the foundation of modern digital computers.
Babbage was active in a variety of areas. Fascinated with rail travel, he performed research on railroad safety and efficiency, invented the cowcatcher , and promoted a standard gauge for train tracks. He established the modern postal system in Britain by developing uniform postal rates. His production of the first dependable actuarial tables of statistical life expectancies helped found the modern insurance industry.
Babbage invented, among many other devices, the dynamometer , better lights for lighthouses, and a speedometer. His ideas contributed to the growth of the machine tool industry. He also developed mathematical approaches to deciphering codes.
Concerned about the level of interest in science, Babbage published Reflections on the Decline of Science in England in 1830. He also helped create the British Association for the Advancement of Science, the Analytical Society, the Statistical Society, and the Royal Astronomical Society.
Babbage's book On the Economy of Machinery and Manufactures (1832) established the scientific study of manufacturing, known as operations research. It made an important contribution to political and social economic theory by regarding manufacturing as the primary component of economics. Quoted by Karl Marx in Das Kapital, its ideas were important in Marxist economic theory. His other writings included Ninth Bridgewater Treatise (1837), in which he attempted to harmonize his scientific and religious beliefs.
Although he was, for many years, a popular member of London society, he became ill-natured and unpopular in his old age. The honorary title of baron was offered to him, but he insisted instead on a life peerage— having all the privileges of a hereditary baron, including a seat in the House of Lords. It was never granted. He died in London in 1871.
see also Mathematical Devices, Mechanical.
J. William Moncrief
Collier, Bruce, and James MacLachlan. Charles Babbage and the Engines of Perfection. Oxford: Oxford University Press, Inc., 2000.
Lindgren, Michael. Glory and Failure: The Difference Engines of Johann Müller, Charles Babbage, and Georg and Edvard Scheutz, trans. Craig G. McKay. Cambridge, MA: MIT Press, 1990.
"Babbage, Charles." Mathematics. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/education/news-wires-white-papers-and-books/babbage-charles
"Babbage, Charles." Mathematics. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/education/news-wires-white-papers-and-books/babbage-charles
Charles Babbage (1791-1871) was an English inventor and mathematician whose mathematical machines foreshadowed the modern computer. He was a pioneer in the scientific analysis of production systems.
Charles Babbage was born on Dec. 26, 1791, in Totnes, Devonshire. Much of his early education was under private tutors. In 1810 he matriculated at Trinity College, Cambridge. Appalled by the state of mathematical instruction there, Babbage helped to organize the Analytical Society, which played a decisive role in weakening the grip of blind Newton-worship at Cambridge and Oxford.
In 1814, the same year in which he took his degree, Babbage married Georgiana Whitmore. They had eight children, only three of whom survived to maturity. Mrs. Babbage died in 1827.
In 1822 Babbage produced the first model of the calculating engine that would be the consuming interest of his life. The machine produced mathematical tables, and since its operation was based upon the mathematical theory of finite differences, he called it a "difference engine." The government was interested, and a vague promise of financial assistance encouraged Babbage to begin building a full-scale machine.
But he had underestimated the difficulties. Many of the precision machine tools needed to shape the wheels, gears, and cranks of the engine did not exist. Babbage and his craftsmen had to design them. The consequent delays worried the government, and the financial support was tied up in red tape.
Meanwhile the conception of a far grander engine had entered Babbage's restless brain, the "analytical engine." It would possess (in modern language) a feedback mechanism and would be able to perform any mathematical operation. Babbage asked the government for a decision on which engine to finish. After an 8-year pause for thought, the government indicated that it wanted neither.
Between bouts with the government and work on his engines, the versatile Babbage managed to squeeze in an incredible variety of activities. He wrote on mathematics, the decline of science in England, codes and ciphers, the rationalization of manufacturing processes, religion, archeology, tool design, and submarine navigation, among other subjects. He was Lucasian professor of mathematics at Cambridge for 10 years, but he was better known for his interminable campaign against organ-grinders in the streets of London.
Always he returned to his great engines, but none of them was ever finished. He died on Oct. 18, 1871, having played a prominent part in the 19th-century revival of British science.
The best source on Babbage is Philip Morrison and Emily Morrison, eds., Charles Babbage and His Calculating Engines: Selected Writings by Charles Babbage and Others (1961). It contains an excellent short biography by the Morrisons, a selection of Babbage's works, and associated material on the engines. For more details on Babbage's life see Maboth Moseley, Irascible Genius: A Life of Charles Babbage, Inventor (1964). □
"Charles Babbage." Encyclopedia of World Biography. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/charles-babbage
"Charles Babbage." Encyclopedia of World Biography. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/charles-babbage
"Babbage, Charles." The Oxford Companion to British History. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/babbage-charles
"Babbage, Charles." The Oxford Companion to British History. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/history/encyclopedias-almanacs-transcripts-and-maps/babbage-charles
Charles Babbage (băb´Ĭj), 1792–1871, English mathematician and inventor. He devoted most of his life and expended much of his private fortune and a government subsidy in an attempt to perfect a mechanical calculating machine that foreshadowed present-day machines. He was a founder of the Royal Astronomical Society. He wrote Tables of Logarithms (1827) and an autobiography (1864).
See biographies by M. Moseley (1970) and D. Halacy (1970).
"Babbage, Charles." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/babbage-charles
"Babbage, Charles." The Columbia Encyclopedia, 6th ed.. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/babbage-charles
"Babbage, Charles." World Encyclopedia. . Encyclopedia.com. (October 16, 2017). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/babbage-charles
"Babbage, Charles." World Encyclopedia. . Retrieved October 16, 2017 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/babbage-charles