Charles Babbage was an English mathematician, philosopher and mechanical engineer who invented the concept of a programmable computer. From 1828 to 1839 he was Lucasian Professor of Mathematics at Cambridge, a position whose holders have included Isaac Newton and Stephen Hawking. A proponent of natural religion, he published The Ninth Bridgewater Treatise in 1837 as his personal response to The Bridgewater Treatises, a series of books on theology and science that had recently appeared. Disputing the claim that science disfavours (...) religion, Babbage wrote 'that there exists no such fatal collision between the words of Scripture and the facts of nature'. He argues on the basis of reason and experience alone, drawing a parallel between his work on the calculating engine and God as the divine programmer of the universe. Eloquently written, and underpinned by mathematical arguments, The Ninth Bridgewater Treatise is a landmark work of natural theology. (shrink)

This book is composed of many short essays which can be read separately; however, read together these commentaries form a compelling exploration of how and why teachers should obey laws, regulations, policies, and contractual obligations, yet should do much more.

Many people_political leaders, school administrators, school board members, interest group leaders, community leaders, parents/guardians_seek to impact education, but efforts to improve education will be enhanced if they are based on reality and the experts on the classroom reality are current teachers. Anyone who seeks to improve education must listen to teachers. This book explains why and shows how.

The design of good notation is a cause that was dear to Charles Babbage's heart throughout his career. He was convinced of the "immense power of signs" (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design (...) of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage's writings, for the first time in a systematic way. Babbage's desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed. (shrink)

Babbage wrote two relatively detailed, yet significantly incongruous, autobiographical accounts of his pre-Cambridge and Cambridge days. He published one in 1864 and in it advertised the existence of the other, which he carefully retained in manuscript form. The aim of this paper is to chart in some detail for the first time the discrepancies between the two accounts, to compare and assess their relative credibility, and to explain their author's possible reasons for knowingly fabricating the less credible of the (...) two. (shrink)

This article examines life assurance and the politics of ‘big data’ in mid-19th-century Britain. The datasets generated by life assurance companies were vast archives of information about human longevity. Actuaries distilled these archives into mortality tables – immensely valuable tools for predicting mortality and so pricing risk. The status of the mortality table was ambiguous, being both a public and a private object: often computed from company records they could also be extrapolated from public projects such as the census, or (...) clerical records. Life assurance more generally straddled the line between private enterprise and collective endeavour, though its advocates stressed the public interest in its success. Reforming actuaries such as Thomas Rowe Edmonds wanted the data on which mortality tables were based to be made publicly available, but faced resistance. Such resistance undermined insurers’ claims to be scientific in spirit and hindered Edmonds’s personal quest for a law of mortality. Edmonds pushed instead for an open actuarial science alongside fellow travellers at the Statistical Society of London, which was populated by statisticians such as William Farr as well as by radical mathematicians such as Charles Babbage. The article explores Babbage’s little-known foray into the world of insurance, both as a budding actuary but also as a fierce critic of the industry. These debates over the construction, ownership, and accessibility of insurance datasets show that concern about the politics of big data did not begin in the 21st century. (shrink)

Charles Babbage'sReflections on the Decline of Science in England… is very well known to historians of science who are aware of its role in the movement to found the British Association for the Advancement of Science and to reform the Royal Society. The work is probably responsible, in large measure, for the assumption that science in Great Britain was in a marked decline in the early decades of the last century, an assumption rarely subject to exact analysis although fairly (...) widely held. Not as widely known is a reply to Babbage written by Gerard Moll of Utrecht and presented to the English reading public by Faraday, one of the men attacked in Babbage's volume. To the best of my knowledge, Babbage's only published rejoinder to Moll appeared in 1851, dismissing Moll and other critics as not having challenged his facts. (shrink)

In what follows, I appeal to Charles Babbage’s discussion of the division of mental labor to provide evidence that—at least with respect to the social acquisition, storage, retrieval, and transmission of knowledge—epistemologists have, for a broad range of phenomena of crucial importance to actual knowers in their epistemic practices in everyday life, failed adequately to appreciate the significance of socially distributed cognition. If the discussion here is successful, I will have demonstrated that a particular presumption widely held within the (...) contemporary discussion of the epistemology of testimony—a presumption that I will term the personalist requirement—fails to account for those very practices of knowers that I detail here. I will then conclude by suggesting that an alternate account of testimonial warrant, one that has heretofore been underappreciated, ought to be given more serious consideration—in particular because it is well suited to account for those actual practices of knowers that the personalist requirement leaves unrecognized. (shrink)

CHARLES BABBAGE, OUTSTANDING 19TH CENTURY FIGURE ON THEORY OF COMPUTING, URGES ON PROTO-GOODMANIAN AND NEO-MAIMONIDEAN GROUNDS THAT HUME IS QUITE WRONG ABOUT THE PROBABILITY OF MIRACLES’ OCCURRING. AQUINAS’ CLASSIFICATIONS OF MIRACLES INDICATE THAT NOT SINGLE PROBABILITY JUDGMENT IS ALWAYS RIGHT. BABBAGE’S WORK ON COMPUTING STILL CIRCULATES, BUT HIS NINTH BRIDGEWATER TREATISE (ON MIRACLES) HAS LONG DESERVED REPUBLICATION.

In the 1860s and 1870s the logic of Boole and the calculating machines of Babbage were key resources in W. S. Jevons’s attempt to construct a mechanical model of the mind, and both therefore played an important role in Jevons’s attempted revolution in economic theory. In this same period both Boole and Babbage were studied within the Cambridge Moral Sciences Tripos, but the Cambridge reading of Boole and Babbage was much more circumspect. Implicitly following the division of (...) the moral sciences into material and ‘real’ as established by the Rev. Grote, John Venn treated Boole’s logic as a purely formal science, while Alfred Marshall based his psychological model of the mechanical part of the human mind upon Babbage’s two-level machine. From the different perspectives of logic and psychology, Venn and Marshall did not simply incorporate their readings of Boole and Babbage, but also attempted to establish the limits to any mechanical explanation of the mind. This comparison of the attitudes to mental science of Jevons and Marshall provides a foundation from which the differing conceptions of economic theory of the two men can be established.Keywords: Alfred Marshall; Charles Babbage; George Boole; John Venn; Logic; Psychology. (shrink)

The possible impact of general philosophical ideas on the choice of research subject in mathematics is the topic of this paper. I examine a specific case in which the philosophical background is provided by a discussion on the role of language in science, which is associated with the work of Condillac. The area of mathematics considered is functional equations, a difficult chapter of mathematical analysis that began to be developed between the end of the eighteenth and the beginning of the (...) nineteenth century. The researcher is Charles Babbage , a young British mathematician deeply interested in the recent work of French mathematicians and philosophers of science. (shrink)

This paper addresses two methodological paths in Artificial Intelligence: the paths of Babbage and anti-Cartesianism. While those researchers who have followed the latter have attempted to reverse the Cartesian dictum according to which machines cannot think in principle, Babbage’s path, which has been partially neglected, implies that the replacement of humans—and not the creation of minds—should provide the foundation of AI. In view of the examined paths, the claim that we support here is this: in line with (...) class='Hi'>Babbage, AI researchers have recently concentrated upon the replacement of human labour, and thus upon the creation of Machine Learning systems. After presenting and analysing the paths, we characterise Machine Learning via its developments and an illustrative example. Then, we put forward an argument that shows that total replacement of human labour will not be feasible for practical and conceptual reasons despite the successful developments in recent AI systems. Our discussion finally leads to optimism and awareness: AI’s advances allow humans to dedicate themselves to higher level tasks, but these advances also require that we be vigilant about the responsibilities granted to ML-based systems. (shrink)

Charles Babbage began the quest to build an intelligent machine in the nineteenth century. Despite finishing neither the Difference nor the Analytical engine, he was aware that the use of mental language for describing the functioning of such machines was figurative. In order to reverse this cautious stance, Alan Turing postulated two decisive ideas that contributed to give birth to Artificial Intelligence: the Turing machine and the Turing test. Nevertheless, a philosophical problem arises from regarding intelligence simulation and make-believe (...) as sufficient to establish that programmed computers are intelligent and have mental states, especially given the nature of mind and its characteristic first-person viewpoint. The origin of Artificial Intelligence is undoubtedly linked to the accounts that inspired John Searle to coin the term strong AI ―or the view that simply equates computers and minds. Especially emphasising the divergence between algorithmic processes and intentional mental states, the Chinese Room thought experiment shows that, since the mind is embodied and able to realise when linguistic understanding takes place, mental states require material implementation, a point that directly conflicts with the accounts that reduce the mind to the functioning of a programmed computer. The experience of linguistic understanding with its typical quale leads to other important philosophical issues. Searle’s theory of intentionality holds that intentional mental states have conditions of satisfaction and appear in semantic networks; thus people know when they understand and what terms are about. In contrast, a number of philosophers maintain that consciousness is only an illusion and that it plays no substantial biological role. However, consciousness is a built-in feature of the system. Moreover, neurological evidence suggests that conscious mental states, qualia and emotions enhance survival chances and are an important part of the phenomenal side of mental life and its causal underpinnings. This renders an important gap between simulating a mind and replicating the properties that allow having mental states and consciousness. On this score, the Turing test and the evidence it offers clearly overestimate simulation and verisimilar make-believe, since such evidence is insufficient to establish that programmed computers have mental life. In summary, this dissertation criticises views which hold that programmed computers are minds and minds are nothing but computers. Despite the arguments in favour of such an equation, they all fail to properly reduce the mind and its first-person viewpoint. Accordingly, the burden of proof still lies with the advocates of strong AI and with those who are willing to deny fundamental parts of the mind to make room for machine intelligence. (shrink)

Lady Lovelace’s notes on Babbage’s Analytical Engine never refer to the concept of surprise. Having some pretension to ‘originate’ something—unlike the Analytical Engine—is neither necessary nor sufficient to being able to surprise someone. Turing nevertheless translates Lovelace’s ‘this machine is incapable of originating something’ in terms of a hypothetical ‘computers cannot take us by surprise’ objection to the idea that machines may be deemed capable of thinking. To understand the contemporary significance of what is missed in Turing’s ‘surprise’ translation (...) of Lovelace’s insight, one needs to distinguish between trivial surprises and those events, propositions or encounters that lead us to question our understanding of ourselves or what surrounds us. Only some of these non-trivial surprises are the product of originality endeavours. Not only is it uncommon for surprises to track such endeavours, the type of autonomy that would be required on the part of ‘digital computers’ for originality and surprise to intersect in that way goes far beyond the operational autonomy that can be achieved by ‘learning machines’. This paper argues that a salient translation of Lovelace’s originality insight—for contemporary and future ‘learning machines’—is an upside-down version of Turing’s surprise question: can computers be surprised by us in a non-trivial, ‘co-produced’ way? (shrink)

Introduction -- Karl Marx's concept of alienation -- Objectification, alienation, and estrangement -- Other origins of alienation and objectification -- Marx's account of alienation : from early to late -- The alienated object of production : commodity fetishism -- The alienated means of production : machine fetishism -- Machines and the transformation of work -- Marx's energeticist turn -- The first law of thermodynamics -- From arbeit to arbeitskraft -- The second law of thermodynamics -- Machines in the communist future (...) -- Technology and the boundaries of nature -- Material wealth and value : the Grundrisse's fragment on machines -- The strife between technology and capital : the fall in the rate of profit -- Enjoyment not value : challenging the logic of exhaustion -- Man himself as fixed capital -- Class kinship and the redistribution of the means of production -- Machines in the capitalist reality -- Between thermodynamics and humanism : approaching capital -- Machinery as an historical category of production -- Machines, trains, and other capitalist monsters -- Rough, foul-mouthed boys : women's monstrous laboring bodies -- Wage labor and race -- Wage labor and sexuality -- Machinery and revolution -- Alienation beyond Marx -- Science and technology in Marx's excerpt notebooks -- Karl Marx and Charles Babbage -- Machines and temporality : the treadmill effect and free time -- Technophobia and technophilia -- Technophobia and twentieth-century theory. (shrink)

This article reviews and brings together two literatures: classical political economists’ views on the skilling or deskilling nature of technological change in England, during the eighteenth and nineteenth centuries when they wrote, are compared with the empirical evidence about the skill effects of technological change that emerges from studies of economic historians. In both literatures, we look at both the skill impacts of technological change and at the “inducement mechanisms” that are envisaged for the introduction of new technologies. Adam Smith (...) and Karl Marx both regarded the deskilling of the labour force as the predominant form of biased technical change, but other authors such as Charles Babbage also took account of capital-skill complementarities and skill-enhancing effects of technological change. For Smith, the deskilling bias was an unintended by-product of the increasing division of labour, which in his view “naturally” led to ever more simplification of workers’ tasks. As opposed to Smith, Marx considered unskilled-biased technical change as a bourgeois weapon in the class struggle for impairing the workers’ bargaining position. Studies of economic historians lend support to Marx’s hypothesis about the inducement mechanisms for the introduction of unskilled-biased innovations, but have produced no clear-cut empirical evidence for a deskilling tendency of eighteenth- and nineteenth-century technological change as a whole. Industrialization in the eighteenth and nineteenth centuries rather led to labour polarization, by simultaneously deskilling a large part of the workforce and raising the demand for some high-skilled workers. (shrink)

More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...) Leibniz with a powerful and comprehensive notation’, wrote the young John Herschel and Charles Babbage of the calculus in 1813, ‘as if the soil of this country [was] unfavourable to its cultivation, it soon drooped and almost faded into neglect; and we now have to re-import the exotic, with nearly a century of foreign improvement, and to render it once more indigenous among us’. (shrink)

This is an early, alternative version of the paper that became Shieber 2013, “Toward a truly social epistemology: Babbage, the division of mental labor, and the possibility of socially distributed warrant,” Philosophy and Phenomenological Research, 86(2), pp. 266-294. This paper differs from the later paper in a few notable respects. In this earlier paper – written in 2008-9 – I use Hutchins to illustrate the phenomenon of socially distributed cognitive processes, rather than Babbage, and I discuss the attributes (...) of such cognitive processes in greater detail. (shrink)

Concern over the nature of AI is, for the tastes many AI scientists, probably overdone. In this they are like all other scientists. Working scientists worry about experiments, data, and theories, not foundational issues such as what their work is really about or whether their discipline is methodologically healthy. However, most scientists aren’t in a field that is approximately fifty years old. Even relatively new fields such as nonlinear dynamics or branches of biochemistry are in fact advances in older established (...) sciences and are therefore much more settled. Of course, by stretching things, AI can be said to have a history reaching back t o Charles Babbage, and possibly back beyond that to Leibnitz. However, all of that is best viewed as prelude. AI’s history is punctuated with the invention of the computer (and, if one wants t o stretch our history back to the 1930s, the development of the notion of computation by Turing, Church, and others). Hence, AI really began (or began in earnest) sometime in the late 1940s or early 1950s (some mark the conference a t Dartmouth in the summer of 1957 as the moment of our birth). And since those years we simply have not had time to settle into a routine science attacking reasonably well understood questions (for example, many of the questions some of us regard as supreme are regarded by others as inconsequential or mere excursions). (shrink)

The history of the dyestuffs industry during the period 1775–1860 is interesting for three reasons. In the first place it was in connection with the manufacture of synthetic dyestuffs, begun in 1856, that the industrial research laboratory and the organization scientist first unmistakably appeared in the last decades of the nineteenth century. Secondly, there are the enigmas of W. H. Perkin, the man who discovered and manufactured the first coal-tar colours, but who retired somewhat abruptly from the industry in 1874: (...) just after the synthesis of alizarine. Thirdly, the dyestuffs industry was in intimate association with the textile industries which had for a long time been subject to frequent radical scientific and technological innovation. Among the most important of these we may mention John Smeaton's classic paper of 1759 on the maximum work obtainable from a given fall of water: a problem important not only for the abstract science of mechanics, but also for the design of waterwheels—the main source of power for the early textile mills. (The waterwheel was not, during the eighteenth century, the epitome of the quaint and picturesque: it was in the van of scientific and technical progress.) Again, the textile industries were quick to employ the Watt rotative engine; previously a two cylinder Newcomen engine had been tried out. Bleaching powders, based on Scheele's discovery of chlorine and its properties, were rapidly adopted: in this context one cannot help contrasting the indifference of medical science to Davy's early suggestion of using nitrous oxide as an anaesthetic; or Faraday's comment in 1818 on the anaesthetic power of sulphuric ether. The textile industries saw, over this period, a rapid succession of new machines, the pace of invention being so hot that in 1832 Charles Babbage reported that machines became obsolete long before they wore out. A Salford cotton mill was the first industrial establishment to use gas lighting: James Thomson, calico printer, introduced gas lighting to the town of Clitheroe when he installed it in his works. And there were many other important technical and scientific innovations. It was to supply these industries, so well accustomed to change, that the synthetic coal-tar dyestuffs were introduced from 1856 onwards. It is interesting that, so far as we can see, the appearance of these synthetic dyestuffs was the last in the series of major innovations in the textiles and related industries: at least until recent times. (shrink)

Machines were introduced as calculating devices to simulate operations carried out by human computors following fixed algorithms: this is true for the early mechanical calculators devised by Pascal and Leibniz, for the analytical engine built by Babbage, and the theoretical machines introduced by Turing. The distinguishing feature of the latter is their universality: They are claimed to be able to capture any algorithm whatsoever and, conversely, any procedure they can carry out is evidently algorithmic. The study of such "paper (...) machines" by mathematical means is the topic of our contribution. This is not only in accord with its usual understanding in computer science, but conceptually and historically right, when we recall the purpose for which Turing machines were introduced. (shrink)

“Holdings” was written for the 2011 Reading Artifacts Summer Institute at the Canada Science and Technology Museum. I spent a week “embedded” with the group, attending workshops and instructional sessions, mostly in a warehouse filled with curious objects from the museum’s collection: a gigantic hard drive platter, an egg-sorting machine, fire engines, iron lungs, a scale model of a Babbage Difference Engine (which had been used to weigh down the back of somebody’s rear-wheel-drive car). Some of the artifacts were (...) historically important, and some were disarmingly ordinary. Others had come loose from their stories, and were just mystifying. The group spent five days exploring the innumerable intersections between these solid things and the people who lived, and live, among them. At the end of the week, during the closing presentations, I read this poem to the group about what I’d seen and felt as I watched them work. (shrink)

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

Michael S. Mahoney, professor of the history of science at Princeton University, died in 2008. Born in 1939, Mahoney was already a seasoned historian of mathematics when he became one of the first senior historians to take an interest in the history of computing. He was by no means the first: for example, individuals such as I. B. Cohen at Harvard University and Derek de Solla Price at Yale University had been interested since the 1960s. Moreover, several institutions were already (...) actively engaged: the Smithsonian Institution, the Charles Babbage Institute (founded 1979), the Computer Museum in Boston, and similar organizations in Europe. A journal, the Annals of the History of Computing, was established in 1979. .. (shrink)

Summary The occasional (and belated) concern of the British Government with science in the nineteenth century is a matter of potential interest to historians of science, yet many previous studies have tended to range over a variety of different aspects of the question. There have been too many vague allusions to financial support as ‘money for science’ in general. It is time that particular parts of the problem were unpacked. For example, the award of money (from the 1820s) to pay (...) a few people of independent means for apparatus was quite distinct from the provision (from the 1830s) of an occasional pension. Even then, to speak of ‘pensions’ uncovers unfortunate ambiguities. For too long science in Britain was regarded as no more than a private hobby for the well-to-do. As late as 1856 an official government statement seemed to make this attitude official. The English attitude to pensions differed remarkably from the French, who established a precedent in the reward of savants, sometimes quoted enviously by British men of science. In 1837 Robert Peel virtually admitted that, in awarding pensions to ‘cultivators of science’, he was following the French practice. It may also be useful to emphasise the contrast between the English (often led by Cambridge professors) and the Scots, mostly from Edinburgh, mainly represented here by Whewell and Brewster, respectively. Babbage had a different role in this story from that usually told. A large part in supporting men of science of modest means could have been played by the British Association for the Advancement of Science but it consistently refused to do so, although it supported an elite among its own members. (shrink)

Dans la première moitié du xixe siècle en Angleterre, autour de Charles babbage (1791–1871), John F. W. Herschel (1792–1871), George Peacock (1791–1858), Duncan F. Gregory (1813–1844), Augustus de Morgan (1806–1871), George Boole (1815–1864), et d'autres auteurs moins connus, un réseau d'algébristes renouvelle singulièrement la conception de l'algèbre, à tel point que leur travail est le plus souvent interprété comme émergence des travaux sur l'algèbre abstraite. Comme ces algébristes sont également des réformateurs impliqués dans la réorganisation de la science, il (...) s'agira de proposer de ces travaux une lecture plus contextuelle, afin d'éclairer leur inscription parmi les effects de la Révolution industrielle (1760–1830), et d'analyser leur rôle de médiation culturelle entre les racines d'un savoir universitaire fondé sur la fidélité aux Anciens, et de nouvelles formes d'élaboration des connaissances. Une médiation marquée par un premier rapprochement entre algèbre et logique. (shrink)