Charles Babbage and the Origins of Modern Computation By Matthew Jordan 1218494 A research paper presented to Dr. Gregory Moore in Partial Fulfillment of the Requirements for Math 3Z03 – History of Mathematics McMaster University 28 March 2014 9023 Words 1 Introduction Charles Babbage was unquestionably a man far ahead of his time. In his lifetime the value of his work was largely unappreciated, but he is now heralded as the “grandfather of the computer” [O’Regan, 200]. A mathematician, inventor, researcher, public figure, and innovator, Babbage’s body of work is prolific, and he has made notable contributions to virtually all human endeavors. Today, he is most remembered for two inventions, one of which was only one- seventh completed by the time progress halted, and another which was never built at all, by Babbage or hence. Incomplete though they were, the Difference and Analytical Engines represented a major step forward in computational technology. In his Engines one sees the conceptual and mechanical linkage between automation and programmability, features that define the modern computer. Babbage had an insatiable desire for perfectibility and a strong personal devotion to Engines, perhaps more so than anything else in his life. His work and his personality are inextricably linked and must therefore be analyzed in tandem to truly appreciate his legacy. This paper will outline the origination, evolution, and function of these two machines, placing particular emphasis on the life of their inventor and the struggles he faced in his work. Babbage, a pioneer of efficiency, conceived of his Difference Engine to bring the principles of the Industrial Revolution to the calculation of mathematical tables. Inspired by the work of French engineer G.F. de Prony, who had in Babbage’s youth facilitated the execution of the largest tabulation of numerical tables yet achieved, Babbage sought to mechanize the process to eliminate human error. He would later abandon this project to commence an even more ambitious venture, the Analytical Engine, the world’s first programmable computer. The latter used punched cards, a technology championed by textile manufacturer Joseph-Marie Jacquard, whose namesake loom was the first automatic machine for silk weaving. The Analytical Engine exists only in Babbage’s sketches and writings, but nonetheless represents a tremendous feat of human intellect and ingenuity. Despite this, Babbage faced much opposition to his work, most of which came from those who did not understand his projects at all. Indeed, even today it is a challenge to piece through all his often scattered writings and obtain a clear picture of his work, especially the Analytical Engine. The precise mechanical details and intricate engineering of Babbage’s machines are therefore beyond the scope of this paper, and more focus will be placed on their development and higher-level operation. The Life of Charles Babbage Charles Babbage was born in Devonshire, England in 1791, the son of Benjamin Babbage, a wealthy banker upon whose death in 1827 Charles received an immense fortune [Hyman, 5]. He was inquisitive-minded from his earliest days, noting in his autobiography that “I commenced the … inquiry into those laws of thought and those aids which assist the human mind in passing from received knowledge to that other knowledge then unknown to our race” [Babbage 1864, 9]. Babbage’s early education was haphazard, and he was taught privately for most of his early life due to his perpetual illness. He often surpassed his tutors in mathematical ability, and upon entering Trinity College in 1810 he had already studied the calculus, and understood “the dots of Newton, the d’s of Leibniz, [and] the dashes of Lagrange” [Babbage 1864, 23]. At Cambridge, along with close colleagues John Herschel and George Peacock, the former the son of astronomer William Herschel, Babbage formed the Analytical Society, the goal of which was to popularize Leibniz’s notation over Newton’s. After receiving his Bachelor’s and 2 subsequently Master’s Degrees, Babbage published a number of mathematical works, though he found little success obtaining a permanent position at any university. He was married to Georgiana Whitmore in 1814, and together they had eight children, only four of whom survived beyond childhood [Moseley, 53]. The majority of Babbage’s time after his graduation from Cambridge was spent corresponding with various English scientific societies, travelling, and publishing results of his observations through his studies. He was named a Fellow of the Royal Society of London at the young age of 24, despite his distaste for the hierarchy of the organization: “The Council of the Royal Society is a collection of men who elect each other to office and then dine together at the expense of the society to praise each other over wine and give each other medals” [Morrison and Morrison, xxxi]. Babbage would remain critical of both the Society and the state of science in England throughout his career. He submitted a plan of reform to the Society, which proposed an added rigour in publication standards, fair election procedures, and liberal discussion of policy, but his plan was outright rejected [Morrison and Morrison, xxx]. Even before the government ceased supporting his projects, he was a prominent dissenter of the lack of state support for technology – he was a self-proclaimed “Scientific gadfly” – and he wrote Reflections on the Decline of Science in England (1830) [Morrison and Morrison, xxxi]. To confront this impending decline, he helped found the Astronomical Society, the British Association for the Advancement of Science, and the Statistical Society. In some sense, Babbage can be considered a pioneer in the public advancement of science due to his relentless calls for equity in scientific societies and for generosity in Governmental endowments [Babbage 1982, xiii]. Due to his ill health, doctors regularly advised Babbage to travel, which proved beneficial for him in many respects. Throughout his travels he was fortunate to befriend and share ideas with many prominent French mathematicians including Laplace, Poisson, and Fourier [Morrison and Morrison, xiii]. His trips around Europe allowed him to learn more about manufacturing techniques and technological advancements, teaching him methods of production unseen in England at the time. His observations led to the publication of On the Economy of Manufactures and Machinery (1832), his most successful work and a foundational piece in the field that would come to be known as operational research [Gridgeman, 355]. The publication emphasized the importance of division of labor, which had already been discussed in great detail in Adam Smith’s An Inquiry into the Nature and Causes of the Wealth of Nations (1776). Babbage’s writings were based on his extensive factory visits and in particular the work of G.F. de Prony, about whom much will be said shortly. Babbage’s influence in this field is seen by the so-called “Babbage principle,” defined as the “general law of the capitalist division of labor” [Hessenfield and Abbott, 211]. The one constant throughout Babbage’s life was his ferocious devotion to his calculating machines. From the early 1820s until his death in 1871 he spent the majority of his working life trying to perfect his Difference and Analytical Engines, sometimes to the detriment of other parts of his career. In 1828 he received notice of his appointment as Cambridge’s Lucasian Chair of Mathematics, the post once held by Isaac Newton (Babbage refers to the position as the “Chair of Newton”) and recently held by Stephen Hawking. He noted that “small as the admitted duties of the Lucasian chair were, I felt that they would absorb time which I thought better devoted to the completion of the Difference Engine” [Babbage 1864, 26]. He resigned from the position in 1839, having neither resided at the university nor given a lecture during his tenure. Among the other subjects investigated by Babbage throughout his career are electromagnetic theory, natural theology, actuarial finance, cryptography, railway engineering, and meteorology [Gridgeman, 3 354]. When Babbage died at the age of 79 he had declined both knighthood and baronetcy in protest of hereditary peerages, and rejected most other awards offered to him throughout his life [James, 50]. Babbage understood the vast potential of technology perhaps more than anyone else of this period, and his inventions clearly foreshadow the progress of science since his time [Essinger, 110]. Influences on Babbage Babbage’s contributions to computational technology are so significant because his work represents the amalgamation of two revolutionary ideas in manufacturing and mathematics. On the one hand, Babbage’s computational engines are directly based on textile manufacturing technologies, rapid improvements in which had occurred right around the time he became interested in mathematics [Essinger, 4]. The physical hardware of Babbage’s Analytical Engine is unquestionably influenced by the Jacquard loom, the most important development in industrial revolution weaving devices [Essinger, 5]. On the other hand, Babbage had always been fascinated by numerical tables and the methods used to produce them. Most notably, Babbage was unsettled by the fact that even the most efficient calculation methods in the world were subject to human error [Swade, 9]. Before one can understand the work of Babbage, one must first grasp the progress made by Joseph Marie Jacquard and Gaspard de Prony in programmable machinery and rapid computation, respectively, the linking of which made Babbage such an innovator. Joseph Marie Jacquard The Industrial Revolution began in England in the mid-18th century and arose in large part from the textile industry. Most clothing and decorative fabrics were made using a loom, the development of which accurately reflects the progress of all technology at the time. Fabrics are woven by laying parallel threads called the warp flat on the loom, and lifting them to pass through a widthwise thread called the weft.